Fig 3- - uploaded by M. Baenitz
Content may be subject to copyright.
Phase diagram of the dioptase magnetic sublattice as obtained by Quantum Monte Carlo simulations. The lines are guides to the eye. The magnetic coupling constants are J1,2 = J(1 ± δ) for inter/intra-chain couplings J1/J2. At δc ≈ 0.3 a quantum phase transition occurs. The Neél temperature of the antiferromagnetically ordered phase for δ < δc is give by the left y-axis. The antiferromagnetic order is of A-B type, with a doubling of the unit-cell along c. For δ > δc a gap, given by the right y-axis, opens in the magnetic excitation spectrum and the state is a quantum spin-liquid.
Source publication
The study of quantum phase transitions, which are zero-temperature phase transitions between distinct states of matter, is of current interest in research since it allows for a description of low-temperature properties based on universal relations. Here we show that the crystal green dioptase Cu_6Si_6O_18 . 6H_2O, known to the ancient Roman as the...
Similar publications
PACS. 71.20.Be-Transition metals and alloys. PACS. 73.43.Nq-Quantum phase transitions. PACS. 75.10.Jm-Quantized spin models. Abstract.-The study of quantum phase transitions [1], which are zero-temperature phase transitions between distinct states of matter, is of current interest in research since it allows for a description of low-temperature pro...
We consider a buckled quantum spin Hall insulator (QSHI), such as silicene, proximity-coupled to a conventional spin-singlet, $s$-wave superconductor. Even limiting the discussion to the disorder-robust $s$-wave pairing symmetry, we find both odd-frequency ($\omega$), spin-singlet and spin-triplet pair amplitudes and where both preserve time-revers...
Citations
... The mineral is a popular collector's piece due to the emerald-green color, the resistance against chemicals and its Mohs hardness of 5. We reported previously on magnetic property and quantum critical behaviour in the dioptase lattice [18] [19] and assigned, for the first time correctly, UV-VIS spectra [20]. Synthesis attempt were initiated by the easy synthesis of a similar lead germanate in the form of nanorods with the formula Pb 6 (Ge 6 O 18 )·2H 2 O [21] and the crystal structure determination of the hydrated and dehydrated phase [22] [23]. ...
The microbially supported synthesis of • 6 (dioptase) by Rao and Krishna is very remarkable and opens further technological applications, when using the nano-crystalline decomposition product CuSiO 3 (orthorhombic) as an effective catalyst. The role of copper silicate nanotubes is acknowledged as catalysts respectively possible LED materials. A found structural relationship between chrysocolla and synthetic fibrous CuSiO 3 may show the way to solve the crystal structure of chrysocolla.
... They are ordered AFM in the chains and ferromagnetically (FM) between them ( Fig. 1) [9]. This is in agreement with the theoretical work of Janson et al. [16] and the inelastic neutron scattering report of Podlesnyak et al. [19], which indicate J c > 0 and J ab < 0. It is, however, in disagreement with the Quantum Monte Carlo calculations of Gros and coworkers who obtained only AFM couplings [20]. Nonetheless, even if the right sign was obtained, the magnitudes of the derived exchange constants (as well as the ratio between them) vary significantly. ...
... The magnetic properties of green dioptase have been reported by a number of authors [14,[16][17][18]20]. We have performed bulk characterization of our sample, and the results agree with those reported in Refs. ...
... We have performed bulk characterization of our sample, and the results agree with those reported in Refs. [16,20]. Figure 4 displays the temperature dependence of the static spin susceptibility M /B measured in magnetic fields of 0.1 and 7 T applied both parallel and perpendicular to the c-axis. ...
The high-field magnetic properties and magnetic order of the gem mineral green dioptase Cu$_6[$Si$_6$O$_{18}]\cdot 6$H$_2$O have been studied by means of single-crystal neutron diffraction in magnetic fields up to $21~$T and magnetization measurements up to $30~$T. In zero field, the Cu$^{2+}$-moments in the antiferromagnetic chains are oriented along the $c$-axis with a small off-axis tilt. For a field applied parallel to the $c$-axis, the magnetization shows a spin-flop-like transition at $B^*=12.2~$T at $1.5~$K. Neutron diffraction experiments show a smooth behavior in the intensities of the magnetic reflections without any change in the periodicity of the magnetic structure. Bulk and microscopic observations are well described by a model of ferromagnetically coupled antiferromagnetic $XXZ$ spin-$\frac{1}{2}$ chains, taking into account a change of the local easy-axis direction. We demonstrate that the magnetic structure evolves smoothly from a deformed N\'eel state at low fields to a deformed spin-flop state in a high field via a strong crossover around $B^*$. The results are generalized for different values of interchain coupling and spin anisotropy.
