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Quantum magnetism in minerals
Abstract
The discovery of magnetism by the ancient Greeks was enabled by the natural occurrence of lodestone – a magnetized version of the mineral magnetite. Nowadays, natural minerals continue to inspire the search for novel magnetic materials with quantum-critical behaviour or exotic ground states such as spin liquids. The recent surge of interest in magnetic frustration and quantum magnetism was largely encouraged by crystalline structures of natural minerals realizing pyrochlore, kagome, or triangular arrangements of magnetic ions. As a result, names like azurite, jarosite, volborthite, and others, which were barely known beyond the mineralogical community a few decades ago, found their way into cutting-edge research in solid-state physics. In some cases, the structures of natural minerals are too complex to be synthesized artificially in a chemistry lab, especially in single-crystalline form, and there is a growing number of examples demonstrating the potential of natural specimens for experimental investigations in the field of quantum magnetism. On many other occasions, minerals may guide chemists in the synthesis of novel compounds with unusual magnetic properties. The present review attempts to embrace this quickly emerging interdisciplinary field that bridges mineralogy with low-temperature condensed-matter physics and quantum chemistry.
... 1,2 Synthetic analogs of the rare phosphate minerals of pegmatites, wyllieite (NaMn 2+ 2.5 Mn 3+ (PO 4 ) 3 ) and arrojadite (K 2 Na 5 Fe 2+ 14 Fe 3+ (PO 4 ) 12 (OH) 2 ), may find application as cathode materials for rechargeable batteries. 3 In addition, some minerals occupy a unique place in the cutting-edge topic of condensed matter physics as objects for studying rare magnetic ground states such as spin liquids, spin ices, etc. 4 In our search for a flexible structural type among mineral phases that was capable of wide isomorphic substitutions and demonstrated features that could be responsible for unusual magnetic properties, we noticed ellenbergerite, (Mg,Ti)-Mg 3 (Mg,Al) 3 (OH) 3 [HSiO 4 ][H 0.33 SiO 4 ] 3 , with a structural motif that was attractive for chemical modifications. 5 Although this silicate crystallizes at high pressures and temperatures in a natural environment, its phosphate, arsenate, vanadate, and other transition metal analogs can be synthesized in the laboratory under middle-temperature hydrothermal conditions. ...
... The crystal chemical formula of the new compound can be written as N a 0 . 5 4 ). This composition was confirmed by the EDX results (Jeol JSM-6480LV, energy-dispersive diffraction spectrometer X-MaxN). ...
... In conclusion, single crystals of Na 0.55 Ni 6 (OH) 3 (H 0.61 PO 4 ) 4 and polycrystalline (Na, Ni) 0.64 Ni 5.68 (OH) 3 (H 0.67 PO 4 ) 4 phosphates have been obtained using a conventional hydrothermal route. X-ray diffraction studies show that both phases belong to the ellenbergerite structure type. ...
... Examples include interpenetrating sublattices with independent spin dynamics and ground states in Sr 2 CoOsO 6 [2,3], self-healing photoelectrode materials like CuRhO 2 [4], covalency-driven collapse of spin-orbit coupling in Ba 5 CuIr 3 O 12 [5], an ultra-high coercive field in Sr 3 NiIrO 6 [6,7], magnetoelectric coupling in Co 4 Nb 2 O 9 [8], surprising spin entropy effects across the magnetic quantum phase transition in CoNb 2 O 6 [9], and nonreciprocal directional dichroism in Ni 3 TeO 6 [10]. Another mixed metal system with exciting properties and curious hybridization is Fe 2 Mo 3 O 8 -also known as the mineral Kamiokite [11]. While magnetism and magnetoelectric coupling have been widely studied [12][13][14][15][16][17][18][19], the charge excitations are highly under-explored. ...
... Fe 2 Mo 3 O 8 is a polar magnet with giant magnetoelectric coupling, strong Dzyaloshinski-Moriya interactions, valence bond condensation (creating a cluster magnet), and the possibility of orbitally-selective transitions [12][13][14][15][16][17][18][19]. Zinc substitution, first on the tetrahedral Fe site and then on the octahedral Fe site [15,20], is of inter-est for magnetic properties as well [11,13,20,21]. The structure of Fe 2 Mo 3 O 8 consists of corner-shared tetrahedral and octahedral sites separated by layers of Mo trimers [ Fig. 1(a,b)] [12,22,23]. ...
We combined optical spectroscopy and first principles electronic structure calculations to reveal the charge gap in the polar magnet Fe$_2$Mo$_3$O$_8$. Iron occupation on the octahedral site draws the gap strongly downward compared to the Zn parent compound, and subsequent occupation of the tetrahedral site creates a narrow resonance near the Fermi energy that draws the gap downward even further. This resonance is a many-body effect that emanates from a flat valence band in a Mott-like state due to screening of the local moment - similar to expectations for a Zhang-Rice singlet, except that here, it appears in a semi-conductor. We discuss the unusual hybridization in terms of orbital occupation and character as well as the structure-property relationships that can be unveiled in various metal-substituted systems (Ni, Mn, Co, Zn).
... Examples include interpenetrating sublattices with independent spin dynamics and ground states in Sr 2 CoOsO 6 [2,3], self-healing photoelectrode materials such as CuRhO 2 [4], covalencydriven collapse of spin-orbit coupling in Ba 5 CuIr 3 O 12 [5], an ultrahigh coercive field in Sr 3 NiIrO 6 [6,7], magnetoelectric coupling in Co 4 Nb 2 O 9 [8], surprising spin entropy effects across the magnetic quantum phase transition in CoNb 2 O 6 [9], and nonreciprocal directional dichroism in Ni 3 TeO 6 [10]. Another mixed metal system with exciting properties and curious hybridization is Fe 2 Mo 3 O 8 -also known as the mineral kamiokite [11]. While magnetism and magnetoelectric coupling have been widely studied [12][13][14][15][16][17][18][19], the charge excitations are highly underexplored. ...
... bond condensation (creating a cluster magnet), and the possibility of orbitally selective transitions [12][13][14][15][16][17][18][19]. Zinc substitution, first on the tetrahedral Fe site and then on the octahedral Fe site [15,20], is of interest for magnetic properties as well [11,13,20,21]. The structure of Fe 2 Mo 3 O 8 consists of corner-shared tetrahedral and octahedral sites separated by layers of Mo trimers [Figs. ...
We combined optical spectroscopy and first-principles electronic structure calculations to reveal the charge gap in the polar magnet Fe2Mo3O8. Iron occupation on the octahedral site draws the gap strongly downward compared to the Zn parent compound, and subsequent occupation of the tetrahedral site creates a narrow resonance near the Fermi energy that draws the gap downward even further. This resonance is a many-body effect that emanates from the flat valence band in a Mott-like state due to screening of the local moment-similar to expectations for a Zhang-Rice singlet, except that here it appears in a semiconductor. We discuss the unusual hybridization in terms of orbital occupation and character as well as the structure-property relationships that can be unveiled in various metal-substituted systems (Ni, Mn, Co, Zn).
... 3,4,6-10 When Cu 2+ spin 1/2 ions appear in a dimensionally restricted crystallographic lattice, they exhibit novel quantum magnetic landscapes. [11][12][13] Lowdimension lattices consist either of quasi-two-dimensional (2D) layers in the form of Kagomé, pyrochlore, square, triangle, and honeycomb or quasi-one-dimensional spin-chains, spin-dimers, and spin-ladders are hosts for various interesting quantum phenomena, including the Bose-Einstein condensation, spinglass state, spin-Peierls transition, quantum spin-liquid state, and multiferroicity. 5,11,[14][15][16][17][18] In many Cu 2+ S = 1/2 compounds, the spin frustration lattice with the competing magnetic exchange interaction between intralayers (chains) and interlayers (chains) invokes a fluctuation-induced quantum multiferroic behavior. ...
... [11][12][13] Lowdimension lattices consist either of quasi-two-dimensional (2D) layers in the form of Kagomé, pyrochlore, square, triangle, and honeycomb or quasi-one-dimensional spin-chains, spin-dimers, and spin-ladders are hosts for various interesting quantum phenomena, including the Bose-Einstein condensation, spinglass state, spin-Peierls transition, quantum spin-liquid state, and multiferroicity. 5,11,[14][15][16][17][18] In many Cu 2+ S = 1/2 compounds, the spin frustration lattice with the competing magnetic exchange interaction between intralayers (chains) and interlayers (chains) invokes a fluctuation-induced quantum multiferroic behavior. 3 Thus far, spin Cu 2+ spin 1/2 systems with quasi-onedimensional spin chains, such as LiCuVO 4 , GeCu 2 O 4 , Rb 2 Cu 2-Mo 3 O 12 , CuCrO 2 , LiCu 2 O 2 , SrCuTe 2 O 6 , and CuCrO 4 , have demonstrated multiferroicity. ...
Single crystals of α-Cu5O2(SeO3)2Cl2 are successfully prepared by the chemical vapor transport method, and their structural, magnetic, thermal, and dielectric properties are investigated as a function of temperature and magnetic field. Magnetization and specific heat measurements indicate a long-range antiferromagnetic transition at TN = 32 K. The spin ordering with a propagation vector q = (1/2 0 0) below TN is determined from the neutron diffraction patterns. The dielectric data reveal an anomaly near TN. Magnetic field-dependent dielectric measurements below TN = 32 K suggest a notable magnetodielectric effect with the scaling of magnetodielectric ∝ M². Additionally, two more dielectric and associated specific heat anomalies are noticed above TN, collaborating with the synchrotron x-ray diffraction studies. These studies provide evidence that the bow-tie lattice of α-Cu5O2(SeO3)2Cl2 is a new magnetoelectric material.
... A number of copper compounds exist in which the lattice is not bipartite, many of which are known primarily as minerals. The copper-based minerals are often composed of distorted Cu 2+ triangles [8], and have proven a rich platform for novel physics. Examples include the candidate quantum spin-liquid state in herbertsmithite ZnCu 3 (OH) 6 Cl 2 [9][10][11]; enormous effective moments in atacamite Cu 2 Cl(OH) 3 [12]; and misfit multipleq order in antlerite Cu 3 SO 4 (OH) 4 [13,14]. ...
Spinon-magnon mixing was recently reported in botallackite Cu$_2$(OH)$_3$Br with a uniaxially compressed triangular lattice of Cu$^{2+}$ quantum spins [Zhang et al., Phys. Rev. Lett. 125, 037204 (2020)]. Its nitrate counterpart rouaite, Cu$_2$(OH)$_3$NO$_3$, has a highly analogous structure and might be expected to exhibit similar physics. To lay a foundation for research on this material, we clarify rouaite's magnetic phase diagram and identify both low-field phases. The low-temperature magnetic state consists of alternating ferro- and antiferromagnetic chains, as in botallackite, but with additional canting, leading to net moments on all chains which rotate from one chain to another to form a 90$^\circ$ cycloidal pattern. The higher-temperature phase is a helical modulation of this order, wherein the spins rotate from one Cu plane to the next. This extends to zero temperature for fields perpendicular to the chains, leading to a set of low-temperature field-induced phase transitions. Rouaite may offer another platform for spinon-magnon mixing, while our results suggest a delicate balance of interactions and high tunability of the magnetism.
... Geometrically frustrated magnets with various structures provide a promising platform for novel states of matter with emerging collective behaviors and strong quantum fluctuations [1][2][3][4]. Recently, kagome-based metals have risen to prominence due to their topological electronic structures, structural instabilities, accompanied by significant electromagnetic and transport properties [5][6][7][8][9][10]. ...
Magnetic metals with geometric frustration offer a fertile ground for studying novel states of matter with strong quantum fluctuations and unique electromagnetic responses from conduction electrons coupled to spin textures. Recently, TbTi$_3$Bi$_4$ has emerged as such an intriguing platform as it behaves as a quasi-one-dimension (quasi-1D) Ising magnet with antiferromagnetic orderings at 20.4 K and 3 K, respectively. Magnetic fields along the Tb zigzag-chain direction reveal plateaus at 1/3 and 2/3 of saturated magnetization, respectively. At metamagnetic transition boundaries, a record-high anomalous Hall conductivity of 6.2 $\times$ 10$^5$ $\Omega^{-1}$ cm$^{-1}$ is observed. Within the plateau, noncollinear magnetic texture is suggested. In addition to the characteristic Kagome 2D electronic structure, ARPES unequivocally demonstrates quasi-1D electronic structure from the Tb 5$d$ bands and a quasi-1D hybridization gap in the magnetic state due to band folding with $q$ = (1/3, 0, 0) possibly from the spin-density-wave order along the Tb chain. These findings emphasize the crucial role of mixed dimensionality and the strong coupling between magnetic texture and electronic band structure in regulating physical properties of materials, offering new strategies for designing materials for future spintronics applications.
... [30,43]. We further note that the magnetic ordering temperature in brochantite is comparable with that reported in some other spin-chain Cu-based minerals, such as dioptase [44,45] or antelerite [46,47]. ...
We report the direct observation of a commensurate-ordered antiferromagnetic (AFM) state but incommensurate helical spin dynamics in the natural mineral brochantite Cu4SO4(OH)6 through neutron diffraction and neutron spectroscopy measurements. Inelastic neutron scattering measurements reveal magnonlike excitations with considerable dispersion along the c axis and almost flat branches in other principal directions, indicating the strong one-dimensional character of the magnetic correlations. We experimentally observe the effect of the uniform Dzyaloshinskii-Moriya (DM) interaction, which elevates the degeneracy of the spin-wave modes, shifting them in opposite directions in reciprocal space. The system has a commensurate AFM ground state, stabilized by the anisotropic symmetric Heisenberg exchange interactions, and quasi-one-dimensional chiral spin dynamics due to the antisymmetric DM interaction. Employing linear spin-wave theory, we were able to construct an effective Heisenberg Hamiltonian. We quantify both the symmetric exchange parameters and the DM vector components in Cu4SO4(OH)6 and determine the mechanism of the magnetic frustration. Our work provides detailed insights into the complex dynamics of the spin chain in the presence of uniform DM interaction.
... 10 The formation of minerals can also reveal synthetic conditions, such as when a lightning discharge over a dune in N e b r a s k a c r e a t e d a n o v e l q u a s i c r y s t a l o f Mn 72.3 Si 15.6 Cr 9.7 Al 1.8 Ni 0.6 with 12-fold symmetry. 11 Therefore, to expand our materials database, especially when looking for inspiration for designing novel quantum materials, crystal structures of naturally occurring minerals can be convenient and robust sources 12 for novel semiconductors, 13−18 thermoelectrics, 19,20 superconductors, 21−23 quantum spin liquids, 24 and topological materials. 25,26 Sulfosalts make up a large group of minerals that exhibit a unique combination of metallic and chalcogen elements. ...
