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Spin-Driven Bond Order in a 1/5-Magnetization Plateau Phase in a Triangular Lattice Antiferromagnet CuFeO2
Abstract
We have investigated spin-wave excitations in a magnetic-field-induced
1/5-magnetization plateau phase in a triangular lattice antiferromagnet CuFeO2
(CFO), by means of inelastic neutron scattering measurements under applied
magnetic fields of up to 13.4 T. Comparing the observed spectra with the
calculations in which spin-lattice coupling effects for the nearest neighbor
exchange interactions are taken into account, we have determined the
Hamiltonian parameters in the field-induced 1/5- plateau phase, which directly
show that CFO exhibits a bond order associated with the magnetic structure in
this phase.
... The magnetic point group for these phases is 2/m1′. The difference in the canting angles between ICM1 and CM1 phases can originate from the different single ion anisotropy (easy axis is along the c hxaxis), which varying with chemical substitution, magnetic field, or temperature [47][48][49][50] . ...
The analysis of three-dimensional neutron spin polarization vectors, using a technique referred to as spherical neutron polarimetry (SNP), is a very powerful means of determining complex magnetic structures in magnetic materials. However, the requirement to maintain neutrons in a highly polarized state has made it difficult to use this technique in conjunction with extreme experimental conditions. We have developed a high pressure cell made completely of nonmagnetic materials and having no effect on neutron polarizations. Herein, we report the first SNP analyses under high pressure up to 4.0 GPa in the magnetoelectric multiferroic delafossite CuFeO2. This study also determined the complex spiral magnetic structures in these pressure-induced phases, by measuring the full neutron polarization matrix. The results presented herein demonstrate that the SNP measurements are feasible under high pressure conditions, and that this method is a useful approach to study pressure-induced physical phenomena.
... Furthermore, the compensation effect does promote the relative role of next-nearest-neighbors (nnn) Fe-O-Fe and next-next-nearest-neighbors (nnnn) Fe-O-O-Fe interactions ( figure 1(b)). Another characteristic feature of the topology of exchangeinteractions in delafossites AFeO 2 is that, different from the most part of ferrites, an O 2− ion belongs to three Fe-O-Fe bonds that makes the exchange coupling to be extremely sensitive to oxygen displacements and its electric polarization thus providing paths for understanding the exotic spin-lattice coupling phenomena, specifically spin-driven bond order, in geometrically frustrated magnets [15]. The comprehensive analysis of the isotropic superexchange coupling in delafossites has to take into account a strong electric polarization of the intermediate oxygen ions. ...
We report new results of a <sup>57</sup>Fe Mössbauer study of hyperfine magnetic interactions in the layered multiferroic 3 R -AgFeO<sub>2</sub> demonstrating two magnetic phase transitions at T <sub>N1</sub> and T <sub>N2</sub>. The asymptotic value β * ≅ 0.34 for the critical exponent obtained from the temperature dependence of the hyperfine field H <sub>hf</sub>( T ) at <sup>57</sup>Fe the nuclei below T <sub>N1</sub> ≅ 14 K indicates that 3 R -AgFeO<sub>2</sub> shows quasi-three-dimensional critical behavior. The spectra just above T <sub>N1</sub> ( T <sub>N1</sub> < T < T * ≅ 41 K) demonstrate a relaxation behavior due to critical spin fluctuations which indicates the occurrence of short-range correlations. At the intermediate temperature range, T <sub>N2</sub> < T < T <sub>N1</sub>, the <sup>57</sup>Fe Mössbauer spectra are described in terms of collinear spin-density-waves (SDW) with the inclusion of many high-order harmonics, indicating that the real magnetic structure of the ferrite appears to be more complicated than a pure sinusoidally modulated SDW. Below T < T <sub>N2</sub> ≅ 9 K, the hyperfine field H <sub>hf</sub> reveals a large spatial anisotropy (Δ H <sub>anis</sub> ≅ 30 kOe) which is related with a local intra-cluster (FeO<sub>6</sub>) spin-dipole term that implies a conventional contribution of the polarized oxygen ions. We proposed a simple two-parametric formula to describe the dependence of Δ H <sub>anis</sub> on the distortions of the (FeO<sub>6</sub>) clusters. Analysis of different mechanisms of spin and hyperfine interactions in 3 R -AgFeO<sub>2</sub> and its structural analogue CuFeO<sub>2</sub> points to a specific role played by the topology of the exchange coupling and the oxygen polarization in the delafossite-like structures.
