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Spin-Wave Spectrum in `Single-Domain' Magnetic Ground State of Triangular Lattice Antiferromagnet CuFeO2
Abstract
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.
... On the other hand, Nakajima et al. have recently demonstrated that volume fractions of the three domains can be controlled by application of uniaxial pressure. 12,13 Since the formation of the three magnetic domains accompanies with monoclinic lattice distortions in each domain as illustrated in Figs. 1(c)-1(e), an application of uniaxial pressure, which is directly coupled with the lattice degree of freedom, results in significant changes in the volume fractions of the magnetic/crystal domains. ...
... 1(c)-1(e), an application of uniaxial pressure, which is directly coupled with the lattice degree of freedom, results in significant changes in the volume fractions of the magnetic/crystal domains. Actually, in Ref. 13, a single-domain 4SL phase is achieved by applying a uniaxial pressure of only 10 MPa onto the [110] surfaces of the single-crystal CFO sample. Recent inelastic neutron scattering measurements using the slightly pressurized CFO sample have successfully identified the spin-wave dispersion relations belonging to a magnetic domain in the 4SL phase. ...
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.
... 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.
Cold multi-chopper instrument is a popular instrument commonly used for variety of scientific fields, built in reactors and sharp pulse sources and will be built in a long pulse source. In this article I compare the performance of those instruments, IN5 at ILL, AMATERAS at J-PARC and CSPEC at ESS, and show a merit/demerit come from the different characters of the source itself, and finally give a suggestion for a further improvement.
Spin-1/2 triangular lattice Heisenberg antiferromagnet has been accepted as an ideal system for quantum magnetism studies and quantum simulations. This system, for which the classical ground state degeneracy is lifted by quantum fluctuations, exhibits a series of novel spin structures for a field applied in-plane and out-of-plane. It has been found that both anisotropy and interlayer interaction play an important role in the stabilization of the spin configurations in a magnetic field. Conversely, the phase transitions and spin-state evolution in a field along various orientations can provide a deep insight into physics of the triangular lattice Heisenberg antiferromagnet system. While the quantum magnetization process in an in-plane field has been studied extensively, the ground state evolution in the field along the c axis requires further investigation. Here we performed high field magnetization and neutron scattering investigations on a model system of spin-1/2 triangular lattice Heisenberg antiferromagnet Ba3CoSb2O9 with field along c axis and with a small offset angle. For H∥c, the magnetization reveals a narrow plateau prompting a UUD-like phase, which could be suppressed by tilting the field away from the c axis. From the neutron data, a phase transition μ0Hc1∼12 T is detected and interpreted as a transition from an umbrella to a coplanar phase. Around about 22.5 T (μ0Hc2) for H∥c, another transition is observed which might be attributed to a transition between the coplanar V and V′ phases based on a comparison with the calculations and previous results. Theoretical calculations using the large-size cluster mean-field plus scaling method predicts a similar phase evolution as the previous semiclassical analysis, and agree with experiment well. The discrepancies between theory and experiment are also discussed, suggesting the physics of a triangular lattice Heisenberg antiferromagnet in a field along c axis has not been fully unraveled.
We investigate phenomena correlated with multiple degrees of freedom in a geometrically frustrated magnet, CuFeO2, by applying uniaxial pressure p and magnetic field H. Ferroelectric polarization is induced by a combination of p and H only in a sinusoidally amplitude-modulated magnetic structure phase, in which the sinusoidal magnetic ordering does not break the inversion symmetry. The crystal structure and magnetic structure in this phase seem to be unchanged, even by the application of p and H within the present neutron diffraction experiments. These results indicate that this phenomenon differs from conventional spin-driven ferroelectricity as observed in an H-induced helical magnetic phase of CuFeO2. We propose that the induction of ferroelectric polarization by the combined application of p and H in CuFeO2 can be regarded as a nonlinear piezomagnetoelectric effect.
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 have investigated effects of uniaxial stress on frustrated magnets by means of neutron scattering experiment. In this article, we focus on a triangular lattice antiferromagnet CuFeO2, which exhibits a strong spin-lattice coupling. We demonstrated uniaxial-stress control of electric polarization in a multiferroic phase of Ga-doped CuFeO2. We also studied magnetic excitations in the collinear four-sublattice (4SL) antiferromagnetic ground state in undoped CuFeO2 by means of inelastic neutron scattering measurements under uniaxial stress. We suggest that application of uniaxial-stress can be a useful tool to investigate geometrically frustrated spin systems, and can also induce novel cross-correlated phenomena in spin-lattice coupled systems.