New minerals have long been a source of inspiration for the design and discovery. Many quantum materials, including superconductors, quantum spin liquids, and topological materials, have been unveiled through mineral samples with unusual structure types. In this report, we present kanatzidisite, a new naturally occurring material with formula [BiSbS3]2[Te2] and monoclinic symmetry (space group of P21/m) with lattice parameters a = 4.0021(5) Å, b = 3.9963(5) Å, c = 21.1009(10) Å, and β = 95.392(3)°. The mineral exhibits a unique structure consisting of alternating BiSbS3 double van der Waals layers and distorted [Te] square nets essentially forming an array of parallel zigzag Te chains. Our theoretical calculations suggest that the band structure of kanatzidisite may exhibit topological features characteristic of a Dirac semimetal.
... The above-outlined theoretical predictions for kagome Heisenberg antiferromagnet at zero and finite magnetic fields go hand in hand with numerous experimental studies; see Refs. [4,46] for an overview. Among many candidate materials Herbertsmithite is a near-perfect S = 1/2 kagome Heisenberg antiferromagnet compound showing characteristic features of a spin liquid [2,47]. ...
We present the results of first-principle calculations using the Vienna Ab initio Simulation Package (vasp) for a class of organometallics labeled TM3C6O6 (TM=Sc, Ti, V, Cr, Fe, Co, Ni, and Cu) in the form of planar, two-dimensional, periodic freestanding layers. These materials, which can be produced by on-surface coordination on metallic surfaces, have a kagome lattice of TM ions. Calculating the structural properties, we show that all considered materials have local magnetic moments in the ground state, but four of them (with Fe, Co, Ni, and Cu) show spin-crossover behavior or switch between magnetic and nonmagnetic states by changing the lattice constant, which could be valuable for possible epitaxy routes on various substrates. Surprisingly, we find a very large richness of electronic and magnetic properties, qualifying these materials as highly promising metal-organic topological quantum materials. We find semiconductors with nearest-neighbor ferromagnetic (FM) or antiferromagnetic (AFM) couplings for V, and Sc, Ti, and Cr, respectively, being of potential interest to study spin ice or spin liquids on the 2D kagome lattice. Other TM ion systems combine AFM couplings with metallic behavior (Fe and Ni) or are ferromagnetic kagome metals like Cu3C6O6 with band crossings at the Fermi surface. For the latter compound, the spin-orbit coupling is shown to be responsible for small gaps which makes them a candidate material to observe the quantum anomalous Hall effect.
... (For other experimental realizations of a sawtooth-chain spin model see Refs. [52][53][54][55][56][57][58][59].) RGM approach works in the fully frustrated case. ...
We apply the rotation-invariant Green's function method to study the finite-temperature properties of a $S{=}1/2$ sawtooth-chain (also called $\Delta$-chain) antiferromagnetic Heisenberg model at the fully frustrated point when the exchange couplings along the straight-line and zig-zag paths are equal. We also use 13 terms of high-temperature expansion series and interpolation methods to get thermodynamic quantities for this model. We check the obtained predictions for observable quantities by comparison with numerics for finite systems. Although our work refers to a one-dimensional case, the utilized methods work in higher dimensions too and are applicable for examining other frustrated quantum spin lattice systems at finite temperatures.
... al. on the maple leaf lattice has yet to be identified. Candidates involving quantum spins are the copper minerals [14,15] spangolite Cu 6 Al(SO 4 )(OH) 12 Cl · 3 H 2 O [16], sabelliite Cu 2 ZnAsO 4 (OH) 3 [17], mojaveite Cu 6 TeO 4 (OH) 9 Cl [18], fuetterite Pb 3 Cu 6 TeO 6 (OH) 7 Cl 5 [19] and finally bluebellite Cu 6 IO 3 (OH) 10 Cl [18]. Magnetic properties have been characterized experimentally for spangolite [20] and bluebellite [21], but the magnetic Hamiltonians for any of these maple leaf compounds remains to be established. ...
As a highly frustrated model Hamiltonian with an exact dimer ground state, the Heisenberg antiferromagnet on the maple leaf lattice is of high theoretical interest, and a material realization is intensely sought after. We determine the magnetic Hamiltonian of the copper mineral bluebellite using density functional theory based energy mapping. As a consequence of the significant distortion of the spin $S=1/2$ maple leaf lattice, we find two of the five distinct nearest neighbor couplings to be ferromagnetic. Solution of this Hamiltonian with density matrix renormalization group calculations points us to the surprising insight that this particular imperfect maple leaf lattice, due to the strongly ferromagnetic Cu$^{2+}$ dimer, realizes an effective $S=1$ breathing kagome Hamiltonian. In fact, this is another highly interesting Hamiltonian which has rarely been realized in materials. Analysis of the effective model within a bond-operator formalism allows us to identify a valence bond solid ground state and to extract thermodynamic quantities using a low-energy bosonic mean-field theory. We resolve the puzzle of the apparent one-dimensional character of bluebellite as our calculated specific heat has a Bonner-Fisher-like shape, in good agreement with experiment.
... The study on low-dimensional magnetic systems has started seeking immense attention globally due to their intriguing rich magnetic phenomena [1][2][3]. They also hold promise for their potential applications in quantum computation [3]. ...
Spin-chain compounds are known to exhibit fascinating magnetic properties, which mostly display magnetic ordering at very low temperatures or remain dynamic even at 0 K. In contrast, the present quasi-one-dimensional spin-chain system BaMn2V2O8 exhibits a collinear antiferromagnetic (AFM) long-range ordering at a relatively higher temperature TN∼37K, wherein the nearest-neighbor spins have AFM coupling along the spin chain, i.e., along the c axis. The present study also reveals a short-range magnetic ordering prevailing at considerably elevated temperatures above its TN. Temperature-dependent Raman spectroscopy demonstrates an occurrence of spin-phonon coupling below TN at least for two phonon modes, whereas the study also shows an unusual thermal evolution of the Raman modes above TN, which is apparently associated to the short-range magnetic ordering. Furthermore, extensive ab initio density functional theory calculations accompanied with classical Heisenberg model based theoretical calculations of various exchange interaction parameters (J0–J5) suggest an AFM ground state, which matches well with the experimentally obtained spin structure.
... have seen how various models with simple Ising interactions and transverse fields can have complex phase diagrams and exotic ground states. Future work understanding the lattices, magnetic ions, and interactions that could result in solid-state realizations of some of these models is a promising direction [168,169]. Although historically much attention has been focused on the SUð2Þ spin symmetric spin-liquid candidate, our work makes the case for studying low-symmetry spin systems. ...
The exploration of quantum spin liquids (QSLs) has been guided by different approaches including the resonating valence bond (RVB) picture, deconfined lattice gauge theories, and the Kitaev model. More recently, a spin-liquid ground state was numerically established on the ruby lattice, inspired by the Rydberg blockade mechanism. Here, we unify these varied approaches in a single parent Hamiltonian, in which local fluctuations of anyons stabilize deconfinement. The parent Hamiltonian is defined on kagomé triangles—each hosting four RVB-like states—and includes only Ising interactions and single-site transverse fields. In the weak-field limit, the ruby spin liquid and exactly soluble kagomé dimer models are recovered, while the strong-field limit reduces to the Kitaev honeycomb model, thereby unifying three seemingly different approaches to QSLs. We similarly obtain the chiral Yao-Kivelson model, the honeycomb toric code, and a new spin-1 quadrupolar Kitaev model. The last is shown to be in a QSL phase by a nonlocal mapping to the kagomé Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagomé dimer model, conclusively establishing the QSL phase in the former and (b) demystifying the dynamical protocol for measuring off-diagonal strings in the Rydberg implementation of the ruby lattice spin liquid. More generally, we find an intimate connection between Kitaev couplings and the repulsive interactions used for emergent dimer models. For instance, we show how a spin-1/2 XXZ model on the ruby lattice encodes a Kitaev honeycomb model, providing a new route toward realizing the latter in cold-atom or solid-state systems.
... Owing to the spin-1/2 nature of the Cu 2+ ion with the electronic configuration [Ar]3d, 9 Cu-containing oxysalts are arguably the best playground for studying collective magnetic phenomena and discovering new quantum magnets. 1 Vanadium in the oxidation state of 4+ has the electronic configuration [Ar]3d 1 and features spin-1/2, too, thus serving as the natural counterpart of Cu 2+ . Several oxide compounds of V 4+ were indeed identified as interesting quantum magnets. ...
A new copper vanadyl arsenate, Cu(VO)2(AsO4)2, was synthesized via the
chemical vapor transport method. Cu(VO)2(AsO4)2 adopts an original structure type. It is
characterized by layers formed by edge-sharing and corner-sharing V-centered octahedra
resulting in a unique topology that was hitherto not reported for vanadates. Single CuO6
octahedra connect vanadate layers into a rigid framework. The thermal expansion of the
framework studied by the single-crystal HT X-ray diffraction is reported. The magnetic
behavior of Cu(VO)2(AsO4)2 shows an interplay of ferromagnetic V4+−V4+ and
antiferromagnetic Cu2+−V4+ interactions that result in a ferrimagnetic long-range order
below TC = 66 K.
... Copper-based minerals are nevertheless a rich source of novel frustrated lattices, often built up of distorted Cu 2+ triangles [7], and have proven a rich platform for novel physics. Examples include the candidate quantum spin liquid state in herbertsmithite [8,9]; enormous effective moments in atacamite Cu 2 Cl(OH) 3 [10]; and spinonmagnon interaction in botallackite Cu 2 (OH) 3 Br [11]. ...
In frustrated magnetic systems, the competition amongst interactions can introduce extremely high degeneracy and prevent the system from readily selecting a unique ground state. In such cases, the magnetic order is often exquisitely sensitive to the balance among the interactions, allowing tuning among novel magnetically ordered phases. In antlerite, Cu$_3$SO$_4$(OH)$_4$, Cu$^{2+}$ ($S=1/2$) quantum spins populate three-leg zigzag ladders in a highly frustrated quasi-one-dimensional structural motif. We demonstrate that at zero applied field, in addition to its recently reported low-temperature phase of coupled ferromagnetic and antiferromagnetic spin chains, this mineral hosts an incommensurate helical+cycloidal state, an idle-spin state, and a multiple-$q$ phase which is the magnetic analog of misfit crystal structures. The antiferromagnetic order on the central leg is reentrant. The high tunability of the magnetism in antlerite makes it a particularly promising platform for pursuing exotic magnetic order.
... Quantum magnetism has attracted much attention over the past decade [1][2][3][4][5], and natural minerals [6] can provide a testbed for particular theories or certain types of behavior. The systems in question tend to be low dimensional in nature and this often drives novel ground states [1]. ...
The Majumder-Ghosh (MG) point is a point in parameter space for a one-dimensional (1D) frustrated system where α=J1/J2=0.5 and the ground state is shown to be a superposition of singlet states. This leads to no magnetic order, instead the ground state is dominated by electronic dynamics, much like that of a spin liquid. Szenicsite is a natural mineral that is predicted to have isolated 1D Cu2+ chains and lies close to or on the MG point. In this work we use muon spin spectroscopy to demonstrate that szenicsite does not magnetically order down to 100 mK and there is an absence of a spin gap, with 1D magnetic excitations dominating. Therefore, we believe szenicsite shows the properties that would put it on the MG point and, as such, it is an interesting system for studying the properties of this quantum mechanical state.
... On the other hand, there are several solid-state realizations of these models, see Refs. [33,[45][46][47][48][49][50][51] (see also [52]) and Refs. [53][54][55]. ...
We apply the rotation-invariant Green's function method (RGM) to study the spin $S=1/2$ Heisenberg model on a one-dimensional sawtooth lattice, which has two nonequivalent sites in the unit cell. We check the RGM predictions for observable quantities by comparison with the exact-diagonalization and finite-temperature-Lanczos calculations. We discuss the thermodynamic and dynamic properties of this model in relation to the mineral atacamite Cu$_2$Cl(OH)$_3$ complementing the RGM outcomes by results of other approaches.
... We have seen how various models with simple Ising interactions and transverse fields can have complex phase diagrams and exotic ground states. Future work understanding the lattices, magnetic ions and interactions that could result in solid state realizations of some of these models is a promising future direction [134,135]. For instance, pathways to the physical realization of the quadrupolar S = 1 Kitaev model which is predicted here to be a spin liquid, would be interesting to pursue. ...
The exploration of quantum spin liquids (QSLs) has been guided by different approaches including the resonating valence bond (RVB) picture, deconfined lattice gauge theories and the Kitaev model. More recently, a spin liquid ground state was numerically established on the ruby lattice, inspired by the Rydberg blockade mechanism. Here we unify these varied approaches in a single parent Hamiltonian, in which local fluctuations of anyons stabilize deconfinement. The parent Hamiltonian is defined on kagom\'e triangles -- each hosting four RVB-like states -- and includes only Ising interactions and single-site transverse fields. In the weak-field limit, the ruby spin liquid and exactly soluble kagom\'e dimer models are recovered, while the strong-field limit reduces to the Kitaev honeycomb model, thereby unifying three seemingly different approaches to QSLs. We similarly obtain the chiral Yao-Kivelson model, honeycomb toric code and a new spin-1 quadrupolar Kitaev model. The last is shown to be in a QSL phase by a non-local mapping to the kagom\'e Ising antiferromagnet. We demonstrate various applications of our framework, including (a) an adiabatic deformation of the ruby lattice model to the exactly soluble kagom\'e dimer model, conclusively establishing the QSL phase in the former; and (b) demystifying the dynamical protocol for measuring off-diagonal strings in the Rydberg implementation of the ruby lattice spin liquid. More generally, we find an intimate connection between Kitaev couplings and the repulsive interactions used for emergent dimer models. For instance, we show how a spin-1/2 XXZ model on the ruby lattice encodes a Kitaev honeycomb model, providing a new route toward realizing the latter in cold-atom or solid-state systems.
... Though our investigation of the spin-1/2 SKHAF as a highly frustrated quantum spin system is of interest in its own right, it is also motivated by the recent discovery of a spin liquid in the square-kagome magnet KCu 6 AlBiO 4 (SO 4 ) 5 Cl [29], which exhibits, however, three different exchange couplings. Moreover, the large variety of magnetic insulators [67,68] as well as the progress in synthesizing new magnetic molecules and compounds with predefined spin lattices may open the window to get access to the observation of the discussed phenomena. ...