... A ferroelectric polarization along the hexagonal [1 1 0] axis is induced by magnetic field in the ferroelectric-incommensurate (FEIC) phase (7 T H 13 T) (see figure 3(c)) [18]. The mechanism regarding ferroelectric polarization has been extensively studied by bulk measurements [30][31][32], neutron scattering [19,[33][34][35][36][37][38][39][40][41][42][43], synchrotron x-ray diffraction [44][45][46][47] Terahertz spectroscopy [48], electron spin resonance [49][50][51], Mössbauer experiments [52] and some theoretical work [53][54][55][56][57][58][59][60][61][62][63], since the discovery of ferroelectric polarization in CuFeO 2 . ...
Coupling between noncollinear magnetic ordering and ferroelectricicty in magnetoelectric multiferroics has been extensively studied in the last decade. Delafossite family compounds with triangular lattice structure provide a great opportunity to study the coupling between spin and electric dipole in multiferroics due to the variety of magnetic phases with different symmetry. This review introduces the magnetic and ferroelectric phase transitions in delafossite ferrites, CuFe1−xXxO2 (X = Al, Ga), AgFeO2 and the related compound α–NaFeO2. In CuFeO2, the ferroelectric phase appears under a magnetic field or chemical substitution. The proper screw magnetic ordering with the magnetic point group 21', which has been determined by detailed analysis in neutron diffraction experiments, induces the ferroelectric polarization along the monoclinic b axis in CuFeO2. The cycloidal magnetic orderings are realized in AgFeO2 and α–NaFeO2, which are of the point group m1' allowing polarization in the ac plane. The emergence of ferroelectric polarization can be explained by both the extended inverse Dzyaloshinsky–Moriya effect and the d − p hybridization mechanism. These mechanisms are supported by experimental evidence in CuFe1−xGaxO2. The polarized neutron diffraction experiment demonstrated one-to-one correspondence between ferroelectric polarization and spin helicity, . The incommensurate orbital ordering with wave vector, observed by the soft x-ray resonant diffraction experiment, proved that the spin–orbit interaction ties spin and orbital orders to each other, playing a crucial role for the emergence of ferroelectricity in CuFe1−xGaxO2.
We have performed high–pressure neutron diffraction studies on the layered oxide, Ca2Mn3O8. Studies up to approximately 6GPa at temperatures of 120 and 290K demonstrate that there are no structural phase transitions within this pressure range. Fits of the unit–cell volume to a Birch-Murngahan equation of state gives values for the bulk modulus of 137(2)GPa and 130(2)GPa at temperatures of 290K and 120K respectively possibly suggesting that Ca2Mn3O8 is more compressible at lower temperature. Furthermore, compression along the principal axes are anisotropic on the local scale. Comparison of individual bond lengths and bond angle environments further demonstrate that compression is complex and likely results in a shearing of the layers.
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.
We performed magnetic susceptibility, dielectric constant, neutron-diffraction, and synchrotron radiation x-ray diffraction measurements on a spin-lattice coupling system CuFeO2 under applied uniaxial pressure p up to 600 MPa. We found that the phase-transition temperature TN1 from the paramagnetic phase to the partially disordered phase increases by as much as 5 K from the original TN1≃14K under applied p of 600 MPa, and that the lattice constant bm of CuFeO2 changes significantly. In contrast, the value of q0, which is the magnetic modulation wave number at TN1 and which should reflect the ratios of the exchange coupling constants, is not changed, even by applied p of 600 MPa. Based on these results, we show that an explanation using only the exchange striction effect is not suitable for the magnetic phase transition in CuFeO2. These results suggest that a lattice degree of freedom via a spin-lattice coupling is indispensable for the determination of the magnetic properties of CuFeO2. A dielectric anomaly under applied p of 600 MPa is also briefly discussed.
The HORACE suite of programs has been developed to work with large multiple-measurement data sets collected from time-of-flight neutron spectrometers equipped with arrays of position-sensitive detectors. The software allows exploratory studies of the four dimensions of reciprocal space and excitation energy to be undertaken, enabling multi-dimensional subsets to be visualized, algebraically manipulated, and models for the scattering to simulated or fitted to the data. The software is designed to be an extensible framework, thus allowing user-customized operations to be performed on the data. Examples of the use of its features are given for measurements exploring the spin waves of the simple antiferromagnet RbMnF$_{3}$ and ferromagnetic iron, and the phonons in URu$_{2}$Si$_{2}$.
