We study geometrically frustrated antiferromagnets with magnetoelastic coupling. Frustration in these systems may be relieved by a structural transition to a low temperature phase with reduced lattice symmetry. We examine the statistical mechanics of this transition and the effects on it of quenched disorder, using Monte Carlo simulations of the classical Heisenberg model on the pyrochlore lattice with coupling to uniform lattice distortions. The model has a transition between a cubic, paramagnetic high-temperature phase and a tetragonal, Neel ordered low-temperature phase. It does not support the spin-Peierls phase, which is predicted as an additional possibility within Landau theory, and the transition is first-order for reasons unconnected with the symmetry analysis of Landau theory. Quenched disorder stabilises the cubic phase, and we find a phase diagram as a function of temperature and disorder strength similar to that observed in ZnCdCrO.
These lecture notes are intended to provide a simple overview of the physics of geometrically frustrated magnets. The emphasis is on classical and semiclassical treatments of the statistical mechanics and dynamics of frustrated Heisenberg models, and on the ways in which the results provide an understanding of some of the main observed properties of these systems.
Starting from the archetypical geometrically frustrated magnetic objects -- equilateral triangle and tetrahedron -- we consider an imaginary object: a multidimensional tetrahedron with spins $1/2$ in the each vertex and equal Heisenberg magnetic exchange along each edge. Many-particle case is obtained by setting dimensionality $d$ to high numbers, hence providing likely the most geometrically frustrated magnetic system ever possible. This problem has an exact solution for each $d$, obtained by simple student-level approach. As a result, this imaginary object clearly demonstrates at $d\to{}\inf…
We investigate the consequences for geometrically frustrated antiferromagnets of weak disorder in the strength of exchange interactions. Taking as a model the classical Heisenberg antiferromagnet with nearest neighbour exchange on the pyrochlore lattice, we examine low-temperature behaviour. We show that random exchange generates long-range effective interactions within the extensively degenerate ground states of the clean system. Using Monte Carlo simulations, we find a spin glass transition at a temperature set by the disorder strength. Disorder of this type, which is generated by random str…
We study the transport properties for a family of geometrically frustrated models on the triangular lattice with an interaction scale far exceeding the single-particle bandwidth. Starting from the interaction-only limit, which can be solved exactly, we analyze the transport and thermodynamic behavior as a function of filling and temperature at the leading non-trivial order in the single-particle hopping. Over a broad range of intermediate temperatures, we find evidence of a dc resistivity scaling linearly with temperature and with typical values far exceeding the quantum of resistance, $h/e^2$…
We show the existence of invariant energy levels in a Kondo lattice model on an isolated complete graph, such as a triangle and a tetrahedron. These energy levels always have fixed eigenenergies $t \pm J/2$, irrespective of the configuration of localized moments ($t$ is the transfer integral of conduction electrons and $J$ is the spin-charge coupling constant). We also extend the analysis to geometrically frustrated lattices by using the complete graphs as basic building blocks. We show that the construction rule for the invariant energy levels leads to the existence condition of localized sta…
Geometrically frustrated magnetic molecules have attracted a lot of interest in the field of molecular magnetism as well as frustrated Heisenberg antiferromagnets. In this article we demonstrate how an approximate diagonalization scheme can be used in order to obtain thermodynamic and spectroscopic information about frustrated magnetic molecules. To this end we theoretically investigate an antiferromagnetically coupled spin system with cuboctahedral structure modeled by an isotropic Heisenberg Hamiltonian.
Above the saturation field, geometrically frustrated quantum antiferromagnets have dispersionless low-energy branches of excitations corresponding to localized spin-flip modes. Transition into a partially magnetized state occurs via condensation of an infinite number of degrees of freedom. The ground state below the phase transition is a magnon crystal, which breaks only translational symmetry and preserves spin-rotations about the field direction. We give a detailed review of recent works on physics of such phase transitions and present further theoretical developments. Specifically, the low-…
The effect of site dilution by non magnetic impurities on the susceptibility of geometrically frustrated antiferromagnets (kagome and pyrochlore lattices) is discussed in the framework of the Generalized Constant Coupling model, for both classical and quantum Heisenberg spins. For the classical diluted pyrochlore lattice, excellent agreement is found when compared with Monte Carlo data. Results for the quantum case are also presented and discussed.