We investigated magnetic excitations in lightly oxygen doped La2NiO4+δ (δ = 0.02 and 0.11) by inelastic neutron scattering over a wide energy range. It is known that two types of two-dimensional (2D) antiferromagnetic (AF) excitations coexist in these systems, i.e., well-defined excitations with effective exchange interactions suppressed by hole doping in the lower energy region (impurity mode) and higher energy excitations with a steep dispersion (host mode). However, details of these excitations, especially the host mode, has not been well studied so far due to the lack of information in the higher energy region. Our results reveal that host modes can be characterized by a simple 2D AF spin-wave model with the same exchange energy as that of the stoichiometric system in the δ = 0.02 phase. In the δ = 0.11 phase, although considerable broadening was observed, the upper band limit of the host modes was on the same level as that in the stoichiometric system, which implies that the magnitude of intrinsic exchange interaction is not affected by doping. The observed results can help understand the microscopic nature of doped holes in this system and other layered-transition metal oxides.
We have investigated magnetic and ferroelectric (dielectric) properties of multiferroic CuFe0.982Ga0.018O2, CuFe0.965Ga0.035O2, and CuFe0.95Al0.05O2 under applied uniaxial pressure p up to 600 MPa. Unlike the results of the almost same experiments on CuFeO2 [Tamatsukuri et al., Phys. Rev. B 94, 174402 (2016)], we have found that the application of p induces a new ferroelectric phase, which is different from the well-studied spin-driven ferroelectric phase with helical magnetic ordering, in all the doped samples investigated here. We have also constructed the temperature versus p magnetoelectric phase diagrams of the three samples. The ferroelectric polarization in the p-induced ferroelectric phase lies along the [110] direction as in the helical magnetoferroelectric phase, and its value is comparable with or larger than that in the helical magnetoferroelectric phase. The magnetic structure in the p-induced ferroelectric phase seems to be of a collinear sinusoidal type. Although this magnetic structure itself does not break the inversion symmetry, it is considered to play an important role in the origin of ferroelectricity in the p-induced ferroelectric phase through the spin-lattice coupling in this system.
We report a study on the thermal conductivity of CuFe$_{1-x}$Ga$_x$O$_2$ ($x =$ 0--0.12) single crystals at temperatures down to 0.3 K and in magnetic fields up to 14 T. CuFeO$_2$ is a well-known geometrically frustrated triangular lattice antiferromagnet and can be made to display multiferroicity either by applying magnetic field along the $c$ axis or by doping nonmagnetic impurities, accompanied with rich behaviors of magnetic phase transitions. The main experimental findings of this work are: (i) the thermal conductivities ($\kappa_a$ and $\kappa_c$) show drastic anomalies at temperature- or field-induced magnetic transitions; (ii) the low-$T$ $\kappa(H)$ isotherms exhibit irreversibility in a broad region of magnetic fields; (iii) there are phonon scattering effect caused by magnetic fluctuations at very low temperatures. These results demonstrate strong spin-phonon coupling in this material and reveal the non-negligible magnetic fluctuations in the "ground state" of pure and Ga-doped samples.
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.
We report neutron diffraction measurement results for an Ising antiferromagnet ${\mathrm{CoNb}}_{2}{\mathrm{O}}_{6}$ under uniaxial pressure along the geometrically frustrated isosceles-triangular-lattice direction. We find that an onset incommensurate wave number at the N\'eel temperature increases with pressure from 0.378 to 0.411 at 400 MPa. The observations suggest that the anisotropic deformation of the lattice by the uniaxial pressure significantly modifies the spin frustration, leading to an increase in the nearest-neighbor to next-nearest-neighbor interaction ratio from 1.33 to 1.81.