Over the last decade, the interest in the spin-1/2 Heisenberg antiferromagnet (HAF) on the square kagome (also called shuriken) lattice has been growing as a model system of quantum magnetism with a quantum paramagnetic ground state, flat-band physics near the saturation field, and quantum scars. A further motivation to study this model comes from the recent discovery of a gapless spin liquid in the square kagome magnet KCu6AlBiO4(SO4)5Cl [M. Fujihala et al., Nat. Commun. 11, 3429 (2020)]. Here, we present large-scale numerical investigations of the specific heat C(T), the entropy S(T), as well as the susceptibility χ(T) by means of the finite-temperature Lanczos method for system sizes of N=18,24,30,36,42,48, and N=54. We find that the specific heat exhibits a low-temperature shoulder below the major maximum which can be attributed to low-lying singlet excitations filling the singlet-triplet gap, which is significantly larger than the singlet-singlet gap. This observation is further supported by the behavior of the entropy S(T), where a change in curvature is present just at about T/J=0.2, the same temperature where the shoulder in C sets in. For the susceptibility the low-lying singlet excitations are irrelevant, and the singlet-triplet gap leads to an exponentially activated low-temperature behavior. The maximum in χ(T) is found at a pretty low temperature Tmax/J=0.146 (for N=42) compared to Tmax/J=0.935 for the unfrustrated square-lattice HAF signaling the crucial role of frustration also for the susceptibility. We find a striking similarity of our square kagome data with the corresponding ones for the kagome HAF down to very low T. The magnetization process featuring plateaus and jumps and the field dependence of the specific heat that exhibits characteristic peculiarities attributed to the existence of a flat one-magnon band are discussed as well.
... Low-dimensional spin systems have attracted a flurry of research interest owing to their rich quantum magnetic phenomena under external perturbations and are anticipated to have key applications in quantum computation [1][2][3][4]. One-dimensional spin-chain systems with low-spinstate compounds with spin S = 1/2 or S = 1 are interesting for quantum magnetism [5,6]. For example, low-dimensional Ni and Cu-based compounds exhibit interesting quantum physical states including Bose-Einstein condensation, spin liquids, spin ice, quantum multiferroics, and spin-flip-induced ferroelectrics [1, 3,4,[6][7][8][9][10]. Dimensionally restricted crystal growth in some compounds stabilizes in unique spinfrustrated lattices such as kagome, honeycomb, triangular, and pyrochlore. ...
A high-quality NiTe2O5 single crystal was grown via the flux method and characterized using synchrotron x-ray diffraction (XRD) and electron probe microscopy techniques. The dc magnetization (M) confirms the antiferromagnetic long-range ordering temperature (TN) at 28.5 K. An apparent domelike dielectric anomaly near TN, with scaling of magnetodielectric (MD) coupling with magnetization (MD%∝M2), signifies higher-order magnetoelectric (ME) coupling. The critical finding is that magnetoelastic coupling plays a pivotal role in bridging the electrical and magnetic dipoles, which was further confirmed by temperature-dependent XRD. In addition, the theoretical charge density difference maps indicate that the emergence of electrical dipoles between the Ni and O atoms below TN originates through p−d hybridization. Thus, the p−d hybridization-induced magnetoelastic coupling is considered a possible mechanism for the higher-order ME effect in this quasi-one-dimensional spin-chain NiTe2O5.
... Natural first-row transition-metal phosphates occupy a special place among phosphates representing minerals mainly of pegmatite genesis and their derivatives, formed as hydrothermally reworked phases or as metasomatic products (Moore, 1973(Moore, , 1984Brown, 1982;Yakubovich & Urusov, 1996;Č erný & Ercit, 2005). These minerals and their synthetic archetypes often have important physical properties, being potential magnets, microporous materials, electrode matrices of alkaline batteries, catalysts and phosphors; they show piezoelectric, pyroelectric and nonlinear optical characteristics (Cheetham et al., 1999;Kohn et al., 2002;Yakubovich, 2008;Inosov, 2018;Yakubovich et al., 2020). Sometimes, one compound can possess several properties, thus representing a multifunctional resource (Maspoch et al., 2007;Lendlein & Trask, 2018). ...
Two new compounds, sodium copper nickel diorthophosphate, Na2CuNi(PO4)2(I), and dimanganese copper diorthophosphate, Mn2Cu(PO4)2 (II), were synthesized hydrothermally, yielding single crystals, and were studied by X-ray diffraction. In the crystal structures, various transition metals of d-elements occupy symmetrically independent crystallographic positions with different coordination geometries. In the crystal structure of Na2NiCu(PO4)2, NiO6 and CuO6 octahedra share edges to form chains that PO4 groups link into a framework with cavities filled with Na atoms. Layered cationic fragments formed from dimers of MnO5 trigonal bipyramids and CuO4 square planes, sharing vertices, are connected through PO4 tetrahedra into a 3-periodic Mn2Cu(PO4)2 crystal structure. Structural correlations between Na2NiCu(PO4)2 and NaCuPO4 are discussed, and crystal–chemical details of the currently known exclusively synthetic mixed Mn/Cu and Ni/Cu phosphates are presented.
... Divalent Cu materials offer a particularly attractive playground for frustration, since a strong tendency toward Jahn-Teller distortions breaks orbital degeneracy, leading to a half-filled band, in which strong on-site interactions drive localization and favor S= 1 2 antiferromagnetism. A wide variety of Cu sublattices are realized in natural minerals, predominantly composed of distorted Cu triangular motifs [8], offering a rich playground for frustrated quantum spin physics. As one very recent example, the interaction of spinons and magnons was reported for the first time in botallackite Cu 2 (OH) 3 Br [9]. ...
Magnetic frustration, the competition among exchange interactions, often leads to novel magnetic ground states with unique physical properties which can hinge on details of interactions that are otherwise difficult to observe. Such states are particularly interesting when it is possible to tune the balance among the interactions to access multiple types of magnetic order. We present antlerite, Cu$_3$SO$_4$(OH)$_4$, as a potential platform for tuning frustration. The low-temperature magnetic state of its three-leg zigzag ladders is a quasi-one-dimensional analog of the magnetic state recently proposed to exhibit spinon-magnon mixing in botallackite. Density functional theory calculations indicate that antlerite's magnetic ground state is exquisitely sensitive to fine details of the atomic positions, with each chain independently on the cusp of a phase transition, indicating an excellent potential for tunability.
... The fascination for the elusive quantum-spin-liquid state did not fade a bit albeit fifty years of research made significant contributions to its understanding. In quantum spin liquids (QSL) no long-range magnetic order develops despite the presence of strong magnetic interactions; besides disorder and quantum effects, the main reason comes from geometrical frustration induced by the crystallographic lattice [1][2][3][4][5]. For that reason, tuning frustrated magnetic systems provides a versatile toolbox for exploring the exotic ground states in the vicinity of a QSL phase [1,6]. ...
Time-domain magneto-THz spectroscopy is utilized to study the frustrated magnet Averievite Cu$_{5-x}$Zn$_x$\-V$_2$O$_{10}$(CsCl). Pronounced THz resonances are observed in unsubstituted samples ($x=0$) when cooling below the onset of short-range magnetic correlations. The influence of external magnetic effects confirms the magnetic origin of these resonances. Increasing Zn substitution suppresses the resonances, as frustration effects dominate, reflecting the non-magnetic phases for $x> 0.25$ compounds. The temperature evolution of the THz spectra is complemented with electrons spin resonance spectroscopy. This comparison allows a direct probe of the different contributions from magnetic order, frustration, and structural properties in the phase diagram of Averievite. Our results illustrate the effect of magnetic interactions in THz spectra of frustrated magnets.
... Natural minerals offer a wealth of crystal structures and magnetic sublattices, and populating these sublattices with quantum spins, notably Cu 2+ , is expected to reveal exotic magnetic ground states and quantum spin dynamics. 1,2 In a few materials, the Cu 2+ ions are well-separated by large anions, aquo or hydroxo ligands, and alkali-metal ions, resulting in large Cu−Cu distances with long and convoluted superexchange paths. This is the case, in particular, in the Tutton salts, which have the general formula A 2 M(XO 4 ) 2 ·6H 2 O a where A is an alkali metal or NH 4 + , M is a 3d transition metal, and X is sulfur or selenium, as well as in kroḧnkite Na 2 Cu(SO 4 ) 2 ·2H 2 O 3 and related minerals. ...
The rare mineral cyanochroite, K2Cu(SO4)2·6H2O, features isolated Cu2+ ions in distorted octahedral coordination, linked via a hydrogen-bond network. We have grown single crystals of cyanochroite as large as ∼0.5 cm3 and investigated structural and magnetic aspects of this material. The positions of hydrogen atoms deviate significantly from those reported previously based on X-ray diffraction data, whereas the magnetic response is fully consistent with free Cu2+ spins. The structure is not changed by deuteration. Density functional theory calculations support our refined hydrogen positions.
... Though our investigation of the spin-1/2 SKHAF as a highly frustrated quantum spin system is of interest in its own right, it is also motivated by the recent discovery of a spin liquid in the square-kagome magnet KCu 6 AlBiO 4 (SO 4 ) 5 Cl [29], which exhibits, however, three different exchange couplings. Moreover, the large variety of magnetic insulators [64,65] as well as the progress in synthesizing new magnetic molecules and compounds with predefined spin lattices may open the window to get access to the observation of the discussed phenomena. ...
Over the last decade, the interest in the spin-$1/2$ Heisenberg antiferromagnet (HAF) on the square-kagome (also called shuriken) lattice has been growing as a model system of quantum magnetism with a quantum paramagnetic ground state, flat-band physics near the saturation field, and quantum scars. Here, we present large-scale numerical investigations of the specific heat $C(T)$, the entropy $S(T)$ as well as the susceptibility $\chi(T)$ by means of the finite-temperature Lanczos method for system sizes of $N=18,24,30,36,42,48$, and $N=54$. We find that the specific heat exhibits a low-temperature shoulder below the major maximum which can be attributed to low-lying singlet excitations filling the singlet-triplet gap, which is significantly larger than the singlet-singlet gap. This observation is further supported by the behavior of the entropy $S(T)$, where a change in the curvature is present just at about $T/J=0.2$, the same temperature where the shoulder in $C$ sets in. For the susceptibility the low-lying singlet excitations are irrelevant, and the singlet-triplet gap leads to an exponentially activated low-temperature behavior. The maximum in $\chi(T)$ is found at a pretty low temperature $T_{\rm max}/J=0.146$ (for $N=42$) compared to $T_{\rm max}/J=0.935$ for the unfrustrated square-lattice HAF signaling the crucial role of frustration also for the susceptibility. We find a striking similarity of our square-kagome data with the corresponding ones for the kagome HAF down to very low $T$. The magnetization process featuring plateaus and jumps and the field dependence of the specific heat that exhibits characteristic peculiarities attributed to the existence of a flat one-magnon band are as well discussed.
... More recently, synthetic Cu II 3-Te VI O 6 has been widely studied for its three-dimensional antiferromagnetic properties (e.g. Herak et al., 2005;Choi et al., 2008;Zhu et al., 2014;Chakraborty, 2019;Wang et al., 2019), while copper tellurium oxides in general are of interest for their magnetic properties (Norman, 2016(Norman, , 2018Inosov, 2018). Recently, we undertook a study to generate synthetic analogues of rare copper(II) tellurate minerals without known crystal structures, such as brumadoite [Cu 3 (Te VI O 4 )-(OH) 4 Á5H 2 O; Atencio et al. (2008)] and xocomecatlite [Cu 3 (Te VI O 4 )(OH) 4 ; Williams (1975)]. ...
Synthetic and naturally occurring forms of tricopper orthotellurate, CuII3TeVIO6 (the mineral mcalpineite) have been investigated by 3D electron diffraction (3D ED), X-ray powder diffraction (XRPD), Raman and infrared (IR) spectroscopic measurements. As a result of the diffraction analyses, CuII3TeVIO6 is shown to occur in two polytypes. The higher-symmetric CuII3TeVIO6-1C polytype is cubic, space group Ia3, with a = 9.537 (1) Å and V = 867.4 (3) ų as reported in previous studies. The 1C polytype is a well characterized structure consisting of alternating layers of CuIIO6 octahedra and both CuIIO6 and TeVIO6 octahedra in a patchwork arrangement. The structure of the lower-symmetric orthorhombic CuII3TeVIO6-2O polytype was determined for the first time in this study by 3D ED and verified by Rietveld refinement. The 2O polytype crystallizes in space group Pcca, with a = 9.745 (3) Å, b = 9.749 (2) Å, c = 9.771 (2) Å and V = 928.3 (4) ų. High-precision XRPD data were also collected on CuII3TeVIO6-2O to verify the lower-symmetric structure by performing a Rietveld refinement. The resultant structure is identical to that determined by 3D ED, with unit-cell parameters a = 9.56157 (19) Å, b = 9.55853 (11) Å, c = 9.62891 (15) Å and V = 880.03 (2) ų. The lower symmetry of the 2O polytype is a consequence of a different cation ordering arrangement, which involves the movement of every second CuIIO6 and TeVIO6 octahedral layer by (1/4, 1/4, 0), leading to an offset of TeVIO6 and CuIIO6 octahedra in every second layer giving an ABAB* stacking arrangement. Syntheses of CuII3TeVIO6 showed that low-temperature (473 K) hydrothermal conditions generally produce the 2O polytype. XRPD measurements in combination with Raman spectroscopic analysis showed that most natural mcalpineite is the orthorhombic 2O polytype. Both XRPD and Raman spectroscopy measurements may be used to differentiate between the two polytypes of CuII3TeVIO6. In Raman spectroscopy, CuII3TeVIO6-1C has a single strong band around 730 cm⁻¹, whereas CuII3TeVIO6-2O shows a broad double maximum with bands centred around 692 and 742 cm⁻¹.
... The same is true also for other highly frustrated antiferromagnetic (AFM) 2D lattices, such as the kagome lattice [26], which is realized in many copper-containing compounds where quantum spins S = 1/2 reside on the magnetic Cu 2+ ions, most famously in herbertsmithite [27][28][29][30]. The difficulty with these systems, however, is that the lattice may experience small structural distortions which are often sufficient to relieve the frustration [30,31]. Moreover, to the best of our knowledge, no realizations of an undistorted AFM triangular lattice of Cu 2+ spins have been identified to date among inorganic compounds. ...