A generalized constant coupling approximation for quantum geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit, we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the static magnetic susceptibility and specific heat are compared with previous results in the framework of this same model for the classical limit. The range of applicability of the model is discussed.
We predict that an external field can induce a spin order in highly frustrated classical Heisenberg magnets. We find analytically stabilization of collinear states by thermal fluctuations at a one-third of the saturation field for kagome and garnet lattices and at a half of the saturation field for pyrochlore and frustrated square lattices. This effect is studied numerically for the frustrated square-lattice antiferromagnet by Monte Carlo simulations for classical spins and by exact diagonalization for $S=1/2$. The field induced collinear states have a spin gap and produce magnetization platea…
The geometrically-frustrated spin glass Y2Mo2O7 has been considered widely to be crystallographically ordered with a unique nearest neighbor magnetic exchange interaction, J. To test this assertion, we present x-ray-absorption fine-structure results for the Mo and Y K edges as a function of temperature and compare them to results from a well-ordered pyrochlore, Tl2Mn2O7. We find that the Mo-Mo pair distances are significantly disordered at approximately right angles to the Y-Mo pairs. These results strongly suggest that lattice disorder nucleates the spin-glass phase in this material.
Using inelastic magnetic neutron scattering we have discovered a localized spin resonance at 4.5 meV in the ordered phase of the geometrically frustrated cubic antiferromagnet $\rm ZnCr_2O_4$. The resonance develops abruptly from quantum critical fluctuations upon cooling through a first order transition to a co-planar antiferromagnet at $T_c=12.5(5)$ K. We argue that this transition is a three dimensional analogue of the spin-Peierls transition.
The search for elementary excitations with fractional quantum numbers is a central challenge in modern condensed matter physics. We explore the possibility in a realistic model for several materials, the spin-1/2 spatially anisotropic frustrated Heisenberg antiferromagnet in two dimensions. By restricting the Hilbert space to that expressed by exact eigenstates of the Heisenberg chain, we derive an effective Schrödinger equation valid in the weak interchain-coupling regime. The dynamical spin correlations from this approach agree quantitatively with inelastic neutron measurements on the triang…
A generalized constant coupling approximation for classical geometrically frustrated antiferromagnets is presented. Starting from a frustrated unit we introduce the interactions with the surrounding units in terms of an internal effective field which is fixed by a self consistency condition. Results for the magnetic susceptibility and specific heat are compared with Monte Carlo data for the classical Heisenberg model for the pyrochlore and kagome lattices. The predictions for the susceptibility are found to be essentially exact, and the corresponding predictions for the specific heat are found…
We determine the magnetic phase diagram of the antiferromagnetic(AF) zigzag spin chain in the strongly frustrated region, using the density matrix renormalization group method. We find the magnetization plateau at 1/3 of the full moment accompanying the spontaneous symmetry breaking of the translation, the cusp singularities above and/or below the plateau, and the even-odd effect in the magnetization curve. We also discuss the formation mechanisms of the plateau and cusps briefly.
We investigate spin diffusion in geometrically frustrated Heisenberg antiferromagnets. It is found that the diffusion constant gradually increases from its high temperature limit as the temperature approaches the peak temperature of the susceptibility. Below the peak, the exponential decrease in the susceptibility leads to a rapid increase in the rate of spin diffusion. Detailed results are presented for the pyrochlore lattice with nearest-neighbor interactions.
SrHo2O4 is a geometrically frustrated compound because the Ho^3+ ions are arranged in a network of triangles and hexagons and coupled with antiferromagnetic exchange interactions. Powder neutron diffraction measurements show that long-range magnetic order is established at T_N = 0.68 K. The low temperature magnetic structure is made up of two distinct components: a k = 0 long-range structure as well as a shorter-range low-dimensional structure with scattering intensity around the (0 0 1/2) position. The diffuse component of the magnetic scattering from SrHo2O4 remains very intense at temperatu…
This paper examines the relation between the spin-wave instabilities of collinear magnetic phases and the resulting non-collinear phases for a geometrically-frustrated triangular-lattice antiferromagnet in the high spin limit. Using a combination of phenomenological and Monte-Carlo techniques, we demonstrate that the instability wave-vector with the strongest intensity in the collinear phase determines the wave-vector of a cycloid or the dominant elastic peak of a more complex non-collinear phase. Our results are related to the observed multi-ferroic phase of Al-doped CuFeO$_2$.