The triangular lattice antiferromagnet CuFeO2 (CFO) is a spin-lattice coupled system, whose magnetic phase transitions are accompanied by crystal lattice distortions to relieve the geometrical spin frustration. Recent neutron diffraction and magnetic susceptibility measurements on CFO have revealed that the application of uniaxial pressure (up to 100 MPa) in the triangular lattice plane shifts the magnetic phase transition temperatures to higher values [Nakajima et al.: J. Phys. Soc. Jpn. 81 (2012) 094710]. In the present study, we have performed synchrotron radiation x-ray diffraction measurements on CFO and CuFe1-xGaxO2 (CFGO) with x = 0.035 under applied uniaxial pressure in order to directly observe the uniaxial-pressure effects on the lattice. As a result, we have revealed that the applied uniaxial pressure certainly affects the crystal structure so that the structural transition temperatures increase as well as the magnetic phase transition temperatures. We have also found that CFO exhibits a pronounced lattice instability in the vicinity of the phase transition from the paramagnetic phase with a trigonal structure to an incommensurate magnetic phase with a monoclinic structure. In addition, the present results for CFGO (x = 0.035) have revealed that the lattice instability is suppressed by the substitution of a small amount of nonmagnetic Ga3+ ions for the magnetic Fe3+ ions. This indicates that the spin degree of freedom plays an important role in the lattice instability in this system.
We have investigated effects of applied uniaxial pressure (p) on
magnetic phase transitions in a triangular lattice antiferromagnet
CuFeO2 (CFO) and a slightly Ga-substituted compound
CuFe1-xGaxO2 (CFGO) with x=0.018. We
have performed neutron diffraction, spherical neutron polarimetry,
magnetic susceptibility and pyroelectric measurements under p up to 100
MPa applied on the [1\bar{1}0] surfaces of the single crystal samples.
As a result, we have revealed that in both of CFO and CFGO (x=0.018),
the application of p significantly increases the transition temperature
from the paramagnetic phase to a collinear incommensurate
antiferromagnetic phase, at which these systems exhibit a crystal
structural distortion associated with the magnetic ordering. This
suggests that the application of p beaks equilateral symmetry of the
triangular lattice above the original transition temperature, and
partially relieves geometrical spin frustration, which generally
suppresses long-range magnetic orderings even at low temperatures. In
CFGO (x=0.018), we have also found that the ferroelectric helimagnetic
phase, which originally shows up as an intermediate phase in zero
pressure, partly remains down to low temperatures under applied p. These
results have demonstrated that uniaxial pressure can be an effective
tool to control magnetic phase transitions in frustrated magnets.
We have performed multifrequency electron spin resonance (ESR) measurements of the triangular lattice antiferromagnet CuFeO2, which shows peculiar magnetic ordering and field-induced phase transitions, in high magnetic fields of up to 53 T. Our analysis of the ESR modes and energy dispersion explains the overall behaviors of magnetic excitations in the collinear 4-sublattice phase of this material. We show changes of the exchange interactions due to the lattice distortion of CuFeO2, suggesting strong spin-lattice coupling in this material. In addition, we evaluate the precise value of the magnetic anisotropy in CuFeO2 from the ESR and magnetization measurements. The presence of relatively large second- and third-nearest-neighbor intralayer exchange interactions is also indicated. We discuss that the strong spin-lattice coupling, the large farther neighbor exchange interactions, and the finite axial anisotropy are important to understand the magnetic phase transitions of CuFeO2.
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.
We report high resolution inelastic neutron scattering measurements and spin dynamics calculations in two multiferroic materials: the geometrically frustrated triangular lattice CuFeOâ and mineral Huebnerite MnWOâ. In un-doped CuFeOâ a low-T collinear spin structure is stabilized by long range magnetic interactions. When doped with a few percent of gallium, the spin order evolves into a complex noncollinear configuration and the system becomes multiferroic. Similarly, the ground state collinear spin order in pure MnWOâ results from delicate balance between competing magnetic interactions up to 11th nearest neighbors and can be tuned by substitution of Mn ions with magnetic or nonmagnetic impurities. The comprehensive investigation of spin dynamics in both systems help to understand the fundamental physical process and the interactions leading to the close interplay of magnetism and ferroelectricity in this type of materials.
Delafossite compound CuFeO2 is a spin-driven magneto-electric multiferroic, in which magnetic field-induced or nonmagnetic impurity-induced proper helical magnetic ordering generates a spontaneous electric polarization through the spin-orbit-interaction mediated modulation of Fe 3d-O 2p hybridization. As is expected from spin-lattice tightly coupled character of this system, we found an enhancement of spin-driven ferroelectric polarization under [11̄0] uniaxial stress as spin-mediated piezoelectric effect. Preparing almost mono-domain state for multiferroic CuFe1−xGaxO2 sample with x = 0.035, we have performed polarized neutron diffraction and in-situ ferroelectric polarization measurements to investigate how the helical magnetic structure is modified and how much ferroelectric polarization increases under application of [11̄0] uniaxial stress up to 100 MPa. The uniaxial-stress variation of magnetic structural parameters characterizing helical magnetic ordering suggests decreasing of the ferroelectric polarization according to the calculation on the basis of d-p hybridization mechanism. Therefore, it is suggested that the enhancement of ferroelectric polarization originates not in variation of the magnetic structure but in the enhancement of the d-p hybridization coupling constants.