Cu5(VO4)2(OH)4 (turanite) is a layered compound, exhibiting a copper(ii) oxide layer in the [0 1 1] plane composed of edge-sharing CuO6 octahedra. Each Cu-O layer is further separated by VO4 tetrahedra. Closer scrutiny found that the copper(ii) oxide layer in the compound represents a totally new geometrically-frustrated lattice, a 1/6 depleted triangular lattice. More specifically, the spin network in the [0 1 1] plane is formed by the alternate ranking of triangular and honeycomb strips. Magnetic measurements show that the Cu5(VO4)2(OH)4 behaves as a spin-1/2 ferrimagnet with a Tc = ∼4.5 K. It exhibits an unusual 1/5 magnetization plateau arising from the competition between antiferromagnetic and ferromagnetic interactions caused by the strong frustration. The possible spin-arrangements are also suggested.
The pressure effect on the frustrated magnetic system CuFeO2 exhibiting multiferroic behavior has been studied by means of time-of-flight single crystal neutron diffraction combined with a hybrid-anvil-type pressure cell. The nonpolar collinear magnetic ground state (CM1 phase) with propagation vector k = (0, 1/2, 1/2) turns into a proper screw magnetic ordering with incommensurate modulation k = (0, q, 1/2; q similar or equal to 0.4) and a polar 21 ' magnetic point group (ICM2 phase), between 3 and 4 GPa. This spin structure is similar to the ferroelectric phase induced by magnetic field or chemical doping under ambient pressure. Above, 4 GPa, a magnetic phase (ICM3) appears, with an incommensurate propagation vector that is unique for the CuFeO2 system, k = (qa, qb, qc; qa similar or equal to 0, qb similar or equal to 0.34, qc similar or equal to 0.43). This propagation vector at the general point results in triclinic magnetic symmetry which implies an admixture of both cycloidal and proper screw spin configurations. The ICM3 phase is stable in a narrow pressure range, and above 6 GPa, the spin-density collinear structure (ICM1 phase), similar to the first ordered state at ambient pressure, takes place. Comparing the degree of lattice distortions among the magnetic phases observed at ambient pressure, we discuss the origin of the pressure-induced magnetic phase transitions in CuFeO2.
We have performed inelastic neutron scattering measurements in the ferroelectric noncollinear-magnetic phase of CuFe{sub 1-x}GaâOâ (CFGO) with x = 0.035 under applied uniaxial pressure. This system has three types of magnetic domains with three different orientations reflecting the trigonal symmetry of the crystal structure. To identify the magnetic excitation spectrum corresponding to a magnetic domain, we have produced a nearly single-domain multiferroic phase by applying a uniaxial pressure of 10 MPa onto the [1{bar 1}0] surfaces of a single crystal CFGO sample. As a result, we have successfully observed the single-domain spectrum in the multiferroic phase. Using the Hamiltonian employed in the previous inelastic neutron scattering study on the multi-domain multiferroic phase of CFGO (x = 0.035) [Haraldsen et al. Phys. Rev. B 82 020404R (2010)], we have refined the Hamiltonian parameters so as to simultaneously reproduce both of the observed single-domain and multi-domain spectra. Comparing between the Hamiltonian parameters in the multiferroic phase of CFGO and in the collinear four-sublattice magnetic ground state of undoped CuFeOâ [Nakajima et al, Phys. Rev. B 84 184401 (2011)], we suggest that the nonmagnetic substitution weakens the spin-lattice coupling, which often favors a collinear magnetic ordering, as a consequence of the partial release of the spin frustration.
The correct stacking of hexagonal layers is used to obtain accurate estimates for the exchange and anisotropy parameters of the geometrically-frustrated antiferromagnet CuFeO2. Those parameters are highly constrained by the stability of a collinear metamagnetic phase between fields of 13.5 and 20 T. Constrained fits of the spin-wave frequencies of the collinear ""## phase below 7 T are used to determine the magnetic unit cell of the metamagnetic """## phase, which contains two hexagonal layers and 10 Fe3+ ions. PACS numbers: 75.30.Ds, 75.50.Ee, 61.12.-q
A cross-platform program, VESTA, has been developed to visualize both structural and volumetric data in multiple windows with tabs. VESTA represents crystal structures by ball-and-stick, space-filling, polyhedral, wireframe, stick, dot-surface and thermal-ellipsoid models. A variety of crystal-chemical information is extractable from fractional coordinates, occupancies and oxidation states of sites. Volumetric data such as electron and nuclear densities, Patterson functions, and wavefunctions are displayed as isosurfaces, bird's-eye views and two-dimensional maps. Isosurfaces can be colored according to other physical quantities. Translucent isosurfaces and/or slices can be overlapped with a structural model. Collaboration with external programs enables the user to locate bonds and bond angles in the `graphics area', simulate powder diffraction patterns, and calculate site potentials and Madelung energies. Electron densities determined experimentally are convertible into their Laplacians and electronic energy densities.