Yb- and Ce-based delafossites were recently identified as effective spin-1/2 antiferromagnets on the triangular lattice. Several Yb-based systems, such as NaYbO2, NaYbS2, and NaYbSe2, exhibit no long-range order down to the lowest measured temperatures and therefore serve as putative candidates for the realization of a quantum spin liquid. However, their isostructural Ce-based counterpart KCeS2 exhibits magnetic order below TN = 400 mK, which was so far identified only in thermodynamic measurements. Here we reveal the magnetic structure of this long-range ordered phase using magnetic neutron diffraction. We show that it represents the so-called "stripe-yz" type of antiferromagnetic order with spins lying approximately in the triangular-lattice planes orthogonal to the nearest-neighbor Ce-Ce bonds. No structural lattice distortions are revealed below TN, indicating that the triangular lattice of Ce3+ ions remains geometrically perfect down to the lowest temperatures. We propose an effective Hamiltonian for KCeS2, based on a fit to the results of ab initio calculations, and demonstrate that its magnetic ground state matches the experimental spin structure.
... In these triangular lattices, magnetic moments lie within the plane and the interesting phase diagrams occur for in-plane applied fields. Another example is CuFeO 2 , where the Fe 3+ moments order perpendicular to the triangular planes [15,16]. ...
The recently discovered material Cs$_3$Fe$_2$Br$_9$ contains Fe$_2$Br$_9$ bi-octahedra forming triangular layers with hexagonal stacking along the $c$ axis. In contrast to isostructural Cr-based compounds, the zero-field ground state is not a nonmagnetic $S=0$ singlet-dimer state. Instead, the Fe$_2$Br$_9$ bi-octahedra host semiclassical $S=5/2$ Fe$^{3+}$ spins with a pronounced easy-axis anisotropy along $c$ and interestingly, the intra-dimer spins are ordered ferromagnetically. The high degree of magnetic frustration due to (various) competing intra- and inter-dimer couplings leads to a surprisingly rich magnetic phase diagram. Already the zero-field ground state is reached via an intermediate phase, and the high-field magnetization and thermal expansion data for $H\parallel c$ identify ten different ordered phases. Among them are phases with constant magnetization of 1/3, respectively 1/2 of the saturation value, and several transitions are strongly hysteretic with pronounced length changes reflecting strong magnetoelastic coupling.
... Transition metal sulphides constitute a group of naturally generated materials with arguably the most diverse electrical and magnetic properties available. They include materials with a variety of properties, including diamagnetic insulators (ZnS), diamagnetic semiconductors (PbS), antiferromagnetic semiconductors (CuFeS 2 ), ferrimagnetic (Fe 7 S 8 ) and antiferromagnetic metallic conductors (Fe 9 S 10 ), or Pauli paramagnetic metals ((Ni,Fe) 9 S 8 ), just to name a few [8][9][10]. Amongst those, iron sulphides constitute a distinct group of solids and complexes that play a key role in marine systems and global biogeochemical sulphur cycles, which are central to fundamental concepts about the evolution of the Earth surface environment [11]. ...
Metal sulphides constitute cheap, naturally abundant, and environmentally friendly materials for energy storage applications and chemistry. In particular, iron (II) monosulphide (FeS, mackinawite) is a material of relevance in theories of the origin of life and for heterogenous catalytic applications in the conversion of carbon dioxide (CO2) towards small organic molecules. In natural mackinawite, Fe is often substituted by other metals, however, little is known about how such substitutions alter the chemical activity of the material. Herein, the effect of Ni doping on the structural, electronic, and catalytic properties of FeS surfaces is explored via dispersion-corrected density functional theory simulations. Substitutional Ni dopants, introduced on the Fe site, are readily incorporated into the pristine matrix of FeS, in good agreement with experimental measurements. The CO2 molecule was found to undergo deactivation and partial desorption from the doped surfaces, mainly at the Ni site when compared to undoped FeS surfaces. This behaviour is attributed to the energetically lowered d-band centre position of the doped surface, as a consequence of the increased number of paired electrons originating from the Ni dopant. The reaction and activation energies of CO2 dissociation atop the doped surfaces were found to be increased when compared to pristine surfaces, thus helping to further elucidate the role Ni could have played in the reactivity of FeS. It is expected that Ni doping in other Fe-sulphides may have a similar effect, limiting the catalytic activity of these phases when this dopant is present at their surfaces.
The crystal and magnetic structures of the spin S=1 hexamer cluster fedotovite-like A2Cu3O(SO4)3 (A2=K2, NaK, Na2) were studied by neutron powder diffraction at temperatures 1.6–290 K. The crystal structures in all compounds are well refined in the monoclinic space group C2/c. The basic magnetic units of the compounds are copper hexamers, which are coupled by weak superexchange interactions giving rise to three-dimensional long-range magnetic order below 3.0<TN<4.7 K. We have found that for A2=K2 and NaK the propagation vector of the magnetic structure is k=[0,0,0], and the coupling of the Cu hexamers is ferromagnetic (FM) along the ab diagonal and antiferromagnetic along the bc diagonal. In contrast, for A=Na the propagation vector is k=[0,1,0], and the Cu hexamers are coupled antiferromagnetically (AFM) along the ab diagonal. The hexamers are formed by three Cu pairs arranged along the b axis. The calculated spin expectation values 〈s〉 for the simplest symmetric spin Hamiltonian (obtained from inelastic neutron spectroscopy) of the isolated hexamers in the mean field amounted to 〈s〉=3/8 for the side spins Cu1 and Cu2 and 〈s〉=1/4 for Cu3 in the middle. The Cu spins are FM coupled in pairs and AFM between neighboring pairs. The experimental magnetic moments of the Cu2+ ions turn out to be not completely collinear due to spin frustrations within the weak interhexamer interactions. The sizes of magnetic moments of Cu in the hexamers determined from the diffraction data are in fair agreement with the calculated values.
Square-lattice systems offer a direct route for realizing two-dimensional (2D) quantum magnetism with frustration induced by competing interactions. In this work, the square lattice materials YbBi2IO4 and YbBi2ClO4 were investigated using a combination of magnetization and specific-heat measurements on polycrystalline samples. Specific-heat measurements provide evidence for long-range magnetic order below TN = 0.21 K (0.25 K) for YbBi2IO4 (YbBi2ClO4). On the other hand, a rather broad maximum is found in the temperature-dependent magnetic susceptibility, located at Tmax = 0.33 K (0.38 K) in YbBi2IO4 (YbBi2ClO4), consistent with the quasi-2D magnetism expected for the large separation between the magnetic layers. Estimation of the magnetic entropy supports the expected Kramers' doublet ground state for Yb3+ and the observed paramagnetic behavior is consistent with a well-isolated doublet. Roughly two-thirds of the entropy is consumed above TN, due to a combination of the quasi-2D behavior and magnetic frustration. The impact of frustration is examined from the viewpoint of a simplified J1−J2 square lattice model, which is frustrated for antiferromagnetic interactions. Specifically, a high-temperature series expansion analysis of the temperature-dependent specific-heat and magnetization data yields J2/J1 = 0.30 (=0.23) for YbBi2IO4 (YbBi2ClO4). This simplified analysis suggests strong frustration that should promote significant quantum fluctuations in these compounds, and thus motivates future work on the static and dynamic magnetic properties of these materials.
Quantum spin liquids (QSLs) are novel phases of matter which remain quantum disordered even at the lowest temperature. They are characterized by emergent gauge fields and fractionalized quasiparticles. Here we show that the sub-kelvin thermal transport of the three-dimensional S=1/2 hyperhyperkagome quantum magnet PbCuTe2O6 is governed by a sizeable charge-neutral fermionic contribution which is compatible with the itinerant fractionalized excitations of a spinon Fermi surface. We demonstrate that this hallmark feature of the QSL state is remarkably robust against sample crystallinity, large magnetic field, and field-induced magnetic order, ruling out the imitation of QSL features by extrinsic effects. Our findings thus reveal the characteristic low-energy features of PbCuTe2O6 which qualify this compound as a true QSL material.
In frustrated magnetic systems, the competition amongst interactions can introduce extremely high degeneracy and prevent the system from readily selecting a unique ground state. In such cases, the magnetic order is often exquisitely sensitive to the balance among the interactions, allowing tuning among novel magnetically ordered phases. In antlerite, Cu3SO4(OH)4, Cu2+ (S=1/2) quantum spins populate three-leg zigzag ladders in a highly frustrated quasi-one-dimensional structural motif. We demonstrate that at zero applied field, in addition to its recently reported low-temperature phase of coupled ferromagnetic and antiferromagnetic spin chains, this mineral hosts an incommensurate helical+cycloidal state, an idle-spin state, and a multiple-q phase which is the magnetic analog of misfit crystal structures. The antiferromagnetic order on the central leg is reentrant. The high tunability of the magnetism in antlerite makes it a particularly promising platform for pursuing exotic magnetic order.
We report on the magneto-structural properties of the rare copper aluminum hydroxo-arsenate mineral liroconite with chemical composition Cu 2 AlAs 1− x P x O 4 (OH) 4 ·4H 2 O ( x ≈ 0.2). In order to characterize the natural mineral sample chemical analyses, X-ray single crystal and powder diffraction, heat capacity and crystal water desorption, anisotropic thermal expansion and Raman scattering and magnetic susceptibility investigations have been carried out. The magnetic properties are well described by two discrete oxygen bridged Cu ²⁺ spin S = 1/2 dimers with antiferromagnetic spin exchange ranging between −320 K and −136 K, depending on to which group-15 five-valent cation, As ⁵⁺ or P ⁵⁺ , the dimer bridging oxygen atoms coordinate to. Accordingly the temperature dependence of the magnetic susceptibilities can be well fitted to a sum of two Bleaney–Bowers type spin S = 1/2 dimer susceptibilities suggesting that the dimers show negligible mixed coordination to (AsO 4 ) ³⁻ /(PO 4 ) ³⁻ tetrahedra. DFT + U calculation confirm the ratio of the spin exchange parameters of the (AsO 4 ) ³⁻ or (PO 4 ) ³⁻ coordinated Cu ²⁺ – Cu ²⁺ dimers. Inter dimer spin exchange is about two orders of magnitude smaller than intra dimer exchange.
Magnetic frustration, the competition among exchange interactions, often leads to novel magnetic ground states with unique physical properties which can hinge on details of interactions that are otherwise difficult to observe. Such states are particularly interesting when it is possible to tune the balance among the interactions to access multiple types of magnetic order. We present antlerite Cu3SO4(OH)4 as a potential platform for tuning frustration. Contrary to previous reports, the low-temperature magnetic state of its three-leg zigzag ladders is a quasi-one-dimensional analog of the magnetic state recently proposed to exhibit spinon-magnon mixing in botallackite. Density functional theory calculations indicate that antlerite's magnetic ground state is exquisitely sensitive to fine details of the atomic positions, with each chain independently on the cusp of a phase transition, indicating an excellent potential for tunability.
We apply the rotation-invariant Green’s function method (RGM) to study the spin S=1/2 Heisenberg model on a one-dimensional sawtooth lattice, which has two nonequivalent sites in the unit cell. We check the RGM predictions for observable quantities by comparison with the exact-diagonalization and finite-temperature-Lanczos calculations. We discuss the thermodynamic and dynamic properties of this model in relation to the mineral atacamite Cu2Cl(OH)3 complementing the RGM outcomes by results of other approaches.
The Gd3Ru4Al12 structure type compounds, where the rare-earth magnetic ions form a breathing kagome lattice present a promising material landscape for exploring the various magnetic frustration-driven exotic states of matter. Here, we highlight the various magnetic, thermodynamic, and transport properties of several of the Gd3Ru4Al12 structure type magnets and provide intuitive insights into their rich electronic and magnetic ground states. The realization of key properties such as spin trimerization and skyrmion textures accompanied by a large topological (geometrical) Hall effect (THE) in some of these compounds is currently at the heart of several research endeavors searching for efficient data storage and spintronic devices. Features such as helical ordering and anomalous Hall effect (AHE) arising from the formation of Berry curvature by the Weyl fermions present an open window to tuning the electron spins for several practical applications. Therefore, these compounds are projected as promising candidates for investigating several other topological phases of matter accessible through the interplay of the degree of frustration and crystal field symmetry of the rare-earth ions.
S=12 Ising kagome antiferromagnets (KAFs) are rare in reality. In this paper, we report the magnetic ground state and field-induced transitions of an S=12 Ising antiferromagnet with a stacked kagome geometry, Na5Co15.5Te6O36. Upon cooling, magnetic susceptibility measurements reveal three successive magnetic transitions at T1 = 45.2 K, T2 = 35.4 K, and T3∼ 20 K. When the magnetic field is applied along the Ising c axis, a strikingly anomalous initial magnetization lying outside the hysteresis loop is observed below T3. Through detailed characterizations, the magnetic field vs temperature phase diagram is established. A partially disordered antiferromagnetic state is proposed below T1, which becomes frozen below T3. Na5Co15.5Te6O36 is therefore a promising candidate for S=12 Ising KAFs, and this unique composite structure may shed light on the exploratory path for S=12 Ising KAFs.
The spin dynamics of the spin-1/2 kagome-lattice antiferromagnet Cs2Cu3SnF12 is studied using high-resolution, time-of-flight inelastic neutron scattering. The flat mode, a characteristic of the frustrated kagome antiferromagnet, and the low-energy dispersive mode, which is dominated by magnons, can be well described by the linear spin-wave theory. However, the theory fails to describe three weakly dispersive modes between 9 and 14 meV. These modes could be attributed to two-spinon bound states, which decay into free spinons away from the zone center and at a high temperature, giving rise to continuum scattering.
Time-domain magneto-THz spectroscopy is utilized to study the frustrated magnet averievite Cu5−xZnxV2O10(CsCl). Pronounced THz resonances are observed in unsubstituted samples (x=0) when cooling below the onset of short-range magnetic correlations. The influence of external magnetic effects confirms the magnetic origin of these resonances. Increasing Zn substitution suppresses the resonances, as frustration effects dominate, reflecting the nonmagnetic phases for x>0.25 compounds. The temperature evolution of the THz spectra is complemented with electron spin resonance spectroscopy. This comparison allows a direct probe of the different contributions from magnetic order, frustration, and structural properties in the phase diagram of averievite. Our results illustrate the effect of magnetic interactions in THz spectra of frustrated magnets.