Above 40K, the magnetic susceptibility of the heavy Fermion spinel LiV2O4 has many features in common with those of geometrically frustrated magnetic insulators, while its room temperature resistivity comfortably exceeds the Mott-Regel limit. This suggests that local magnetic moments, and the underlying geometry of the pyrochlore lattice, play an important role in determining its magnetic properties. We extend a recently introduced tetragonal mean field theory for insulating pyrochlore antiferromagnets to the case where individual tetrahedra contain spins of different lengths, and use this as …
Using muon-spin-relaxation measurements we show that the pyrochlore compound Gd2Ti2O7, in its magnetically orderered phase below ~ 1 K, displays persistent spin dynamics down to temperatures as low as 20 mK. The characteristics of the induced muon relaxation can be accounted for by a scattering process involving two magnetic excitations, with a density of states characterized by an upturn at low energy and a small gap depending linearly on the temperature. We propose that such a density of states is a generic feature of geometrically frustrated magnetic materials.
We report the observation of a Griffiths Phase in the geometrically frustrated antiferromagnet DyBaCo${_4}$O${_{7+δ}}$. Its onset is determined using measurements of the thermoremanent magnetization, which is shown to be superior to conventional in-field measurement protocols for the identification of the Griffiths Phase. Within this phase, the temporal relaxation of magnetization exhibits a functional form which is expected for Heisenberg systems, reflecting the nature of spin interactions in this class of materials. Interestingly, the effective Co${^{2+}}$/Co${^{3+}}$ ratio tailored by varyi…
Spin crossover materials contain metal ions that can access two spin-states: one low-spin (LS), the other high-spin (HS). We propose that frustrated elastic interactions can give rise to spin-state ices -- phases of matter without long-range order, characterized by a local constraint or `ice rule'. The low-energy physics of spin-state ices is described by an emergent divergence-less gauge field with a gap to topological excitations that are deconfined quasi-particles with spin fractionalized midway between the spins of the LS and HS states.
We have formulated a twist operator argument for the geometrically frustrated quantum spin systems on the kagome and triangular lattices, thereby extending the application of the Lieb-Schultz-Mattis (LSM) and Oshikawa-Yamanaka-Affleck (OYA) theorems to these systems. The equivalent large gauge transformation for the geometrically frustrated lattice differs from that for non-frustrated systems due to the existence of multiple sublattices in the unit cell and non-orthogonal basis vectors. Our study for the $S=1/2$ kagome Heisenberg antiferromagnet at zero external magnetic field gives a criterio…
We present a comprehensive review of nuclear magnetic resonance (NMR) studies performed on three nanoscale molecular magnets with different configurations of geometrically frustrated antiferromagnetic (AFM) triangles, new spin frustration systems with different novel structures: (1) the isolated single AFM triangle K$_6$[V$_{15}$As$_6$O$_{42}$(H$_2$O)]$\cdot$8H$_2$O (in short V15), (2) the spin ball [Mo$_{72}$Fe$_{30}$O$_{252}$(Mo$_2$O$_7$(H$_2$O))$_2$ (Mo$_2$O$_8$H$_2$(H$_2$O))(CH$_3$COO)$_{12}$(H$_2$O)$_{91}$]$\cdot$150H$_2$O (in short Fe30 spin ball), and (3) the twisted triangular spin tub…
We investigate the doping of a geometrically frustrated spin ladder with static holes by a complementary approach using exact diagonalization and quantum dimers. Results for thermodynamic properties, the singlet density of states, the hole-binding energy and the spin correlations will be presented. For the undoped systems the ground state is non-degenerate, with translationally invariant nearest-neighbor spin correlations. In the doped case, we find that static holes polarize their vicinity by a localization of singlets in order to reduce the frustration. This polarization induces short range …
Magnetic excitations in the triangular-lattice Heisenberg antiferromagnet (TLHA) CuCrO2 were studied using single-crystal inelastic neutron scattering. A diffusive quasielastic component that persisted without developing a correlation length over a wide temperature range both below and above the ordering temperature was observed. Furthermore, characteristic momentum dependence was observed that was reproduced using minimum spin clusters. The robust spin clusters contrast with conventional magnetic ordering and may be universal in TLHAs.