The high-magnetic-field behavior of the triangular-lattice antiferromagnet CuFeO2 is studied using single crystal neutron diffraction measurements in a field of up to 14.5 T and also by magnetization measurements in a field of up to 12 T. At low temperature, two well-defined first order magnetic phase transitions are found in this range of applied magnetic field (H‖c): at Hc1=7.6(3)/7.1(3) T and Hc2=13.2(1)/12.7(1) T when ramping the field up/down. In a field above Hc2 the magnetic Bragg peaks show unusual history dependence. In zero field TN1=14.2(1) K separates a high-temperature paramagnetic and an intermediate incommensurate structure, while TN2=11.1(3) K divides an incommensurate phase from the low-temperature four-sublattice ground state. The ordering temperature TN1 is found to be almost field independent, while TN2 decreases noticeably in applied field. The magnetic phase diagram is discussed in terms of the interactions between an applied magnetic field and the highly frustrated magnetic structure of CuFeO2.
We have investigated spin-wave excitations in a four-sublattice (4SL)
magnetic ground state of a frustrated magnet CuFeO2, in which `electromagnon'
(electric-field-active magnon) excitation has been discovered by recent
terahertz time-domain spectroscopy [Seki et al. Phys. Rev. Lett. 105 097207
(2010)]. In previous study, we have identified two spin-wave branches in the
4SL phase by means of inelastic neutron scattering measurements under applied
uniaxial pressure. [T. Nakajima et al. J. Phys. Soc. Jpn. 80 014714 (2011) ] In
the present study, we have performed high-energy-resolution inelastic neutron
scattering measurements in the 4SL phase, resolving fine structures of the
lower-energy spin-wave branch near the zone center. Taking account of the
spin-driven lattice distortions in the 4SL phase, we have developed a model
Hamiltonian to describe the spin-wave excitations. The determined Hamiltonian
parameters have successfully reproduced the spin-wave dispersion relations and
intensity maps obtained in the inelastic neutron scattering measurements. The
results of the spin-wave analysis have also revealed physical pictures of the
magnon and electromagnon modes in the 4SL phase, suggesting that collinear and
noncollinear characters of the two spin-wave modes are the keys to understand
the dynamical coupling between the spins and electric dipole moments in this
system.
Using synchrotron x-ray and neutron diffraction, we disentangle spin-lattice order in highly frustrated ZnCr2O4 where magnetic chromium ions occupy the vertices of regular tetrahedra. Upon cooling below 12.5 K the quandary of antialigning spins surrounding the triangular faces of tetrahedra is resolved by establishing weak interactions on each triangle through an intricate lattice distortion. However, the resulting spin order is not simply a Néel state on strong bonds, but rather a complex coplanar spin structure, indicating that antisymmetric and/or further neighbor exchange interactions also play a role as ZnCr2O4 resolves conflicting magnetic interactions.
We have performed synchrotron radiation X-ray and neutron diffraction measurements on magnetoelectric multiferroic CuFe1-xAlxO2 (x=0.0155), which has a proper helical magnetic structure with incommensurate propagation wave vector in the ferroelectric phase. The present measurements revealed that the ferroelectric phase is accompanied by lattice modulation with a wave number 2q, where q is the magnetic modulation wave number. We have calculated the Fourier spectrum of the spatial modulations in the local electric polarization using a microscopic model proposed by Arima [T. Arima, J. Phys. Soc. Jpn. 76, 073702 (2007)]. Comparing the experimental results with the calculation results, we found that the origin of the 2q-lattice modulation is not conventional magnetostriction but the variation in the metal-ligand hybridization between the magnetic Fe^3+ ions and ligand O^2- ions. Combining the present results with the results of a previous polarized neutron diffraction study [Nakajima et al., Phys. Rev. B 77 052401 (2008)], we conclude that the microscopic origin of the ferroelectricity in CuFe1-xAlxO2 is the variation in the metal-ligand hybridization with spin-orbit coupling.