We report an initial magnetic study of highly crystalline nanoparticles of the layered-kagome compound BaCo3(VO4)2(OH)2. Quasi-spherical nanoparticles with size in the range of 9-25 nm were elaborated for the first time via a new synthetic route at ambient pressure. Rietveld refinement of X-ray diffraction data, vibrational spectrocopies and high-resolution scanning transmission electron microscopy indicates that the rhombohedral crystal structure of BaCo3(VO4)2(OH)2 is not modified by nanostructuring. Magnetisation measurements are consistent with high-spin Co2+ ions for which unquenched orbital angular momentum is present. Temperature-dependent magnetic susceptibility shows no apparent magnetic ordering or spin freezing down to 2 K and suggests finite-size or surface effects at low temperatures.
The minerals A2Cu3O(SO4)3(A2=Na2,NaK,K2) constitute quantum spin systems with copper hexamers as basic structural units. Strong intrahexamer spin couplings give rise to an effective triplet ground state. Weak interhexamer spin couplings are responsible for two-dimensional long-range magnetic order in the (b,c) plane below 3.0<Tc<4.7K. We investigated the magnetic excitations at T=1.5 K by inelastic neutron scattering (INS). The INS technique was based on the observation of wave vector dependent slices in reciprocal space in order to selectively probe the magnetic signals in different Brillouin zones with different weight. Due to the imbalance of the spin couplings, the data analysis relies on a model in which the interhexamer spin couplings are treated perturbatively on top of the exact S=1 ground state. The interhexamer spin couplings turn out to be ferromagnetic.
Henmilite {Ca2Cu(OH)4[B(OH)4]2} is a blue calcium copper borate mineral found only in the Fuka mine, Okayama Prefecture, Japan. Crystal structure refinement, magnetic and specific heat measurements, and density functional theory (DFT) calculations are performed to clarify its magnetic properties. Synchrotron x-ray diffraction experiments reveal that the hydrogen-bonded chains are arranged in an antiferroelectric manner, doubling the unit cell along the a axis. An antiferromagnetic transition is observed at 0.2 K at zero magnetic field. Furthermore, a dome-shaped antiferromagnetic ordering region exists in the temperature–magnetic-field phase diagram, indicating the presence of quantum spin fluctuations. The obtained crystal structure in combination with DFT calculations suggests that the system has a coupled two-leg ladder magnetic lattice, explaining the very low ordering temperature.
Studies on magnetic frustration continue to attract much attention in condensed matter physics due to the richness of physics it offers and the unraveling of various exotic ground states of matter driven by magnetic instabilities. In the search for candidate quantum spin-liquid, rare-earth antiferromagnets provide a profitable test field for exploring the various emergent ground states formed when strong magnetic exchange produced by well-defined local magnetic moments compete not only with thermal energy but also with the degree of frustration or symmetry parameter. Here, we explore several CaCo2Al8 structure type antiferromagnets and elucidate their strong magnetic frustration-driven ground states occasioned by the arrangements of the magnetic ions on a Shastry-Sutherland lattice and the interplay with quantum fluctuations.
The development of sophisticated sample environments to control temperature, pressure, and magnetic field has grown in parallel with neutron source and instrumentation development. High-pressure apparatus, with high- and low-temperature capability, novel designs for diamond cells, and large volume presses are matched with next-generation neutron sources and moderator designs to provide unprecedented neutron beam brightness. Recent developments in sample environments are expanding the pressure–temperature space accessible to neutron scattering experiments. Researchers are using new capabilities and an increased understanding of the fundamentals of structural and magnetic transitions to explore new territories, including hydrogenous minerals (e.g., ices and hydrates) and magnetic structural phase diagrams.
The recently discovered material Cs3Fe2Br9 contains Fe2Br9 bi-octahedra forming triangular layers with hexagonal stacking along the c axis. In contrast to isostructural Cr-based compounds, the zero-field ground state is not a nonmagnetic S=0 singlet-dimer state. Instead, the Fe2Br9 bi-octahedra host semiclassical S=52Fe3+ spins with a pronounced easy-axis anisotropy along c, and interestingly, the intradimer spins are ordered ferromagnetically. The high degree of magnetic frustration due to (various) competing intradimer and interdimer couplings leads to a surprisingly rich magnetic phase diagram. The zero-field ground state is already reached via an intermediate phase, and the high-field magnetization and thermal expansion data for H∥c identify 10 different ordered phases. Among them are phases with constant magnetization of 13, respectively 12, of the saturation value, and several transitions are strongly hysteretic with pronounced length changes, reflecting strong magnetoelastic coupling.
The structural-magnetic models of 25 antiferromagnetic kagome cuprates similar to herbertsmithite (ZnCu3(OH)6Cl2) - a perspective spin liquid - have been calculated and analyzed. Main correlations between the structure and magnetic properties of these compounds were revealed. It has been demonstrated that, in all AFM kagome cuprates, including herbertsmithite, there exists the competition between the exchange interaction and the antisymmetric anisotropic exchange one (the Dzyaloshinskii-Moriya interaction), as magnetic ions are not linked to the center of inversion in the kagome lattice. This competition is strengthened in all the kagome AFM, except herbertsmithite, by one more type of the anisotropy (duality) of the third in length J3 magnetic couplings (strong J3(J12) next-to-nearest-neighbor couplings in linear chains along the triangle edges and very weak FM or AFM J3(Jd) couplings along the hexagon diagonals). The above couplings are crystallographically identical, but are divided to two types of different in strength magnetic interactions. The existence of duality of J3 couplings originated from the structure of the kagome lattice itself. Only combined contributions of dual J3 couplings with anisotropic Dzyaloshinskii-Moriya interactions are capable to suppress frustration of kagome antiferromagnetics. It has been demonstrated that the possibility of elimination of such a duality in herbertsmithite, which made it a spin liquid, constitutes a rare lucky event in the kagome system. Three crystal chemistry criteria of the existence of spin liquids on the kagome lattice have been identified: first, the presence of frustrated kagome lattices with strong dominant antiferromagnetic nearest-neighbor J1 couplings competing only with each other in small triangles; second, magnetic isolation of these frustrated kagome lattices; and third, the absence of duality of the third in length J3 magnetic couplings.
We present a combined experimental and theoretical study of the mineral atacamite Cu2Cl(OH)3. Density-functional theory yields a Hamiltonian describing anisotropic sawtooth chains with weak 3D connections. Experimentally, we fully characterize the antiferromagnetically ordered state. Magnetic order shows a complex evolution with the magnetic field, while, starting at 31.5 T, we observe a plateaulike magnetization at about Msat/2. Based on complementary theoretical approaches, we show that the latter is unrelated to the known magnetization plateau of a sawtooth chain. Instead, we provide evidence that the magnetization process in atacamite is a field-driven canting of a 3D network of weakly coupled sawtooth chains that form giant moments.
Magnetism of any material depends on its crystal structure. However, two isostructural compounds such as MCuMoO4(OH) (M = Na, K) can have markedly different magnetic properties. Herein, we introduce a new method to describe the linkages between the O-atoms and their bridged Cu2+ ions in order to clearly illustrate the structure-magnetic property relationships. This new method can account for magnetic differences between the two isostructural MCuMoO4(OH) and is further confirmed by the rational design and development of a new compound KGaCu(PO4)2 with different linkages. The title compound crystalized in a space group of P21/c adopts a one-dimensional (1D) magnetically isolated S = 1/2 zigzag chain composed of elongated [CuO6] octahedra via sharing alternately equatorial and skew edges. O atoms at the skew edges bridge the equatorial and axial orbitals of neighbouring Cu2+ ions (denoted EOA), while those at the equatorial edges bridge the equatorial orbitals of Cu2+ ions (EOE). The nearest-neighbour (NN) magnetic coupling of Cu2+ ions with the EOA linkage at 2.821 Å in the title compound is negligible, whereas the NN magnetic coupling of Cu2+ ions with the EOE linkage at 2.974 Å is essential. Therefore, the zigzag chain containing alternating spin-exchange dimers and no-spin-exchange ones is similar in electronic configuration to the dimerization of the quasi-one-dimensional antiferromagnet. Magnetic investigation of analogous compounds with a 'trans-cis-trans-cis' configuration observed in the title compound may shed light on structural evolutions associated with spin-Peierls (SP) transition.
Abst r act The crystal structure of an oxysalt mineral may be divided into two parts: (1) the structural unit, an array of high-bond-valence polyhedra that is usually anionic in character, and (2) the interstitial complex, an array of large low-valence cations, simple anions, (OH) and (H 2 O) groups that is usually cationic in character. The chemical compositions of interstitial complexes in sulfate minerals are explained and predicted using intrinsic properties such as polarity, Lewis acidity, coordination numbers and the average charge of oxygen atoms in the structural unit (average basicity). The interstitial complex can be characterized by its Lewis acidity, a measure of the electrophilic character of the complex, and the structural unit can be characterized by its range in Lewis basicity. Any complex structural unit [M z+ (H 2 O) n (OH) m (SO 4) k ] can be divided into an acidic component of (M z+ n) polyhedra and a basic component of (SO 4) groups. The ligands of the acidic component are primarily bond-valence donors, and the O atoms of the basic component are bond-valence acceptors. Neutral structural units must arrange themselves such that their acidic and basic parts match each other in order to allow linkage via hydrogen bonds. Additional (H 2 O) groups between structural units are required where hydrogen bonds cannot be accepted directly by a donor atom of the basic part of the structural unit. The Lewis acidities of interstitial complexes in sulfate minerals range from 0.10 to 0.25 vu (valence units), with frequency maxima at 0.13, 0.17, 0.20-0.21 and 0.25 vu. These maxima correspond to average coordination-numbers of oxygen atoms in the basic component of the structural unit. Using the characteristic range in Lewis basicity of a structural unit and the maximum frequencies of Lewis acidities, the most probable number of bonds from the interstitial complex to the structural unit may be predicted using the valence-matching principle. This number allows prediction of the types of interstitial complexes for a given structural unit. SOMMAIRE On peur diviser la structure cristalline d'un minéral de type oxysel en deux parties, (1) une unité structurale, agencement de polyèdres à valence de liaison élevée, généralement à caractère anionique, et (2) un complexe interstitiel, agencement de cations relativement gros, à faible valence, ou bien des groupes (OH) and (H 2 O), généralement à caractère cationique. Il est possible d'expliquer et de prédire les compositions chimiques des complexes interstitiels des minéraux sulfatés en utilisant des propriétés intrinsèques telles que polarité, acidité de Lewis, coordinence, et charge moyenne sur les atomes d'oxygène de l'unité structurale (basicité moyenne). On peut aussi caractériser le complexe interstitiel par son acidité de Lewis, mesure du caractère électro-phile du complexe, et l'unité structurale par son intervalle de valeurs de sa basicité de Lewis. Toute unité structurale complexe [M z+ (H 2 O) n (OH) m (SO 4) k ] peut être divisée en une composante acidique de polyèdres (M z+ n) et une composante basique de groupes (SO 4). Les ligands de la composante acide seraient surtout des donateurs de valences de liaison, tandis que les atomes d'oxygène de la composante basique seraient surtout des accepteurs de valences de liaison. Les unités structurales neutres doivent se disposer de façon à ce que les parties acide et basique concordent l'une avec l'autre pour permettre un couplage grâce à des liaisons hydrogène. Des groupes (H 2 O) additionnels entre unités structurales seront nécessaires où les liaisons hydrogène ne peuvent pas être acceptées directement par un atome donateur situé dans la partie basique de l'unité structurale. Les acidités de Lewis des complexes interstitiels des minéraux sulfatés ont une valeur entre 0.10 et 0.25 vu (unités de valence), avec des maxima en fréquence à 0.13, 0.17, 0.20-0.21 et 0.25 vu. Ces maxima correspondent à la coordinence moyenne des atomes d'oxygène de la composante basique de l'unité structurale. En employant l'intervalle caractéristique de la basicité de Lewis d'une unité structurale et les maxima en fréquence des acidités de Lewis, on peut prédire le nombre probable des liaisons partant du complexe interstitiel vers l'unité structurale en se servant du principe de la concordance des valences. Ce nombre permet la prédiction des types de complexes interstitiels d'une unité structurale quelconque. (Traduit par la Rédaction)
The search for quantum spin liquid (QSL) materials has attracted significant attention in the field of condensed matter physics in recent years, however so far only a handful of them are considered as candidates hosting QSL ground state. Owning to their geometrically frustrated structures, Kagome materials are ideal systems to realize QSL. We synthesize the kagome structured material claringbullite (Cu 4 (OH) 6 FCl) and then replace inter-layer Cu with Zn to form Cu 3 Zn(OH) 6 FCl. Comprehensive measurements reveal that doping Zn ²⁺ ions transforms magnetically ordered Cu4(OH) 6 FCl into a non-magnetic QSL candidate Cu 3 Zn(OH)6FCl. Therefore, the successful syntheses of Cu 4 (OH)6FCl and Cu 3 Zn(OH) 6 FCl provide not only a new platform for the study of QSL but also a novel pathway of investigating the transition between QSL and magnetically ordered systems.
The interplay between lattice topology, frustration, and spin quantum number, s, is explored for the Heisenberg antiferromagnet (HAFM) on the 11 two-dimensional Archimedean lattices (square, honeycomb, CaVO, SHD, SrCuBO, triangle, bounce, trellis, maple-leaf, star, and kagome). We show that the coupled cluster method (CCM) provides consistently accurate results when compared to the results of other approximate methods. The CCM also provides valuable information relating to the selection of ground states and we find that this depends on spin quantum number for the kagome and star lattices. Specifically, the 3×3 model state provides lower ground-state energies than those of the q=0 model state for the kagome and star lattices for most values of s. The q=0 model state provides lower ground-state energies only for s=1/2 for the kagome lattice and s=1/2 and s=1 for the star lattice. The kagome and star lattices demonstrate the least amount of magnetic ordering and the unfrustrated lattices (square, honeycomb, SHD, and CaVO) demonstrate the most magnetic ordering for all values of s. The SrCuBO and triangular lattices also demonstrate high levels of magnetic ordering, while the remaining lattices (bounce, maple-leaf, and trellis) tend to lie between these extremes, again for all values of s. These results also clearly reflect the strong increase in magnetic order with increasing spin quantum number s for all lattices. The ground-state energy, Eg/(NJs2), scales with s−1 to first order, as expected from spin-wave theory, although the order parameter, M/s, scales with s−1 for most of the lattices only. Self-consistent spin-wave theory calculations indicated previously that M/s scales with s−2/3 for the kagome lattice HAFM, whereas previous CCM results (replicated here also) suggested that M/s scales with s−1/2. It is probable, therefore, that different scaling for M/s than with s−1 does indeed occur for the kagome lattice. By using similar arguments, we find here also that M/s scales with s−1/3 for the star lattice and with s−2/3 for the SrCuBO lattice.