... ESR measurements showed a shift in the resonance frequency at 47006-p1 50 K where there was a maximum in the magnetic susceptibility, but there was the clear onset of an antiferromagnetic ground state with an energy gap of 350 GHz (∼17 K) [5]. Recent reports have, however, suggested that green dioptase is an ideal candidate to show quantum critical behaviour since the inter-and intra-chain exchange energies may be similar leading to frustration and a dynamic magnetic ground state [6]. Further work conducted suggested that strong quantum fluctuations were present in the broad maximum in the magnetic susceptibility but theoretical models suggested that the system is 3D and not frustrated [7]. ...
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 rhombohedral title compound Cu 6 (Ge,Si) 6 O 18 ·6H 2 O represents a hexacyclo-germanate (silicate) that contains copper-oxygen spiral chains along the c-axis, which are connected (intra-chain) by edgesharing dimers (Figure 1). This structure is interesting because it allows for a quantum phase transition between an anti-ferromagnetically ordered state and a quantum spin liquid [8]. Large quantum fluctuations in green dioptase have been described [9]. ...
Low-dimensional quantum spin systems with the Cu2+ central ion are still in the focus of experimental and theoretical research. Here is reported on growth of mm-sized single-crystals of the low-dimensional S = ½ spin compound Cu6(Ge,Si)6O18•6H2O by a diffusion technique in aqueous solution. A route to form Si-rich crystals down to possible dioptase, the pure silicate, is discussed. Motivated by previously reported incorrect assignments of UV-VIS spectra, the assignment of dd excitations from such spectra of the hexahydrate and the fully dehydrated compound is proposed in comparison to dioptase and selected Cu(II) oxo-compounds using bond strength considerations. Non-doped cuprates as layer compounds show higher excitation energies than the title compound. However, when the antiferromagnetic interaction energy as Jz•ln(2) is taken into account for cuprates, a single linear relationship between the Dqe excitation energy and equatorial Cu(II)-O bond strength is confirmed for all compounds. A linear representation is also confirmed between 2A1g energies and a function of axial and equatorial Cu-O bond distances if auxiliary axial bonds are used for four-coordinated compounds. The quotient Dt/Ds of experimental orbital energies deviating from the general trend to smaller values indicates the existence of H2O respectively Cl1- axial ligands in comparison to oxo-ligands, whereas larger Dt/Dqe values indicate missing axial bonds. The quotient of the excitation energy 2A1g by 2•2Eg-2B2g allows to check for correctness of the assignment and to distinguish between axial oxo-ligands and others like H2O or Cl1-.
... The rhombohedral title compound Cu 6 (Ge,Si) 6 O 18 ·6H 2 O represents a hexacyclo-germanate (silicate) that contains copper-oxygen spiral chains along the c-axis, which are connected (intra-chain) by edgesharing dimers (Figure 1). This structure is interesting because it allows for a quantum phase transition between an anti-ferromagnetically ordered state and a quantum spin liquid [9]. Large quantum fluctuations in green dioptase have been described [10]. ...
... Finally, the assignment of the dd excitations can be compared with results of EPR measurements. For 3d 9 ions in (nearly) tetragonal ligand symmetry one can apply the following two formulas for the principal components g || and g ﬩ , if the ground state is 2 B 1g : ...
It is reported on growth of mm-sized single-crystals of the low-dimensional S = ½ spin compound Cu6(Ge,Si)6O18•6H2O by a diffusion technique in aqueous solution. A route to form Si-rich crystals down to possibly dioptase, the pure silicate, is discussed. Further, the assignment of dd excitations from UV-VIS spectra of the hexahydrate and the fully dehydrated compound is proposed in comparison to dioptase and selected Cu(II) oxo-compounds using bond strength considerations. Non-doped cuprates as layer compounds show higher excitations energies than the title compound. However, when the antiferromagnetic interaction energy as Jz•ln(2) is taken into account for cuprates, a single linear relationship between the Dqe excitation energy and equatorial Cu(II)-O bond strength is confirmed for all compounds. A linear representation is also confirmed between 2A1g energies and a function of axial and equatorial Cu-O bond distances. The quotient Dt/Ds of experimental orbital energies deviating from the general trend to smaller values indicates the existence of H2O respectively Cl1- axial ligands in comparison to oxo-ligands, whereas larger Dt/Dqe values indicate missing axial bonds. The quotient of the excitation energy 2A1g by 2•2Eg-2B2g allows to check for correctness of the assignment and to distinguish between axial oxo-ligands and others like H2O or Cl1-.