We predict the spin-wave dynamics for the high-field phases of the frustrated antiferromagnet CuFeO2. After determining the appropriate magnetic ground state using a combination of Monte-Carlo simulations and variational methods for a two-dimensional triangular lattice, we evaluate the spin excitation frequencies and intensities using a rotational Holstein-Primakoff expansion for both the collinear and non-collinear states. These predictions will help experimentalists to identify the magnetic ground states of CuFeO2 with inelastic neutron scattering.
LET is a new multi-chopper direct geometry cold neutron spectrometer, recently installed on target station 2 (TS2) at the ISIS spallation neutron source. The characteristics of the primary spectrometer are a 25 m straight super-mirror guide viewing the new highly efficient coupled solid methane moderator system. This combination yields a high incident flux of neutrons with a wide dynamic range of 0.6-80 meV. LET employs a novel flux compression guide design which in combination with two 300 Hz counter rotating choppers produces fine energy resolutions of >=0.8%deltaE/Ei , to be realised with very little flux sacrifice compared to conventional methods. The multi-chopper system is designed to make full use of the long 100 ms time frames of TS2, allowing the user to make multiple measurements within a single frame. The secondary spectrometer is characterised by a wide area position sensitive 3He multidetector with pi steradians of nearly gapless coverage over the angular range from -40° to +140° in the horizontal plane and ±30° in the vertical plane. The multidetector utilises the worlds first 4 m position sensitive 3He neutron detector tubes.LET has been designed specifically to allow the use of polarised neutrons allowing the user to exploit full XYZ neutron polarisation analysis. In addition a new 9 T magnet has been designed for LET allowing the use of large samples of 25 mm×25 mm with a 30° vertical opening to make use of the large multidetector.
The results of synchrotron X-ray diffraction measurements on a single crystal of the triangular lattice antiferromagnet CuFeO2 under zero and non-zero applied magnetic fields are reported. We find four satellite reflections at (0, 3+q, 1/2), (0, 4-q, 1/2), (0, 4-2q, 0), and (0, 3+2q, 0) with the incommensurate wave number q ˜ 0.415 in the ferroelectric incommensurate (FEIC) phase which appears in the magnetic field, H, between 7 and 13 T at low temperatures. In the partially disordered (PD) phase which exists in the temperature, T, range between 11 and 14 K, we find two satellite reflections at (0, 4-q, 1/2) and (0, 4-2q, 0) with the incommensurate wave number q ˜ 0.4. The T and H dependence of these satellite reflections are studied. We interpret that the reflections observed in the FEIC phase arise from incommensurate lattice modulations caused by a magnetoelastic coupling with the underlying magnetic structure. The observation of the reflection (0, 4-q, 1/2) in finite fields and the (0, 4-2q, 0) reflection at 0
Magnetic ordering in a rhombohedrally stacked triangular lattice antiferromagnet, CuFeO2 was investigated on powder and single crystals by measurements of neutron diffraction, magnetic susceptibility, Mössbauer effect together with Monte Carlo simulations. CuFeO2 was found to exhibit transitions at TN1{=}16± 0.5 K and TN2{=}11± 0.5 K. The low temperature phase has an orthorhombic magnetic unit cell with collinear moments along the c-axis, whereas the intermediate temperature phase is a partially disordered phase with a monoclinic magnetic unit cell where 1/5 of moments remain paramagnetic. The Monte Carlo simulations for the Ising spin tiangular lattice antiferromagnet can reproduce the observed successive transition in the case of the exchange parameters 4J3
Neutron diffraction study revealed that a powdered CuFeO2, a quasi-two-dimensional antiferromagnet on a triangular lattice (AFT), has two successive magnetic phase transitions at low temperatures. In the high-temperature phase below TN1{=}16 K, it has a monoclinic magnetic unit cell with five spins in a layer (\sqrt{7}a×\sqrt{7}a× 2c, gamma{=}141.78°). At TN2{=}10 K, it shows a discontinuous transition and enters the low-temperature phase with an orthorhombic magnetic unit cell with four spins in a layer (\sqrt{3}a× 2a× 2c). In both magnetic structures, spins are collinear and parallel to the c axis.