Two-dimensional electron systems, as exploited for device applications, can lose their conducting properties because of local Coulomb repulsion, leading to a Mott-insulating state. In triangular geometries, any concomitant antiferromagnetic spin ordering can be prevented by geometric frustration, spurring speculations about 'melted' phases, known as spin liquid. Here we show that for a realization of a triangular electron system by epitaxial atom adsorption on a semiconductor, such spin disorder, however, does not appear. Our study compares the electron excitation spectra obtained from theoretical simulations of the correlated electron lattice with data from high-resolution photoemission. We find that an unusual row-wise antiferromagnetic spin alignment occurs that is reflected in the photoemission spectra as characteristic 'shadow bands' induced by the spin pattern. The magnetic order in a frustrated lattice of otherwise non-magnetic components emerges from longer-range electron hopping between the atoms. This finding can offer new ways of controlling magnetism on surfaces.
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.
We have demonstrated that ferroelectric polarization in a spin-driven
multiferroic CuFe1-xGaxO2 with x = 0.035 can be controlled by the application
of uniaxial pressure. Our neutron diffraction and in-situ ferroelectric
polarization measurements have revealed that the pressure dependence of the
ferroelectric polarization is explained by repopulation of three types of
magnetic domains originating from the trigonal symmetry of the crystal. We
conclude that the spin-driven anisotropic lattice distortion and the fixed
relationship between the directions of the magnetic modulation wave vector and
the ferroelectric polarization are the keys to this spin-mediated piezoelectric
effect.
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.
Dielectric responses have been investigated on the triangular-lattice
antiferromagnet CuFeO2 and its site-diluted analogs CuFe1-xAlxO2 (x=0.01 and
0.02) with and without application of magnetic field. We have found a
ferroelectric behavior at zero magnetic field for x=0.02. At any doping level,
the onset field of the ferroelectricity always coincides with that of the
noncollinear magnetic structure while the transition field dramatically
decreases to zero field with Al doping. The results imply the further
possibility of producing the ferroelectricity by modifying the frustrated spin
structure in terms of site-doping and external magnetic field.
Terahertz time-domain spectroscopy was performed to directly probe the
low-energy (1-5 meV) electrodynamics of triangular lattice antiferromagnets
CuFe1-xGaxO2 (x = 0.00, 0.01, and 0.035). We discovered an electromagnon
(electric-field-active magnon) excitation at 2.3 meV in the paraelectric
up-up-down-down collinear magnetic phase, while this electromagnon vanishes in
the ferroelectric helimagnetic phase. Anti-correlation with noncollinear
magnetism excludes the exchange-striction mechanism as the origin of dynamical
magnetoelectric coupling, and hence evidences the observation of spin-orbit
coupling mediated electromagnon in the present compound.
The magnetic excitation spectrum has been investigated by inelastic
neutron scattering on triangular lattice antiferromagnets
CuFeO2 and CuFe0.98Al0.02O2.
While the normal acoustic spin-wave dispersion curve was obtained in
CuFe0.98Al0.02O2, the anomalous
dispersion curve with energy gap whose bottom positions do not
correspond to the magnetic Bragg point for the 4-sublattice
(↑↑↓↓) ground state was obtained in
CuFeO2.
The effect of substitution at the Fe site in the CuFeO2 delafossite is known to induce a magnetic structure responsible for the appearance of electric polarization. A CuFe1−xRhxO2 series of ceramic samples is studied in order to determine the composition range exhibiting such a polar state. It is found that for the CuFe1−xRhxO2 (x≤0.15) solid solution, the Néel temperature TN2 decreases monotonously with x from 11.5 K to 5.9 K, for x=0.00 to 0.15, respectively, and that the dielectric peak and the polarization transition temperatures coincide with TN2. In contrast, the dielectric peak and polarization magnitudes go through an optimum for CuFe0.92Rh0.08O2 (x=0.08). These results demonstrate that, compared to other substituting elements, the Rh3+ for Fe3+ substitution in CuFeO2 allows to extend significantly the ferroelectric region in the (x, T) phase diagram in connection with the slower TN2 decrease.