We theoretically study magnetic and topological properties of antiferromagnetic kagome spin systems in the presence of both in- and out-of-plane Dzyaloshinskii-Moriya interactions. In materials such as the iron jarosites, the in-plane interactions stabilize a canted noncollinear “umbrella” magnetic configuration with finite scalar spin chirality. We derive expressions for the canting angle and use the resulting order as a starting point for a spin-wave analysis. We find topological magnon bands, characterized by nonzero Chern numbers. We calculate the magnon thermal Hall conductivity and propose the iron jarosites as a promising candidate system for observing the magnon thermal Hall effect in a noncollinear spin configuration. We also show that the thermal conductivity can be tuned by varying an applied magnetic field or the in-plane Dzyaloshinskii-Moriya strength. In contrast to previous studies of topological magnon bands, the effect is found to be large even in the limit of small canting.
The objective of the present work was to analyze the possibility of realization of quantum spin liquid (QSL) in three volcanic minerals - averievite (Cu5O2(VO4)2(CuCl)), ilinskite (NaCu5O2(SeO3)2Cl3), and avdononite (K2Cu5Cl8(OH)4·2H2O) - from the crystal chemistry point of view. Based on the structural data, the sign and strength of magnetic interactions have been calculated and the geometric frustrations serving as the main reason of the existence of spin liquids have been investigated. According to our calculations, the magnetic structures of averievite and ilinskite are composed of AFM spin-frustrated layers of corner-sharing Cu4 tetrahedra on the kagome lattice. However, the direction of nonshared corners of tetrahedra is different in them. The oxygen ions centering the OCu4 tetrahedra in averievite and ilinskite provide the main contribution to the formation of antiferromagnetic interactions along the tetrahedra edges. The local electric polarization in averievite and the possibility of spin configuration fluctuations due to vibrations of tetrahedra-centering oxygen ions have been discussed. The existence of structural phase transitions accompanied with magnetic transitions was assumed in ilinskite because of the effect of a lone electron pair by Se4+ ions. As was demonstrated through comparison of averievite and avdoninite, at the removal of centering oxygen ions from tetrahedra, the magnetic structure of the pyrochlore layer present in averievite transformed into an openwork curled net with large cells woven from corner-sharing open AFM spin-frustrated tetrahedra ("butterflies") in avdoninite.
Topological magnons are emergent quantum spin excitations featured by magnon bands crossing linearly at the points dubbed nodes, analogous to fermions in topological electronic systems. Experimental realisation of topological magnons in three dimensions has not been reported so far. Here, by measuring spin excitations (magnons) of a three-dimensional antiferromagnet Cu3TeO6 with inelastic neutron scattering, we provide direct spectroscopic evidence for the coexistence of symmetry-protected Dirac and triply degenerate nodes, the latter involving three-component magnons beyond the Dirac-Weyl framework. Our theoretical calculations show that the observed topological magnon band structure can be well described by the linear-spin-wave theory based on a Hamiltonian dominated by the nearest-neighbour exchange interaction J1. As such, we showcase Cu3TeO6 as an example system where Dirac and triply degenerate magnonic nodal excitations coexist, demonstrate an exotic topological state of matter, and provide a fresh ground to explore the topological properties in quantum materials.
We present the hydrothermal synthesis, as well as structural and chemical analysis, of single crystals of EuCu3(OH)6Cl3, ZnxCu4−x(OH)6(NO3)2 and haydeeite, and MgCu3(OH)6Cl2 compounds, all arising from the atacamite family. Magnetic and specific-heat measurements down to 1.8 K are carried out for these systems. EuCu3(OH)6Cl3 has a frustrated antiferromagnetic Cu2+ ground state with order at 15 K, and a strong anisotropy and increased magnetization from Van Vleck paramagnetic Eu3+ contributions. ZnCu3(OH)6(NO3)2 reveals antiferromagnetic order at 9 K and measurements on haydeeite single crystals confirm the ferromagnetic order at 4.2 K with the easy axis within the kagome plane. These results prove that the atacamite family presents a broad class of materials with interesting magnetic ground states.
We report the $\mathbf{H}-T$ phase diagram of $S=1/2$ strongly frustrated anisotropic spin chain material linarite PbCuSO$_4$(OH)$_2$ in tilted magnetic fields up to 10 T and temperatures down to 0.2 K. By means of torque magnetometry we investigate the phase diagram evolution as the magnetic field undergoes rotation in $\mathbf{ba}^{\ast}$ and $\mathbf{bc}$ planes. The key finding is the robustness of the high field spin density wave-like phase, which may persist even as the external field goes orthogonal to the chain direction $\mathbf{b}$. In contrast, the intermediate collinear antiferromagnetic phase collapses at moderate deflection angles with respect to $\mathbf{b}$ axis.
Temperature- and field- dependent $^1$H-, $^{19}$F-, and $^{79,81}$Br- NMR measurements together with zero - field $^{79,81}$Br-NQR measurements on polycrystalline samples of barlowite, Cu$_4$(OH)$_6$FBr are conducted to study the magnetism and possible structural distortions on a microscopic level. The temperature dependence of the $^{79,81}$Br- NMR spin-lattice relaxation rates 1/$T_1$ indicate a phase transition at $T_{\rm N}\simeq$15 K which is of magnetic origin, but with an unusually weak slowing down of fluctuations below $T_{\rm N}$. Moreover, 1/$T_1T$ scales linear with the bulk susceptibility which indicates persisting spin fluctuations down to 2 K. Quadupolare resonance (NQR) studies reveal a pair of zero-field NQR- lines associated with the two isotopes of Br with the nuclear spins of $I$ = 3/2. Quadrupole coupling constants of $\nu_Q\simeq$ 28.5~MHz and 24.7~MHz for $^{79}$Br- and $^{81}$Br- nuclei are determined from Br-NMR and the asymmetry parameter of the electric field gradient was estimated to $\eta \simeq 0.2$. The Br-NQR lines are consistent with our findings from Br-NMR and they are relatively broad, even above $T_{\rm N}$. This broadening and the relative large $\eta $ value suggests a symmetry reduction at the Br- site reflecting the presence of a local distortion in the lattice. Our density-functional calculations show that the displacements of Cu2 atoms located between the kagome planes do not account for this relatively large $\eta$. On the other hand, full structural relaxation, including the deformation of kagome planes, leads to a better agreement with the experiment.
Green dioptase is a naturally occurring antiferromagnetic mineral that in recent years has been suggested as a candidate to exhibit quantum fluctuations at both above and below T N. Our work uses muon spectroscopy to study the dynamic and static properties of the magnetism in zero applied field. We observe the antiferromagnetic transition through tracking out the evolution of the muon spin precession frequency as a function of temperature. T N is calculated to be 15 K and the critical exponent of the transition matches with that of a 3D Heisenberg system. We also note that no evidence for any quantum magnetic fluctuations is observed either above or below T N.
The mineral linarite, PbCuSO4(OH)2, is a spin-1/2 chain with frustrating nearest-neighbor ferromagnetic and next-nearest-neighbor antiferromagnetic exchange interactions. Our inelastic neutron scattering experiments performed above the saturation field establish that the ratio between these exchanges is such that linarite is extremely close to the quantum critical point between spin-multipolar phases and the ferromagnetic state. We show that the predicted quantum multipolar phases are fragile and actually suppressed by a tiny orthorhombic exchange anisotropy and weak interchain interactions in favor of a dipolar fan phase. Including this anisotropy in classical simulations of a nearly critical model explains the field-dependent phase sequence of the phase diagram of linarite, its strong dependence of the magnetic field direction, and the measured variations of the wave vector as well as the staggered and the uniform magnetizations in an applied field.
The magnetic susceptibility $\chi(T)$ of spin-1/2 chains is widely used to quantify exchange interactions, even though $\chi(T)$ is similar for different combinations of ferromagnetic $J_1$ between first neighbors and antiferromagnetic $J_2$ between second neighbors. We point out that the spin specific heat $C(T)$ directly determines the ratio $\alpha = J_2/|J_1|$ of competing interactions. The $J_1-J_2$ model is used to fit the isothermal magnetization $M(T,H)$ and $C(T,H)$ of spin-1/2 Cu(II) chains in LiCuSbO$_4$. By fixing $\alpha$, $C(T)$ resolves the offsetting $J_1$, $\alpha$ combinations obtained from $M(T,H)$ in cuprates with frustrated spin chains.
Synthetic barlowite, Cu4(OH)6BrF, has emerged as a new quantum spin liquid (QSL) host, containing kagome layers of S=1/2 Cu2+ ions separated by interlayer Cu2+ ions. Similar to synthetic herbertsmithite, ZnCu3(OH)6Cl2, it has been reported that Zn2+ substitution for the interlayer Cu2+ induces a QSL ground state. Here we report a scalable synthesis of single crystals of Cu4(OH)6BrF. Through x-ray, neutron, and electron diffraction measurements coupled with magic angle spinning 19F and 1H NMR spectroscopy, we resolve the previously reported positional disorder of the interlayer Cu2+ ions and find that the structure is best described in the orthorhombic space group, Cmcm, with lattice parameters a = 6.665(13) A, b = 11.521(2) A, c = 9.256(18) A and an ordered arrangement of interlayer Cu2+ ions. Infrared spectroscopy measurements of the O-H and F-H stretching frequencies demonstrate that the orthorhombic symmetry persists upon substitution of Zn2+ for Cu2+. Specific heat and magnetic susceptibility measurements of Zn-substituted barlowite, ZnxCu4-x(OH)6BrF, reveal striking similarities with the behavior of ZnxCu4-x(OH)6Cl2. These parallels imply universal behavior of copper kagome lattices even in the presence of small symmetry breaking distortions. Thus synthetic barlowite demonstrates universality of the physics of synthetic Cu2+ kagome minerals and furthers the development of real QSL states.
Barlowite Cu$_4$(OH)$_6$FBr shows three dimensional (3D) long-range antiferromagnetism, which is fully suppressed in Cu$_3$Zn(OH)$_6$FBr with a kagome quantum spin liquid ground state. Here we report systematic studies on the evolution of magnetism in the Cu$_{4-x}$Zn$_x$(OH)$_{6}$FBr system, as a function of $x$, to bridge the two limits of Cu$_4$(OH)$_6$FBr ($x=0$) and Cu$_3$Zn(OH)$_6$FBr ($x=1$). Neutron diffraction measurements reveal a hexagonal-to-orthorhombic structural change with decreasing temperature in the $x$ = 0 sample. While confirming the 3D antiferromagnetic nature of low-temperature magnetism, the magnetic moments on some Cu$^{2+}$ sites in the kagome planes are found to be vanishingly small, suggesting strong frustration already exist in barlowite. Substitution of interlayer Cu$^{2+}$ with Zn$^{2+}$, with gradually increasing $x$, completely suppresses the bulk magnetic order at around $x$ = 0.4, but leaves a local, secondary magnetic order up to $x\sim 0.8$ with slight decrease of its transition temperature. The high-temperature magnetic susceptibility and specific heat measurements further suggest that the intrinsic magnetic properties of kagome spin liquid planes may already appear from $x>0.3$ samples. Our results therefore reveal that the Cu$_{4-x}$Zn$_x$(OH)$_6$FBr may be the long-thought experimental playground for the systematic investigations of the quantum phase transition from a long-range antiferromagnet to a topologically ordered quantum spin liquid.
We report single-crystal V51 NMR studies on volborthite Cu3V2O7(OH)2·2H2O, which is regarded as a quasi-two-dimensional frustrated magnet with competing ferromagnetic and antiferromagnetic interactions. In the 1/3 magnetization plateau above 28 T, the nuclear spin-lattice relaxation rate 1/T1 indicates an excitation gap with a large effective g factor in the range of 4.6–5.9, pointing to magnon bound states. Below 26 T where the gap has closed, the NMR spectra indicate small internal fields with a Gaussian-like distribution, whereas 1/T1 shows a power-law-like temperature dependence in the paramagnetic state, which resembles a slowing down of spin fluctuations associated with magnetic order. We discuss the possibility of an exotic spin state caused by the condensation of magnon bound states below the magnetization plateau.
By means of symmetry analysis, density functional theory calculations, and Monte Carlo simulations we show that goethite, alpha-FeOOH, is a linear magnetoelectric below its Neel temperature T_N=400 K. The experimentally observed magnetic field induced spin-flop phase transition results in either change of direction of electric polarization or its suppression. Estimated value of magnetoelectric coefficient is 0.57 muC/(m^2 T). The abundance of goethite in nature makes it arguably the most widespread magnetoelectric material.
Band topology, or global wave-function structure that enforces novel properties in the bulk and on the surface of crystalline materials, is currently under intense investigations for both fundamental interest and its technological promises. While band crossing of non-trivial topological nature was first studied in three dimensions for electrons, the underlying physical idea is not restricted to fermionic excitations. In fact, experiments have confirmed the possibility to have topological band crossing of electromagnetic waves in artificial structures. Fundamental bosonic excitations in real crystals, however, have not been observed to exhibit the counterpart under ambient pressure and magnetic field, where the difficulty is in part because natural materials cannot be precisely engineered like artificial structures. Here, we use inelastic neutron scattering to reveal the presence of topological spin excitations (magnons) in a three-dimensional antiferromagnet, Cu3TeO6, which features a unique lattice of magnetic spin-1/2 Cu2+ ions. Beyond previous understanding, we find that the material's spin lattice possesses a variety of exchange interactions, with the interaction between the ninth-nearest neighbours being as strong as that between the nearest neighbours. Although theoretical analysis indicates that the presence of topological magnon band crossing is independent of model details, Cu3TeO6 turns out to be highly favourable for the experimental observation, as its optical magnons are spectrally sharp and intense due to the highly interconnected spin network and the large magnetic cell. The observed magnon band crossing generally has the form of a special type of Z2-topological nodal lines that are yet to be found in fermion systems, rendering magnon systems a fertile ground for exploring novel band topology.