By considering the constrained motion of classical spins in a geometrically frustrated magnet, we find a dynamical freezing temperature below which the system gets trapped in metastable states with a "frozen" moment and dynamical heterogeneities. The residual collective degrees of freedom are strongly correlated, and by spontaneously forming aggregates, they are unable to reorganize the system. The phase space is then fragmented in a macroscopic number of disconnected sectors (broken ergodicity), resulting in self-induced disorder and "thermodynamic" anomalies, measured by the loss of a finite…
The correct stacking of hexagonal layers is used to obtain accurate estimates for the exchange and anisotropy parameters of the geometrically-frustrated antiferromagnet CuFeO$_2$. 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 $\uudd $ phase below 7 T are used to identify the magnetic unit cell of the metamagnetic $\uuudd $ phase, which contains two hexagonal layers and 10 Fe$^{3+}$ spins.
In the pyrochlore compounds, Tb$_2$Ti$_2$O$_7$ and Tb$_2$Sn$_2$O$_7$, only the Tb$^{3+}$ ions are magnetic. They exhibit quite abnormal -- and, in view of their chemical similarity, strikingly different -- magnetic behaviour, as probed by neutron diffraction at ambient and applied pressure. Tb$_2$Ti$_2$O$_7$ is a cooperative paramagnet (`spin liquid'), without long range order at ambient pressure; however, it does become ordered under pressure. By contrast, Tb$_2$Sn$_2$O$_7$ enters an "ordered spin ice" state already at ambient pressure. We analyse a simple model which already clearly exhibits…
We investigate a (semi-)metal to insulator transition (MIT) realized in geometrically frustrated electron systems on the basis of the Hubbard model on a three-dimensional pyrochlore lattice and a two-dimensional checkerboard lattice. Using the renormalization group method and mean field analysis, we show that in the half-filling case, MIT occurs as a result of the interplay between geometrical frustration and electron correlation. In the insulating phase, which has a spin gap, the spin rotational symmetry is not broken, while charge ordering exists. The charge ordered state is stabilized so as…
Charge dynamics in an interacting fermionic model on a geometrically frustrated lattice are examined. We analyze a spinless fermion model on a paired triangular lattice, an electronic model for layered iron oxides, in zero and finite temperatures by the exact diagonalization methods. We focus on the two charge ordered (CO) phases, termed CO_1/2 and CO_1/3, which, respectively, are realized by the inter-site Coulomb interaction and the quantum/thermal fluctuations. The optical spectra in CO_1/3 show multiple components and their low-energy weights are survived even below the ordering temperatur…
We have measured the thermal conductivity of the geometrically frustrated quasi-onedimensional spin system Cu$_3$Mo$_2$O$_9$ in magnetic fields. A contribution of the thermal conductivity due to spins has been observed in the thermal conductivity along the spin chains. The thermal conductivity due to phonons, $κ_{\rm phonon}$, has been found to decrease by the application of a magnetic field, which has been explained as being due to the reduction in the spin gap originating from the spin-singlet dimers. Moreover, it has been found that $κ_{\rm phonon}$ increases with increasing field in high f…
We report neutron scattering studies of the spin correlations of the geometrically frustrated pyrochlore Tb2Mo2O7 using single crystal samples. This material undergoes a spin-freezing transition below Tg~24 K, similar to Y2Mo2O7, and has little apparent chemical disorder. Diffuse elastic peaks are observed at low temperatures, indicating short-range ordering of the Tb moments in an arrangement where the Tb moments are slightly rotated from the preferred directions of the spin ice structure. In addition, a Q-independent signal is observed which likely originates from frozen, but completely unco…
We report single-crystal neutron diffraction studies on a spinel antiferromagnet GeCo$_2$O$_4$, which exhibits magnetic order with a trigonal propagation vector and tetragonal lattice expansion ($c/a\simeq1.001$) below $T_{\rm N}=21$ K. For this inconsistency between spin and lattice in symmetry, magnetic Bragg reflections with a tetragonal propagation vector were discovered below $T_{\rm N}$. We discuss spin and orbital states of Co$^{2+}$ ion underlying the new magnetic component.