... It is isotypic to CuGeO 3 but does not show the spin-Peierls transition, instead an antiferromagnetic ordering below T N = 7.9 K (Baenitz et al., 2000 [6]; Wolfram et al., 2004 [7]). Dioptase itself is interesting because it allows for a quantum phase transition between an anti-ferromagnetically ordered state and a quantum spin liquid (Gros et al., 2002) [8]. Also, the germanate analogue, Cu 6 Ge 6 O 18 ·6H 2 O (Brand and Otto, 1997 [9]), is recently the object of detailed magnetic and structural investigations (Law et al., 2010) [10]. ...
... It is isotypic to CuGeO 3 but does not show the spin-Peierls transition, instead an antiferromagnetic ordering below T N = 7.9 K (Baenitz et al., 2000 [6]; Wolfram et al., 2004 [7]). Dioptase itself is interesting because it allows for a quantum phase transition between an anti-ferromagnetically ordered state and a quantum spin liquid (Gros et al., 2002) [8]. Also, the germanate analogue, Cu 6 Ge 6 O 18 ·6H 2 O (Brand and Otto, 1997 [9]), is recently the object of detailed magnetic and structural investigations (Law et al., 2010) [10]. ...
IIt is reported on a new cost-efficient ambient pressure synthesis of the Vesuvius mineral litidionite, KNaCuSi4O10, via a two-step synthesis route. X-ray powder data were recorded with our IP double-radius Guinier diffractometer. The lattice parameters of the triclinic compound with space group P¯1 are a = 9.7971(12) Å, b = 8.0149
(8) Å, c = 6.9679(7) Å, α = 114.027(4)°, β = 99.603(6)°, and γ = 105.678(6)°. From the X-ray powder data, one obtains by the Rietveld method structural parameters in agreement with those previously determined on single crystals of the mineral. In addition, a first UV-VIS spectrum of the light blue compound is presented, and antiferromagnetic super-exchange is discussed. The d-d excitations were assigned via bond strengths calculations and compared to excitations of similar compounds like dioptase. Some possible applications of the weather-proof synthetic pigment were indicated
... Each Cu 2+ ion has two Cu nearest neighbors (NN) in a helical chain along the c axis and only one Cu in-plane neighbor forming a threefold spin-1 2 network. Two exchange interactions thus have major importance and determine the magnetic structure, namely, NN intrachain coupling J c along the spiral chain and NN interchain coupling J ab which forms Cu dimers in the ab plane ( Fig. 1) [10,11]. Depending on the J ab /J c ratio, different kinds of the magnetic ordering can be expected, going from one-dimensional (1D) helical chainlike ordering for |J c | |J ab | to magnetic dimer * Corresponding author: podlesnyakaa@ornl.gov ...
... These conclusions were supported by extended Hückel tight-binding calculations which found that black dioptase is an S = 1 2 uniform AFM chain system in which the interchain spin exchange is weaker than the intrachain exchange by two orders of magnitude [12]. On the other hand, Gros and co-workers proposed that for fully hydrated green dioptase both J c and J ab are positive, corresponding to AFM coupling within and between the chains [10]. Their quantum Monte Carlo calculations predict that the system is close to a quantum critical point (QCP) between an AFM ordered state (J ab /J c < 1.86) and a quantum spin liquid (J ab /J c > 1.86). ...
... Our study proves that the magnetic ground state features spiral AFM spin chains along the hexagonal c axis with FM interchain coupling, in agreement with Refs. [9,11], and it disagrees with the picture of green dioptase as an antiferromagnet close to a quantum critical point, as suggested by Ref. [10]. ...