Brownmillerite Ca2Fe2O5 has been observed to exhibit many outstanding properties that are applicable to ecotechnology. However, very little work on doped Ca2Fe2O5 compounds has been carried out to widen their application scope. We present herein a detailed study of the crystalline/geometric and electronic structures and magnetic and electrical properties of Ca2−xLaxFe2O5 (x = 0 to 1) prepared by conventional solid-state reaction. X-ray diffraction patterns indicated that the compounds with x = 0 to 0.05 exhibited brownmillerite-type single phase. La doping with higher content (x ≥ 0.1) stimulated additive formation of Grenier- (LaCa2Fe3O8) and perovskite-type (LaFeO3) phases. Extended x-ray absorption fine structure spectroscopy at the Fe K-edge and electron spin resonance spectroscopy revealed presence of Fe³⁺ in the parent Ca2Fe2O5 (x = 0) and both Fe³⁺ and Fe⁴⁺ in the doped compounds (x ≥ 0.05). The Fe⁴⁺ content tended to increase with increasing x. This stimulates ferromagnetic exchange interactions between Fe³⁺ and Fe⁴⁺ ions and directly influences the magnetic properties of Ca2−xLaxFe2O5. Electrical resistivity (ρ) measurements in the temperature range of T = 20 K to 400 K revealed that all the compounds exhibit insulator behavior; the ρ(T) data for x ≥ 0.1 could be described based on the adiabatic small polaron hopping model.
The new mineral centennialite (IMA 2013-110), CaCu3(OH)6Cl2.nH2O, was identified from three cotype specimens originating from the Centennial Mine, Houghton County, Michigan, USA, where it occurs as a secondary product, after acidwater action upon supergene Cu mineralization in associationwith, and essentially indivisible from, other copper-containing minerals such as calumetite and atacamite familyminerals. It forms as pale to azure blue encrustations, often taking a botryoidal form.Centennialite is trigonal,P3m1, a = 6.6606(9) A, c = 5.8004(8) A, V = 222.85(6) A3, Z = 1. The strongest powder X-ray diffraction lines are dobs/A [I%] (hkl), 5.799 [100] (001), 2.583 [75] (201), 2.886 [51] (111), 1.665 [20] (220), 1.605 [17] (023), 1.600 [15] (221), 1.444 [11] (222). The X-ray refined structure forms a kagome net of planar coordinated CuO4 units with Jahn-Teller coordinated Cl apices to form octahedra that edge-share to in-plane adjacent and flattened CaO6 octahedra, which are centred about the lattice origin. All oxygen sites are protonated and shared between one Ca-octahedron and one CuO4 planar unit. Three protonated sites are linked, by hydrogen-bonding to Cl sites, which sit on the triad axis. Each lattice has one Cl above and one below the Ca-Cu polyhedral plane. Consequently, the layers are stacked, along <001>, with two Cl sites between layers. In addition to this kapellasite-like topology, an extra c/2 site is identified as being variably water-hosting and extends the coordination of the Ca-site to 8-fold, akin to the body-diagonal Pb-Cu sheet in murdochite. Centennialite conforms to the description of the 'Unidentified Cu-Ca-Cl Mineral' noted in Heinrich's Mineralogy of Michigan and is almost certainly identical to the supposed hexagonal basic calcium-copper hydroxychloride monohydrate of Erdös et al. (1981).We comment upon relationships between calumetite and centennialite and propose a substructure model for a synthetic calumetite-like phase that is related directly to centennialite.
Fedotovite K$_2$Cu$_3$O(SO$_4$)$_3$ is a candidate of new quantum spin systems, in which the edge-shared tetrahedral (EST) spin-clusters consisting of Cu$^{2+}$ are connected by weak inter-cluster couplings to from one-dimensional array. Comprehensive experimental studies by magnetic susceptibility, magnetization, heat capacity, and inelastic neutron scattering measurements reveal the presence of an effective $S$ = 1 Haldane state below $T \cong 4$ K. Rigorous theoretical studies provide an insight into the magnetic state of K$_2$Cu$_3$O(SO$_4$)$_3$: an EST cluster makes a triplet in the ground state and one-dimensional chain of the EST induces a cluster-based Haldane state. We predict that the cluster-based Haldene state emerges whenever the number of tetrahedra in the EST is $even$.
Gaudefroyite contains chains of edge-linked MnO6 octahedra on a Kagomé lattice which results in magnetic frustration between the chains and overall spin-liquid behaviour below 9 K. Magnetization and specific heat measurements indicate very large entropy increases for temperatures of 10 – 30 K on removal of applied magnetic fields as low as 2 T. This is attributed to the degenerate magnetic ground states originating from the frustrated Kagomé lattice. Direct temperature change measurements confirm that the mineral has excellent low-field magnetocaloric properties suitable for refrigeration to produce liquid hydrogen.
In this paper, we explore the relationship between strong spin-orbit coupling
and spin liquid physics. We study a very general model on the triangular
lattice where spin-orbit coupling leads to the presence of highly anisotropic
interactions. We use variational Monte Carlo to study both $U(1)$ quantum spin
liquid states and ordered ones, via the Gutzwiller projected fermion
construction. We thereby obtain the ground state phase diagram in this phase
space. We furthermore consider effects beyond the Gutzwiller wavefunctions for
the spinon Fermi surface quantum spin liquid, which are of particular
importance when spin-orbit coupling is present.
On the basis of extensive studies of synthetic perovskite-structured compounds it is possible to derive a hierarchy of hettotype structures which are derivatives of the arisotypic cubic perovskite structure (ABX3), exemplified by SrTiO3 (tausonite) or KMgF3 (parascandolaite) by: (1) tilting and distortion of the BX6 octahedra; (2) ordering of A- and B-site cations; (3) formation of A-, B- or X-site vacancies. This hierarchical scheme can be applied to some naturally-occurring oxides, fluorides, hydroxides, chlorides, arsenides, intermetallic compounds and silicates which adopt such derivative crystal structures. Application of this hierarchical scheme to naturally-occurringminerals results in the recognition of a perovskite supergroupwhich is divided into stoichiometric and non-stoichiometric perovskite groups, with both groups further divided into single ABX3 or double A2BB'X6 perovskites. Subgroups, and potential subgroups, of stoichiometric perovskites include: (1) silicate single perovskites of the bridgmanite subgroup; (2) oxide single perovskites of the perovskite subgroup (tausonite, perovskite, loparite, lueshite, isolueshite, lakargiite, megawite); (3) oxide single perovskites of the macedonite subgroup which exhibit second order Jahn-Teller distortions (macedonite, barioperovskite); (4) fluoride single perovskites of the neighborite subgroup (neighborite, parascandolaite); (5) chloride single perovskites of the chlorocalcite subgroup; (6) B-site cation ordered double fluoride perovskites of the cryolite subgroup (cryolite, elpasolite, simmonsite); (7) B-site cation ordered oxide double perovskites of the vapnikite subgroup [vapnikite, (?) latrappite]. Non-stoichiometric perovskites include: (1) A-site vacant double hydroxides, or hydroxide perovskites, belonging to the söhngeite, schoenfliesite and stottite subgroups; (2) Anion-deficient perovskites of the brownmillerite subgroup (srebrodolskite, shulamitite); (3) A-site vacant quadruple perovskites (skutterudite subgroup); (4) B-site vacant single perovskites of the oskarssonite subgroup [oskarssonite]; (5) B-site vacant inverse single perovskites of the cohenite and auricupride subgroups; (6) B-site vacant double perovskites of the diaboleite subgroup; (7) anion-deficient partly-inverse B-site quadruple perovskites of the hematophanite subgroup.
We propose a theoretical model with Dzyaloshinskii-Moriya interaction for the polar magnet Fe2Mo3O8. Via Wigner-Jordan transformation, the electric polarization P x and the magnetization M formula are obtained. Combined with the Green's function equation of motion method, we show that the electric polarization can be induced by a magnetic ordering and manipulated by a magnetic field. There exist structural and metamagnetic transitions in the Fe2Mo3O8 system, which is in agreement with the experimental results.
We report first-principles density-functional theory results on the electronic and magnetic properties of the recently discovered superconducting FeS, which reveals important differences with the other members of the iron-chalcogenides (FeSe and FeTe). The band structure of FeS is characterized by two hole bands at the Fermi energy with a fully occupied dxy band at Γ. A stripe-antiferromagnetic phase with a small magnetic moment is the most stable magnetic solution, but different magnetic phases have comparable energies indicating a tight competition. Including local interactions treated within dynamical mean-field theory, we find significant correlation effects with orbital-dependent strength and character, even if all the fingerprints of correlations are slightly weaker than in FeSe. The study of the effect of pressure reveals significant changes in the electronic structure of the material and of the correlation effects. These results point toward further studies on the possible superconducting phase stabilized by pressure effects or two dimensionality, in analogy with pressurized and monolayer FeSe.
The uptake of aqueous Ni(II) by synthetic mackinawite (FeS) was examined in anaerobic batch experiments at near-neutral pH (5.2 to 8.4). Initial molar ratios of Ni(II) to FeS ranged from 0.008 to 0.83 and maximum Ni concentrations in mackinawite, expressed as the cation mol fraction, were as high as XNi = 0.56 (Fe1 − xNixS; 0 ≤ x ≤ 1). Greater than 99% Ni removal from solution occurred when Ni loading remained below 0.13 ± 0.03 (1σ) mol Ni per mol FeS due to sorption of Ni at the mackinawite surface. Characterization of experimental solids using X-ray diffraction and Raman spectroscopy showed patterns characteristic of nanocrystalline mackinawite; no evidence of nickel monosulfide (α-NiS or millerite), polydymite (Ni3S4), or godlevskite [(Ni,Fe)9S8] formation was indicated regardless of the amount of Ni loading. Slight expansion of the c-axis correlated with increasing Ni content in synthetic mackinawite, from c = 5.07 ± 0.01 Å at XNi = 0.02 to c = 5.10 ± 0.01 Å at XNi = 0.38.
Ni K-edge extended X-ray absorption fine structure (EXAFS) spectra of synthetic Ni-bearing mackinawite are similar in phase and amplitude to the Fe K-edge EXAFS spectrum of Ni-free mackinawite, indicating that the molecular environment of Ni²⁺ in Ni-bearing mackinawite is similar to that of Fe²⁺ in Ni-free mackinawite. EXAFS data fitting of Ni-bearing mackinawite with XNi = 0.42 indicated a coordination number of 4.04 ± 0.30 and an average NiS bond distance of 2.28 Å, in good agreement with the FeS bond distance of 2.26 Å in mackinawite, tetrahedral Fe coordination, and slight lattice expansion along the c-axis. At lower Ni loadings (XNi = 0.05–0.11), EXAFS analysis showed a decrease in NiS coordination towards CN = 3, which reflects the influence of sorbed Ni. Continued Ni uptake, past the maximum amount of sorption, was accompanied by proportional molar release of Fe to solution. Interstitial occupancy of Ni within the mackinawite interlayer may be transitional to structural substitution of Fe.
The Ni-mackinawite solid-solution is described by a one-site binary mixing model:lnKd=lnKe−WRT1−2XNi
where Kd is the distribution coefficient, Ke is the ratio of equilibrium constants for Ni-mackinawite and mackinawite (14.4 ± 1.3), W is an ion interaction parameter, and XNi is the mole fraction of end-member NiS in the solid solution. The experimentally determined value of W is 17.74 ± 1.15 kJ/mol and indicates significant non-ideality of the solid solution.
Transformation processes were evaluated by aging Ni-mackinawite with polysulfides and solutions saturated with air. Reaction of Ni-mackinawite with polysulfides led to the formation of pyrite (FeS2) and Ni retention in the solid phase. When Ni-mackinawite was aged in the presence of dissolved oxygen, transformation to goethite (FeOOH) and violarite (FeNi2S4) was observed.
Since its proposal by Anderson, resonating valence bonds (RVB) formed by a superposition of fluctuating singlet pairs have been a paradigmatic concept in understanding quantum spin liquids (QSL). Here, we show that excitations related to singlet breaking on nearest-neighbor bonds describe the high-energy part of the excitation spectrum in YbMgGaO4, the effective spin-1/2 frustrated antiferromagnet on the triangular lattice, as originally considered by Anderson. By a thorough single-crystal inelastic neutron scattering (INS) study, we demonstrate that nearest-neighbor RVB excitations account for the bulk of the spectral weight above 0.5 meV. This renders YbMgGaO4 the first experimental system where putative RVB correlations restricted to nearest neighbors are observed, and poses a fundamental question of how complex interactions on the triangular lattice conspire to form this unique many-body state.
Rock Magnetism, first published in 1997, is a comprehensive treatment of fine particle magnetism and the magnetic properties of rocks. Starting from atomic magnetism and magnetostatic principles, the authors explain why domains and micromagnetic structures form in ferromagnetic crystals and how these lead to magnetic memory in the form of thermal, chemical and other remanent magnetizations. The phenomenal stability of these magnetizations, providing a record of plate tectonic motions over millions of years, is explained by thermal activation theory. One chapter is devoted to practical tests of domain state and paleomagnetic stability; another deals with pseudo-single-domain magnetism. The final four chapters place magnetism in the context of igneous, sedimentary, metamorphic, and extraterrestrial rocks. This book will be of great value to graduate students and researchers in geophysics and geology, particularly in paleomagnetism and rock magnetism, as well as physicists and electrical engineers interested in fine-particle magnetism and magnetic recording.
Platelike high-quality NaYbS2 rhombohedral single crystals with lateral dimensions of a few mm have been grown and investigated in great detail by bulk methods such as magnetization and specific heat, but also by local probes such as nuclear magnetic resonance (NMR), electron-spin resonance (ESR), muon-spin relaxation (μSR), and inelastic neutron scattering over a wide field and temperature range. Our single-crystal studies clearly evidence a strongly anisotropic quasi-two-dimensional magnetism and an emerging spin-orbit entangled Jeff=12 state of Yb towards low temperatures together with an absence of long-range magnetic order down to 260 mK. In particular, the clear and narrow Yb ESR lines together with narrow Na23 NMR lines evidence an absence of inherent structural distortions in the system, which is in strong contrast to the related spin-liquid candidate YbMgGaO4 falling within the same space group R3¯m. This identifies NaYbS2 as a rather pure spin-12 triangular-lattice magnet and a putative quantum spin liquid.
The compounds A2Cu3O(SO4)3(A=Na,K) are characterized by copper hexamers which are weakly coupled along the b axis to realize one-dimensional antiferromagnetic chains below TN≈3K, whereas the interchain interactions along the a and c axes are negligible. We investigated the energy-level splittings of the copper hexamers by inelastic neutron scattering below and above TN. The eight lowest-lying hexamer states could be unambiguously assigned and parametrized in terms of a Heisenberg exchange Hamiltonian, providing direct experimental evidence for an S=1 triplet ground-state associated with the copper hexamers. Therefore, the compounds A2Cu3O(SO4)3 serve as cluster-based spin-1 antiferromagnets to support Haldane's conjecture that a gap appears in the excitation spectrum below TN, which was verified by inelastic neutron scattering.