Neutron diffraction and bulk measurements are used to determine the nature of the low-temperature ordered state in LiCu$_2$O$_2$, a $S=1/2$ spin-chain compound with competing interactions. The magnetic structure is found to be helimagnetic, with a propagation vector $(0.5,ζ,0)$, $ζ=0.174$. The nearest-neighbor exchange constant and frustration ratio are estimated to be $J=5.8$ meV and $J_2/J_1=0.29$, respectively. For idealized spin chains these parameter values would signify a gapped spin-liquid ground state. Long-range ordering is attributed to intrinsic non-stoichiometry.
Motivated by experiments on the double perovskites La2ZnIrO6 and La2MgIrO6, we study the magnetism of spin-orbit coupled j=1/2 iridium moments on the three-dimensional, geometrically frustrated, face-centered cubic lattice. The symmetry-allowed nearest-neighbor interaction includes Heisenberg, Kitaev, and symmetric off-diagonal exchange. A Luttinger-Tisza analysis shows a rich variety of orders, including collinear A-type antiferromagnetism, stripe order with moments along the [111]-direction, and incommensurate non-coplanar spirals, and we use Monte Carlo simulations to determine their magnet…
By using the density matrix renormalization group method, we investigate ground- and excited-state properties of the e_g-orbital degenerate Hubbard model at quarter filling for two kinds of lattices, zigzag chain and ladder. In the zigzag chain, the system is effectively regarded as a decoupled double chain of the S=1/2 antiferromagnetic Heisenberg model, and the spin gap is approximately zero, similar to the case of weakly coupled Heisenberg chains. On the other hand, in the ladder, the spin correlation on the rung remains robust and the spin gap exists.
Structural and magnetic properties of the geometrically frustrated layered compound YBaCo4O7 have been studied by magnetization and neutron diffraction. A layered type crystal structure, with alternating tetrahedral layers of Kagomé and triangular types, along the c axis (hexagonal symmetry, space group P63mc) has been found. The oxygen content of the present compound was determined by iodometric titration to be 7.00{\pm}0.01. Presence of a short-range antiferromagnetic ordering (below TN ~ 110 K) has been concluded from the appearance of an addition broad magnetic peak (at Q ~ 1.35 Å-1) in th…
From the electrical resistivity and ac susceptibility measurements down to $T$ = 40 mK, a rich temperature-field phase diagram has been constructed for the geometrically frustrated heavy-fermion compound CePdAl. In the limit of zero temperature, the field-induced suppression of the antiferromagnetism in this compound results in a sequence of phase transitions/corssovers, rather than a single critical point, in a critical region of field 3$-$5 T. In the lowest temperature region, a power-law description of the temperature-dependent resistivity yields $A$$\cdot$$T^n$ with $n$$>$2 for all applied…
We present a detailed study of magnetism in LuFe2O4, combining magnetization measurements with neutron and soft x-ray diffraction. The magnetic phase diagram in the vicinity of T_N involves a metamagnetic transition separating an antiferro- and a ferrimagnetic phase. For both phases the spin structure is refined by neutron diffraction. Observed diffuse magnetic scattering far above T_N is explained in terms of near degeneracy of the magnetic phases.
We study a frustrated 3D antiferromagnet of stacked $J_1 - J_2$ layers. The intermediate 'quantum spin liquid' phase, present in the 2D case, narrows with increasing interlayer coupling and vanishes at a triple point. Beyond this there is a direct first-order transition from N{\' e}el to columnar order. Possible applications to real materials are discussed.
The local atomic and magnetic structures of the compounds $A$MnO$_2$ ($A$ = Na, Cu), which realize a geometrically frustrated, spatially anisotropic triangular lattice of Mn spins, have been investigated by atomic and magnetic pair distribution function analysis of neutron total scattering data. Relief of frustration in CuMnO$_2$ is accompanied by a conventional cooperative symmetry-lowering lattice distortion driven by Néel order. In NaMnO$_2$, however, the distortion has a short-range nature. A cooperative interaction between the locally broken symmetry and short-range magnetic correlations …
We argue that collinearly ordered states which exist in strongly frustrated spin systems for special rational values of the magnetization are stabilized by thermal as well as quantum fluctuations. These general predictions are tested by Monte Carlo simulations for the classical and Lanczos diagonalization for the S=1/2 frustrated square-lattice antiferromagnet.