In this paper, we report inelastic neutron scattering measurements of the magnetic excitations of green dioptase Cu6[Si6O18]·6H2O. The observed spectrum contains two magnetic modes and a prominent spin gap that is consistent with the ordered ground state of Cu moments coupled antiferromagnetically in spiral chains along the c axis and ferromagnetically in ab planes on the hexagonal cell. The data are in excellent agreement with a spin-12 Hamiltonian that includes antiferromagnetic nearest-neighbor intrachain coupling Jc=10.6(1) meV, ferromagnetic interchain coupling Jab=−1.2(1) meV, and exchange anisotropy ΔJc=0.14(1) meV. We calculated the sublattice magnetization to be strongly reduced, ∼0.39μB. This appears compatible with a reduced Néel temperature, TN=14.5K≪Jc, and can be explained by a presence of quantum spin fluctuations.
... This projection operation does not keep time reversal symmetry. For example, the exact spin liquid we established on 'Cu'-sublattice of crystal green dioptase, which is the crystal structure of a material Cu 6 Si 6 O 3 · 6H 2 O [24], projects out the very two dimensional chiral spin model constructed in Ref. [13]. ...
... The triangle helix model is established on a three dimensional lattice which exist in nature. The Cu atoms in dioptase Cu 6 Si 6 O 3 · 6H 2 O construct the exact triangle helix lattice, Cu-atoms form chiral chains along z-axes and project a honeycomb configuration to the X − Y plane [24]. ...
We established a large class of exactly soluble spin liquids and chiral spin liquids on three-dimensional helix lattices by introducing Kitaev-type's spin coupling. In the chiral spin liquids, exact stable ground states with spontaneous breaking of the time reversal symmetry are found. The fractionalized loop excitations in both the spin and chiral spin liquids obey non-Abelian statistics. We characterize this kind of statistics by non-Abelian Berry phase and quantum algebra relation. The topological correlation of loops is independent of local order parameter and it measures the intrinsic global quantum entanglement of degenerate ground states.
... By contrast, the spin half HAFM on the star lattice has not been considered in the literature so far, nor is a physical realization currently known. However, we mention that a projection of the three-dimensional non-frustrated magnetic compound green dioptase Cu 6 Si 6 O 18 · 6H 2 O has the shape of the star lattice [124]. ...
It is known from the Mermin-Wagner theorem that magnetic long-range order can exist in two dimensions only at zero temperature, but even then it can still be destroyed e.g. by quantum fluctuations or geometric frustration. In this context, we review ground-state features of the s=1/2 Heisenberg antiferromagnet on two-dimensional lattices. In order to discuss the interplay of lattice topology and quantum fluctuations we focus on the 11 two-dimensional uniform Archimedean lattices which include e.g. the square, triangular and kagomé lattice. The ground state of the spin-1/2 Heisenberg antiferromagnet is likely to be semi-classically ordered in most cases. However, the interplay of geometric frustration and quantum fluctuations gives rise to a quantum paramagnetic ground state without semi-classical long-range order on two lattices which are precisely those among the 11 uniform Archimedean with a highly degenerate ground state in the classical limit s→∞. The first one is the famous kagomé lattice where many low-lying singlet excitations are known to arise in the spin gap. The second lattice, called star lattice, is a new example for a quantum paramagnet and has a clear gap to all excitations.
Modification of certain bonds leads to quantum phase transitions which are also discussed briefly. Furthermore, we discuss the magnetization process of the Heisenberg antiferromagnet on the 11 Archimedean lattices, focusing on anomalies like plateaus and a magnetization jump just below the saturation field. As an illustration we discuss the two-dimensional Shastry-Sutherland model which is used to describe SrCu2(BO3)2.
The high-field magnetic properties and magnetic order of the gem mineral green dioptase Cu6[Si6O18]·6H2O have been studied by means of single-crystal neutron diffraction in magnetic fields up to 21 T and magnetization measurements up to 30 T. In zero field, the Cu2+ moments in the antiferromagnetic chains are oriented along the c axis with a small off-axis tilt. For a field applied parallel to the c axis, the magnetization shows a spin-flop-like transition at B*=12.2 T at 1.5 K. Neutron diffraction experiments show a smooth behavior in the intensities of the magnetic reflections without any change in the periodicity of the magnetic structure. Bulk and microscopic observations are well described by a model of ferromagnetically coupled antiferromagnetic XXZ spin-12 chains, taking into account a change of the local easy-axis direction. We demonstrate that the magnetic structure evolves smoothly from a deformed Néel state at low fields to a deformed spin-flop state in a high field via a strong crossover around B*. The results are generalized for different values of interchain coupling and spin anisotropy.