The combination of high-frequency electron magnetic resonance (EMR) and magnetization measurements enables us to evaluate the exchange interactions in high-field phases of polycrystalline samples of the chromium spinel oxide HgCr2O4. The evaluation indicates that the lattice distortion in this compound largely modulates the exchange interactions between the Cr3+ spins to stabilize its distinct plateau with one-half of the saturation magnetization. Furthermore, we show that a release of the lattice distortion occurs in very high magnetic fields. Our result suggests that the spin-lattice coupling, which causes the large changes in the exchange interactions, plays a crucial role in giving rise to the peculiar magnetization process of HgCr2O4.
We have performed synchrotron radiation X-ray diffraction measurements on a triangular lattice antiferromagnet CuFeO2, using the single crystal. The crystal lattice symmetry lowers from hexagonal to orthorhombic below the magnetic phase transition (from a partially disordered phase to four-sublattice phase) temperature TN2. In addition, superlattice reflections were observed below TN2; this suggests that the ``scalene triangle model'' lattice distortion splits the nearest neighbor exchange interaction in the basal plane into three different exchange interactions. This distortion lifts the vast degeneracy of the strongly frustrated spin system, leading to the four-sublattice ground state. Thus we argue that the lattice degree of freedom plays an important role in the stabilization of the four-sublattice ground state in CuFeO2.
Structural deformations associated with magnetic phase transitions have been studied by synchrotron radiation X-ray diffraction in high magnetic fields up to 14 T for the geometrically frustrated triangular lattice antiferromagnet CuFeO2. When a magnetic field is applied along the hexagonal c-axis, ``scalene triangular'' (ST) lattice distortion, which causes the three different exchange interaction paths in the basal plane, is successively relieved at the critical fields corresponding to field-induced magnetic phase transitions. In particular, the ST lattice is deformed into the higher symmetric ``isosceles triangular'' lattice at the second-field-induced magnetic phase transition (˜13.5 T). We thus conclude that the spontaneous lattice distortion in CuFeO2, which occurs without any orbital degrees of freedom, originates from a magnetoelastic coupling produced by spin frustration.
The growth of bulk cuprous ferrite (CuFeO2) single crystals by the travelling-solvent, floating-zone technique is reported. Crystals 5 to 8 mm in diameter by 10 to 30 mm have been grown from two sets of starting materials: Cu2O + Fe2O3 and 2CuO + Fe2O3, respectively. The trigonal unit-cell parameters determined by X-ray diffraction are ah = 3.035(1) Å and ch = 17.161(4) Å in the hexagonal description. Mössbauer studies reveal an isomer shift for 57Fe at room temperature of 0.40 mm/s with respect to metallic iron, confirming that iron is in the trivalent state and that CuFeO2 is cuprous metaferrite (Cu+Fe3+O2). Magnetic susceptibility indicates that CuFeO2 undergoes two successive magnetic transition temperatures around TN1 = 13.5 K and TN2 = 9.5 K, respectively. Thermal analysis reveals that, under an argon atmosphere, CuFeO2 partially decomposes at 1180°C to form Fe2O3 (or Fe3O4) and Cu2O.
We reinvestigated successive magnetic phase transitions (T N1˜14.0 K, T N2˜10.5 K) in a frustrated triangular lattice antiferromagnet (TLA) CuFeO2 by neutron diffraction measurements using single crystals. The magnetic structure of the intermediate-temperature phase between T N1 and T N2 is found to be a quasi-long range ordered sinusoidally amplitude-modulated structure with a temperature dependent propagation wave vector (q q 0). These features of successive phase transitions are well explained by reinvestigated Monte-Carlo simulation of a 2D Ising TLA with competing exchange interactions up to 3rd neighbors, in spite of the Heisenberg spin character of orbital singlet Fe3+ magnetic ions.
The results of synchrotron x-ray-diffraction and magnetization measurements on a triangular lattice antiferromagnet CuFeO2 under pulsed high magnetic fields are reported. This material exhibits a distorted triangular lattice structure below ∼11 K to relieve partially the geometric frustration. We find stepwise changes in the lattice constants, associated with the magnetization changes parallel (H‖) and perpendicular (H⊥) to the trigonal c axis. The relative changes in the lattice constant b with H‖ are reproduced by a calculation based on a model in which the number of bonds connecting two parallel spins along the b axis increases with increasing field and the lattice contracts to gain the ferromagnetic direct and antiferromagnetic superexchange energies. For H⊥, we find a discontinuous change in b and c at ∼24 T, and a plateau in b and c at 24<H⊥<30 T. The change in b with increasing H⊥ agrees also with the same calculation. We discuss the anisotropic behavior in CuFeO2 observed at the low fields and find that the anisotropy is closely correlated with the lattice distortion.