Barlowite, Cu4(OH)6FBr, has attracted much attention as the parent compound of a new series of quantum spin-liquid candidates, ZnxCu4−x(OH)6FBr. While it is known to undergo a magnetic phase transition to a long-range ordered state at TN=15 K, there is still no consensus over either its nuclear or magnetic structures. Here, we use comprehensive, high-flux powder neutron diffraction studies on deuterated samples of barlowite to demonstrate that the only space group consistent with the observed nuclear and magnetic diffraction at low temperatures is the orthorhombic Pnma space group. We furthermore conclude that the magnetic intensity at T<TN is correctly described by the Pn′m′a magnetic space group, which crucially allows the ferromagnetic component observed in previous single-crystal and powder magnetization measurements. As such, the magnetic structure of barlowite resembles that of the related material clinoatacamite, Cu4(OH)6Cl2, the parent compound of the well-known quantum spin-liquid candidate hebertsmithite, ZnCu3(OH)6Cl2.
The spin-12 kagome antiferromagnet is an archetypal frustrated system predicted to host a variety of exotic magnetic states. We show using neutron scattering measurements that deuterated vesignieite BaCu3V2O8(OD)2, a fully stoichiometric S=1/2 kagome magnet with <1% lattice distortion, orders magnetically at TN=9 K into a multi-k coplanar variant of the predicted triple-k octahedral structure. We find that this structure is stabilized by a dominant antiferromagnetic third-neighbor exchange J3 with minor first- or second-neighbor exchanges. The spin-wave spectrum is well described by a J3-only model including a tiny symmetric exchange anisotropy.
Averievite, Cu5V2O10(CsCl), is an oxide mineral composed of Cu2+ kagome layers sandwiched by Cu2+−V5+ honeycomb layers. We have synthesized this oxide and investigated its properties from ab initio calculations along with susceptibility and specific heat measurements. The data indicate a Curie-Weiss temperature of 185 K as well as long-range magnetic order at 24 K due to the significant interlayer coupling from the honeycomb copper ions. This order is suppressed by substituting copper by isoelectronic zinc, suggesting that Zn-substituted averievite is a promising spin liquid candidate. A further proposed substitution that replaces V5+ by Ti4+ not only dopes the material but is predicted to give rise to a two-dimensional electronic structure featuring Dirac crossings. As such, averievite is an attractive platform for S=1/2 kagome physics with the potential for realizing novel electronic states.
The mineral barlowite, Cu$_4$(OH)$_6$FBr, has been the focus of recent attention due to the possibility of substituting the interlayer Cu$^{2+}$ site with non-magnetic ions to develop new quantum spin liquid materials. We re-examine previous methods of synthesizing barlowite and describe a novel hydrothermal synthesis method that produces large single crystals of barlowite and Zn-substituted barlowite (Cu$_3$Zn$_x$Cu$_{1-x}$(OH)$_6$FBr). The two synthesis techniques yield barlowite with indistinguishable crystal structures and spectroscopic properties at room temperature; however, the magnetic ordering temperatures differ by 4 K and the thermodynamic properties are clearly different. The dependence of properties upon synthetic conditions implies that the defect chemistry of barlowite and related materials is complex and significant. Zn-substituted barlowite exhibits a lack of magnetic order down to T = 2 K, characteristic of a quantum spin liquid, and we provide a synthetic route towards producing large crystals suitable for neutron scattering.
We present a combination of first-principles and experimental results regarding the structural and magnetic properties of olivine-type LiFePO4 under pressure. Our investigations indicate that the starting Pbnm phase of LiFePO4 persists up to 70 GPa. Further compression leads to an isostructural transition in the pressure range of 70–75 GPa, inconsistent with a former theoretical study. Considering our first-principles prediction for a high-spin to low-spin transition of Fe2+ close to 72 GPa, we attribute the experimentally observed isostructural transition to a change in the spin state of Fe2+ in
LiFePO4. Compared to relevant Fe-bearing minerals, LiFePO4 exhibits the largest onset pressure for a pressure-induced spin state transition.
A series of MnxFe1-xNb2O6 compounds (0⩽x⩽1) is investigated by both X-ray and neutron powder diffraction, as well as specific-heat and magnetic measurements. The samples present orthorhombic Pbcn crystal symmetry, and exhibit weakly coupled magnetic chains. These chains are of Heisenberg type (weak anisotropy) on the Mn-rich side, and Ising-like (strong anisotropy) on the Fe-rich side. Except for 100% Fe (x=0), which has weakly-interacting ferromagnetic Ising chains, a negative Curie-Weiss temperature is obtained from the magnetic susceptibility, indicating dominant antiferromagnetic interactions. At the lowest probed temperature, View the MathML source, true long-range magnetic order is only observed for x=1, 0.8, and 0. Although the ordering is globally antiferromagnetic in all cases, the first two are characterized by a two-sublattice structure with propagation vector k=(0,0,0), while the latter presents alternatingly oriented ferromagnetic chains described by View the MathML source. For other compositions, short-range magnetic correlations are extracted from diffuse neutron-scattering data.
The crystal structure of the mineral boleite contains clusters of 24 S=1/2Cu2+ ions that have the shape of a truncated cube formed of eight trimers connected by edges. Susceptibility measurements and exact diagonalization calculations suggest that there are strong antiferromagnetic intratrimer interactions, such that effective S=1/2 degrees of freedom emerge on the trimers below T≲100 K. Weaker intertrimer interactions lead to the formation of a singlet ground state for these effective spins at T≲5 K. The clusters in boleite offer a situation similar to single molecule magnetism, accessible to both experiment and numerics, in which the interplay of quantum spins, geometric frustration, spin entanglement, and mesoscopic system size can be studied.
Brownmillerite Ca2Fe2O5(CFO) exhibits a magnetic transition at TN=~730 K. Many studies have reported the magnetic properties of CFO. However, the magnetic structure of CFO is still debated, i.e., whether the magnetic ordering is pure antiferromagnetic or weakly ferromagnetic, which originated from canted magnetic moments. In addition, the reason for the CFO showing large magnetoresistance is still unclear. This study attempts to address the unresolved issues stated above by multiple investigations on the crystal structure, magnetization, and Mössbauer parameters. Based on the results of the investigation, we conclude that the CFO is not purely antiferromagnetic but weakly ferromagnetic. That is the reason for the disappearance of the spontaneous magnetization at the magnetic critical temperature TN. The Mössbauer spectroscopy showed that the magnetic moment is slightly canted against the a-direction, resulting in the presence of a net magnetic moment along the c-direction under space group of Pnma. A reason for the canted magnetic moments is due to the presence of the Dzyalosinskii–Moriya (DM) interaction. The electric field gradient (EFG) refined from the Mössbauer spectroscopies investigated at 287 K is larger than that at 750 K, which is higher than TN. This suggests that the EFG changes below TN. A local electric polarization induced by the DM interaction is a possible reason for the change in the EFG. As a result, strong correlations between the magnetic ordering and the electrical properties appear in the CFO. The Arrhenius plot of the total electrical conductivity showed a kink at TN, which is one of these strong correlations.
The structural and magnetic properties of siderite FeCO3 have been studied by means of neutron powder diffraction at pressures up to 7.5 GPa and first-principles theoretical calculations. The lattice compression in the rhombohedral calcite-type structure is dominated by the reduction of the Fe-O bonds, while the changes of the C-O bonds are much less pronounced. The Néel temperature of the antiferromagnetic (AFM) ground state increases substantially under pressure with a coefficient dTN/dP=1.8K/GPa, which is about 1.5 times larger in comparison with those predicted by the empirical Bloch rule. The ab initio calculations were performed in the framework of the density functional theory including Hubbard-U correction. The calculated structural parameters and Néel temperature as functions of pressure provide a reasonable agreement with the experimental results. The analysis of the density of electronic states points toward increased covalent bonding between the Fe and O atoms upon pressure, giving rise to unexpectedly large pressure coefficient of the Néel temperature and reduced ordered magnetic moments of Fe atoms.
Specific heat C, thermal conductivity κ, dielectric permittivity ε, electric polarization P, and Raman scattering experiments are performed on Cu3Bi(SeO3)2O2X (X=Br,Cl) single crystals. The Cl compound undergoes a structural phase transition at T*∼115K evident in C(T), ɛ(T), and κ(T) and accompanied by the appearance of unique phonon lines in Raman scattering. No evident structural changes are detected in the Br compound. At T<T*, a very weak polarization loop with a P∥c axis is observed in the Cl compound. Both compounds order antiferromagnetically at comparable temperatures TN∼25K marked by sharp λ-type singularities. For T<TN, an intensive mode of magnetic origin appears in both compounds. At the lowest temperatures, the energy of this mode is in good agreement with both the magnon excitation observed in infrared spectroscopy and the spin gap found recently in inelastic neutron scattering of the Cl compound.
We present susceptibility measurements on the natural mineral atacamite, Cu2Cl(OH)3, for the first time along the three crystallographic axes. Further, we have carried out an elastic neutron diffraction experiment which shows that the symmetry of the magnetic ground state of atacamite is described by a propagation vector q=(1/2 0 1/2).
The g factors for Cu²⁺ in meta-zeunerite (Cu(UO2)2(AsO4)2·3H2O), kroehnkite (Na2Cu(SO4)2·2H2O), copper benzoate (Cu(PhCO2)2·3H2O) and diaboleite (Pb2Cu(OH)4Cl2) of the tetragonal phase are uniformly treated by high order perturbation formulas for 3d⁹ ions in tetragonally elongated octahedra. The calculation results are in good agreement with the observed values and systematically analyzed in view of the local structures around Cu²⁺. The g anisotropies Δg (= g‖−g⊥) are largely ascribed to the local tetragonal elongations of the Cu²⁺ sites, characterized by the relative elongation ratios (R‖−R⊥)/R̅ ≈ 19%, 21%, 27% and 30% for metazeunertie, kroehnkite, copper benzoate and diaboletie, respectively. The anomalous valley (minimum) of relative g anisotropy for copper benzoate is attributed to the modification of the Cu²⁺ electronic states due to the phenyl ring. The ligand orbital contributions are found to be significant due to covalency, and should be taken into account. The present study would be helpful to the unified investigations of structures and properties of the copper oxygen compounds.
The ground state of the quantum kagome antiferromagnet Zn-brochantite, ZnCu$_3$(OH)$_6$SO$_4$, which is one of only a few known spin-liquid (SL) realizations in two or three dimensions, has been described as a gapless SL with a spinon Fermi surface. Employing nuclear magnetic resonance in a broad magnetic-field range down to millikelvin temperatures, we show that in applied magnetic fields this enigmatic state is intrinsically unstable against a SL with a full or a partial gap. A similar instability of the gapless Fermi-surface SL was previously encountered in an organic triangular-lattice antiferromagnet, suggesting a common destabilization mechanism that most likely arises from spinon pairing. A salient property of this instability is that an infinitesimal field suffices to induce it, as predicted theoretically for some other types of gapless SL's.
We overview physical effects of exchange frustration and quantum spin fluctuations in (quasi-) two dimensional (2D) quantum magnets (S=1/2) with square, rectangular and triangular structure. Our discussion is based on the J1-J2 type frustrated exchange model and its generalizations. These models are closely related and allow to tune between different phases, magnetically ordered as well as more exotic nonmagnetic quantum phases by changing only one or two control parameters. We survey ground state properties like magnetization, saturation fields, ordered moment and structure factor in the full phase diagram as obtained from numerical exact diagonalization computations and analytical linear spin wave theory. We also review finite temperature properties like susceptibility, specific heat and magnetocaloric effect using the finite temperature Lanczos method. This method is powerful to determine the exchange parameters and g-factors from experimental results. We focus mostly on the observable physical frustration effects in magnetic phases where plenty of quasi-2D material examples exist to identify the influence of quantum fluctuations on magnetism.
A variety of copper tellurium oxide minerals are known, and many of them exhibit either unusual forms of magnetism, or potentially novel spin liquid behavior. Here, I review a number of the more interesting materials with a focus on their crystalline symmetry and, if known, the nature of their magnetism. Many of these exist (so far) in mineral form only, and most have yet to have their magnetic properties studied. This means a largely unexplored space of materials awaits our exploration.
Single crystals are indispensable for understanding the fundamental properties of materials, although obtaining them are often challenging. To investigate the magnetic properties of a kagome-lattice antiferromagnet, we have performed a topochemical crystal transformation from a copper mineral volborthite with a distorted kagome lattice into another copper mineral vesignieite with an almost perfect kagome lattice. A millimeter-sized crystal of vesignieite, which is difficult to prepare via direct chemical reactions, has been successfully obtained. Magnetization measurements on the crystals reveal a unique magnetic order with weak-ferromagnetic moments lying within the kagome plane and successive anomalies in the magnetization curve, which would give important information on the magnetic order of the kagome-lattice antiferromagnet. The present results demonstrate a novel route via the topochemical crystal transformation in preparing a hard-to-obtain crystal.
We report a single-crystal neutron diffraction and inelastic neutron scattering study on the spin 1/2 cuprate Cu3Bi(SeO3)2O2Cl, complemented by dielectric and electric polarization measurements. The study clarifies a number of open issues concerning this complex material, whose frustrated interactions on a kagomelike lattice, combined with Dzyaloshinskii-Moriya interactions, are expected to stabilize an exotic canted antiferromagnetic order. In particular, we determine the nature of the structural transition occurring at 115 K, the magnetic structure below 25 K resolved in the updated space group, and the microscopic ingredients at the origin of this magnetic arrangement. This was achieved by an analysis of the measured gapped spin waves, which signifies the need for an unexpected and significant anisotropic exchange beyond the proposed Dzyaloshinskii-Moriya interactions. Finally, we discuss the multiferroic properties of this material with respect to the space group symmetries.
We propose that resonant inelastic X-ray scattering (RIXS) is an effective probe of the fractionalized excitations in three-dimensional (3D) Kitaev spin liquids. While the non-spin-conserving RIXS responses are dominated by the gauge-flux excitations and reproduce the inelastic-neutron-scattering response, the spin-conserving (SC) RIXS response picks up the Majorana-fermion excitations and detects whether they are gapless at Weyl points, nodal lines, or Fermi surfaces. As a signature of symmetry fractionalization, the SC RIXS response is suppressed around the $\Gamma$ point. On a technical level, we calculate the exact SC RIXS responses of the Kitaev models on the hyperhoneycomb, stripyhoneycomb, hyperhexagon, and hyperoctagon lattices, arguing that our main results also apply to generic 3D Kitaev spin liquids beyond these exactly solvable models.