We have performed magnetic susceptibility, neutron diffraction and specific heat measurements on the triangular lattice antiferromagnet CuFe 1-xAlxO2 for x ≤ 0:050. A magnetic phase diagram for temperature vs x was determined. The various magnetically ordered phases compete with each other on the x-T magnetic phase diagram, strongly suggesting that the quasi-Ising orderings are stabilized in CuFeO2 with delicate balance of competing interactions. In the ground state for 0:014 < x < 0:030 [low-temperature (LT) phase], the magnetic structure consists of two magnetic modulations with slightly different wave numbers. Moreover, we observed the change in magnetic diffraction patterns in the LT phase, which corresponds to a crystallographic distortion from "hexagonal" to "orthorhombic", suggesting that the Ising anisotropy in CuFeO 2 is closely related to the crystallographic distortion.
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.
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.
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.
We have performed multi-frequency ESR measurements on the geometry frustrated triangular lattice antiferromagnet CuFeO2. The observed ESR modes are analyzed based on a mean field theory, taking into account a distortion of the triangular lattice,
which was found by recent synchrotron X-ray diffraction measurements.
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 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.
We have studied the magnetic excitation spectrum of the geometrically frustrated triangular lattice antiferromagnets of CuFeO2 with collinear ground state and CuFe1−xAlxO2 (0.014≤x≤0.030) with noncollinear ground state, using inelastic neutron scattering measurements on the single crystals. We have reported almost complete spin-wave dispersion relations and the temperature dependence of the magnetic excitation spectrum in both pure and slightly diluted samples. While the higher-energy spin-wave branches remain almost unchanged between the pure and diluted samples, the energy gap of the lowest-energy branch in CuFeO2 becomes zero as a result of the dilution, suggesting the retrieval of the original Heisenberg spin character of the orbital singlet Fe3+. Furthermore, by comparing with recent elastic neutron diffraction and x-ray measurements, we discuss the interrelation among the magnetic ordering, crystal lattice distortion and magnetic excitation qualitatively.
The design and fundamental properties of a uniaxial pressure cell for use with a four-circle
neutron diffractometer are reported. It is aimed at facilitating studies on the physical and/or
structural properties of solids. The results obtained for a uniaxial-pressure-induced ferromagnet
Sr3Ru2O7
showed that the unit cell volume increases upon applying uniaxial pressure along the
c-axis.
We report a neutron diffraction study of the magnetic field- and impurity-induced ferroelectric states of the triangular lattice antiferromagnet CuFe1-xAlxO2. The magnetic structure of the ferroelectric phase was elucidated to be not a cycloidal structure, which can successfully lead to the electric polarization through the formula P ∝ eij x (Si x Sj) [H. Katsura et al.: Phys. Rev. Lett. 95 (2005) 057205], but a proper helical structure. Nevertheless, the fact that the helical magnetic ordering appears only in the ferroelectric phase among various magnetically ordered phases of CuFe1-xAlxO 2 strongly suggests that a spin noncollinearlity is relevant to the multiferroic nature in CuFe1-xAlxO2.
The first submillimeter wave ESR on triangular lattice antiferromagnet, CuFeO2 has been performed in frequencies up to 762 GHz. The changes of AFMR modes were observed for H‖c, corresponding to the metamagnetic transition which occurred below TN2. In a phase between TN1 and TN2, we observed an easy-plane type AFMR mode which could not explain a partially disordered model suggested by neutron diffraction experiments.
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 spin-wave excitations of the geometrically frustrated triangular lattice antiferromagnet CuFeO2 have been measured using high resolution inelastic neutron scattering. Antiferromagnetic interactions up to third nearest neighbors in the ab plane (J1, J2, J3, with J{2}/J{1} approximately 0.44 and J{3}/J{1} approximately 0.57), as well as out-of-plane coupling (J{z}, with J{z}/J{1} approximately 0.29) are required to describe the spin-wave dispersion relations, indicating a three-dimensional character of the magnetic interactions. Two energy dips in the spin-wave dispersion occur at the incommensurate wave vectors associated with multiferroic phase and can be interpreted as dynamic precursors to the magnetoelectric behavior in this system.
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