We report inelastic neutron scattering measurements that provide a distinct dynamical “fingerprint” for the multiferroic ground state of 3.5% Ga-doped CuFeO2. The complex ground state is stabilized by the displacement of the oxygen atoms, which contribute to the multiferroic coupling predicted in the “spin-driven” model. By comparing the observed and calculated spectrum of spin excitations, we conclude that the magnetic ground state is a distorted screw-type spin configuration with a distribution of turn angles.
We use high-resolution synchrotron x-ray and neutron diffraction to study the geometrically frustrated triangular lattice antiferromagnet CuFeO2. On cooling from room temperature, CuFeO2 undergoes two antiferromagnetic phase transitions with incommensurate and commensurate magnetic order at TN1=14 K and TN2=11 K, respectively. The occurrence of these two magnetic transitions is accompanied by second- and first-order structural phase transitions from hexagonal to monoclinic symmetry. Application of a 6.9 T magnetic field lowers both transition temperatures by ∼1 K, and induces an additional incommensurate structural modulation in the temperature region where the field-driven ferroelectricity occurs. These results suggest that a strong magneto-elastic coupling is intimately related to the multiferroic effect.
Magnetoelectric and magnetoelastic phenomena have been investigated on a frustrated triangular antiferromagnetic lattice in CuFeO2. Inversion-symmetry breaking, manifested as a finite electric polarization, was observed in noncollinear (helical) magnetic phases and not in collinear magnetic phases. This result demonstrates that the noncollinear spin structure plays an important role in inducing electric polarization. Based on these results we suggest that frustrated magnets (often favoring noncollinear configurations) are favorable candidates for a new class of magnetoelectric materials.
One of the most fascinating frustrated antiferromagnets, CuFeO2, contains stacked hexagonal layers, each with an ↑↑↓↓ magnetic structure. Recent neutron-scattering studies have found that the spin-wave spectrum softens with increasing magnetic field or by substituting Al for Fe. We present a theory of the spin-wave excitations that fits the observed frequencies quite well and explains this softening.
By means of neutron scattering measurements, we have investigated spin-wave
excitation in a collinear four-sublattice (4SL) magnetic ground state of a
triangular lattice antiferromagnet CuFeO2, which has been of recent interest as
a strongly frustrated magnet, a spin-lattice coupled system and a multiferroic.
To avoid mixing of spin-wave spectrum from magnetic domains having three
different orientations reflecting trigonal symmetry of the crystal structure,
we have applied uniaxial pressure on [1-10] direction of a single crystal
CuFeO2. By elastic neutron scattering measurements, we have found that only 10
MPa of the uniaxial pressure results in almost 'single domain' state in the 4SL
phase. We have thus performed inelastic neutron scattering measurements using
the single domain sample, and have identified two distinct spin- wave branches.
The dispersion relation of the upper spin-wave branch cannot be explained by
the previous theoretical model [R. S. Fishman: J. Appl. Phys. 103 (2008)
07B109]. This implies the importance of the lattice degree of freedom in the
spin-wave excitation in this system, because the previous calculation neglected
the effect of the spin-driven lattice distortion in the 4SL phase. We have also
discussed relationship between the present results and the recently discovered
"electromagnon" excitation.
We refined the magnetic structure of a ferroelectric FE phase of multiferroic CuFe1 amp; 8722;xGaxO2 with x 0.035 by complementary use of spherical neutron polarimetry and a four circle neutron diffraction measurement, revealing that the proper screw type magnetic structure in the ferroelectric phase has a finite ellipticity of 0.9. By means of polarized neutron diffraction and in situ pyroelectric measurements, we also investigated the quantitative relationship between the macroscopic ferroelectric polarization P and the asymmetry in volume fractions with left handed and right handed helical magnetic order in CuFe1 amp; 8722;xAlxO2 with x 0.0155 and CuFe1 amp; 8722;xGaxO2 with x 0.035. These measurements revealed that the substitution of a small amount of nonmagnetic Ga3 or Al3 ions does not significantly change the magnitude of the local ferroelectric polarization but does reduce the sensitivity of P to the poling electric field Ep . This implies that the mobility of the magnetic domain walls, which is sensitive to magnetic defects due to nonmagnetic substitution, determines the sensitivity of P to Ep because of a one to one correspondence between the magnetic and ferroelectric domains.
Neutron diffraction studies on a frustrated triangular lattice antiferromagnet (TLA) CuFeO2 have been performed under an applied magnetic field up to 14.5 T. The first-field-induced state was found to be not the commensurate 5-sublattice (up arrow up arrow up arrow down arrow down arrow) magnetic state but rather an incommensurate complex helical state reflecting the Heisenberg spin character of orbital singlet Fe3+ magnetic ions. In contrast, the second-field-induced state was found to be the 5-sublattice (up arrow up arrow up arrow down arrow down arrow) magnetic state predicted by the two-dimensional (2D) Ising spin TLA model with compeling exchange interactions up to the 3rd neighbors.
The ground-state properties of the spin-1 antiferromagnetic Heisenberg model on the corner-sharing tetrahedra, the pyrochlore lattice, are investigated. By breaking up each spin into a pair of 1/2-spins, the problem is reduced to the equivalent one of the spin-1/2 tetrahedral network in analogy with the valence bond solid state in one dimension. The twofold degeneracy of the spin singlets of a tetrahedron is lifted by a Jahn-Teller mechanism, leading to a cubic to tetragonal structural transition. It is proposed that the present mechanism is responsible for the phase transition observed in the spin-1 spinel compounds ZnV2O4 and MgV2O4.
We study the effects of magnetoelastic couplings on pyrochlore antiferromagnets. We employ Landau theory, extending an investigation begun by Yamashita and Ueda for the case of S = 1, and classical analyses to argue that such couplings generate bond order via a spin-Peierls transition. This is followed by, or concurrent with, a transition into one of several possible low-temperature Néel phases, with most simply collinear, but also coplanar or mixed spin patterns. In a collinear Néel phase, a dispersionless stringlike magnon mode dominates the resulting excitation spectrum, providing a distinctive signature of the parent geometrically frustrated state. We comment on the experimental situation.
Magnetization plateaus, visible as anomalies in magnetic susceptibility at low temperatures, are one of the hallmarks of frustrated magnetism. We show how an extremely robust half-magnetization plateau can arise from coupling between spin and lattice degrees of freedom in a pyrochlore antiferromagnet and develop a detailed symmetry of analysis of the simplest possible scenario for such a plateau state. The application of this theory to the spinel oxides CdCr2O4 and HgCr2O4, where a robust half-magnetization plateau has been observed, is discussed.
The magnetization of the geometrically frustrated spinel CdCr2O4 was measured in pulsed fields of up to 47 T. We found a metamagnetic transition to a very wide magnetization plateau state with one half of the full moment of S=3/2 Cr3+ at 28 T, independent of the field direction. This is the first observation of magnetization plateau state realized in Heisenberg pyrochlore magnet. The plateau state can be ascribed to a collinear spin configuration with three-up and one-down spins out of four spins of each Cr tetrahedron. A large magnetostriction is observed at the transition in spite of the negligible spin-orbit couplings. We argue that spin frustration plays a vital role in this large spin-lattice coupling.
We study the effect of spin-lattice coupling on triangular and kagome antiferromagnets and find that even moderate couplings can induce complex collinear orders. On coupling classical Heisenberg spins on the triangular lattice to Einstein phonons, a rich variety of phases emerge including the experimentally observed four sublattice state and the five sublattice 1/5th plateau state seen in the magnetoelectric material CuFeO(2). Also, we predict magnetization plateaus at 1/3, 3/7, 1/2, 3/5, and 5/7 at these couplings. Strong spin-lattice couplings induce a striped collinear state, seen in alpha-NaFeO(2) and MnBr(2). On the kagome lattice, moderate spin-lattice couplings induce collinear order, but an extensive degeneracy remains.
Magnetic systems are fertile ground for the emergence of exotic states when the magnetic interactions cannot be satisfied simultaneously due to the topology of the lattice - a situation known as geometrical frustration. Spinels, AB2O4, can realize the most highly frustrated network of corner-sharing tetrahedra. Several novel states have been discovered in spinels, such as composite spin clusters and novel charge-ordered states. Here we use neutron and synchrotron X-ray scattering to characterize the fractional magnetization state of HgCr2O4 under an external magnetic field, H. When the field is applied in its Neel ground state, a phase transition occurs at H ~ 10 Tesla at which each tetrahedron changes from a canted Neel state to a fractional spin state with the total spin, Stet, of S/2 and the lattice undergoes orthorhombic to cubic symmetry change. Our results provide the microscopic one-to-one correspondence between the spin state and the lattice distortion.
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