The anomalous Hall effect is investigated for ferromagnetic Fe3Sn2 single crystal with geometrically frustrated kagome bilayer of Fe. The scaling behavior between anomalous Hall resistivity rho_{xy}^{A} and longitudinal resistivity rho_{xx} is quadratic and further analysis implies that the AHE in Fe3Sn2 single crystal should be dominated by the intrinsic Karplus-Luttinger mechanism rather than extrinsic skew-scattering or side-jump mechanisms. Moreover, there is a sudden jump of anomalous Hall conductivity sigma_{xy}^{A} appearing at about 100 K where the spin-reorientation transition from th…
New frustrated antiferromagnetic compounds CuRE2Ge2O8 (RE=Pr, Nd, Sm, Eu) have been investigated using high-resolution x-ray diffraction, magnetic and heat capacity measurements. These systems show different magnetic lattices depending on rare-earth element. The nonmagnetic Eu compound is a S=1/2 two-dimensional triangular antiferromagnetic lattice oriented in the ac plane with geometrical frustration. On the other hand, the Pr, Nd, and Sm compounds show a three-dimensional honeycomb-tunnel-like lattice made of RE^3+ running along the a axis with the characteristic behavior of frustrated antif…
This work examines the critical anisotropy required for the local stability of the collinear ground states of a geometrically-frustrated triangular-lattice antiferromagnet (TLA). Using a Holstein-Primakoff expansion, we calculate the spin-wave frequencies for the 1, 2, 3, 4, and 8-sublattice (SL) ground states of a TLA with up to third neighbor interactions. Local stability requires that all spin-wave frequencies are real and positive. The 2, 4, and 8-SL phases break up into several regions where the critical anisotropy is a different function of the exchange parameters. We find that the criti…
We report synchrotron radiation diffraction and muon spin rotation (muSR) measurements on the frustrated pyrochlore magnet Tb2Ti2O7. The powder diffraction study of a crushed crystal fragment does not reveal any structural change down to 4 K. The muSR measurements performed at 20 mK on a mosaic of single crystals with an external magnetic field applied along a three-fold axis are consistent with published a.c. magnetic-susceptibility measurements at 16 mK. While an inflection point could be present around an internal field intensity slightly above 0.3 T, the data barely support the presence of…
The crystal structure of Ba4NbRu3O12 is based on triangular planes of elongated Ru3O12 trimers oriented perpendicular to the plane. We report that it is semiconducting, that its Weiss temperature and effective magnetic moment are -155 K and 2.59 μB/f.u. respectively, and that magnetic susceptibility and specific heat data indicate that it exhibits magnetic ordering near 4 K. The presence of a high density of low energy states is evidenced by a substantial Sommerfeld-like T-linear term (gamma = 31(2) mJ/mole-K^2) in the specific heat. Electronic structure calculations reveal that the electronic…
The frustrated magnet has been regarded as a system that could be a promising host material for the quantum spin liquid (QSL). However, it is difficult to determine the spin configuration and the corresponding mechanism in this system, because of its geometrical frustration (i.e., crystal structure and symmetry). Herein, we systematically investigate one of the geometrically frustrated magnets, the TbB$_{4}$ compound. Using resonant soft x-ray scattering (RSXS), we explored its spin configuration, as well as Tb's quadrupole. Comprehensive evaluations of the temperature and photon energy / pola…
We present a systematic investigation of the low-frequency charge carrier dynamics in different charge states of the organic conductors $θ$-(BEDT-TTF)$_2$$M$Zn(SCN)$_4$ with $M$=Rb,Tl, which result from quenching or relaxing the charge degrees of freedom on a geometrically frustrated triangular lattice. Due to strong electronic correlations these materials exhibit a charge-ordering transition, which can be kinetically avoided by rapid cooling resulting in a so-called charge-glass state without long-range order. The combination of fluctuation spectroscopy and a heat pulse method allows us to st…
The critical cooling rate $R_{\rm c}$ above which charge ordering is kinetically avoided upon cooling, which results in charge-glass formation, was investigated for the geometrically frustrated system $θ$-(BEDT-TTF)$_2X$. X-ray diffraction experiments revealed that $θ$-(BEDT-TTF)$_2$TlCo(SCN)$_4$ exhibits a horizontally charge-ordered state, and kinetic avoidance of this state requires rapid cooling of faster than 150 K/min. This value is markedly higher than that reported for two other isostructural $θ$-type compounds, thus demonstrating the lower charge-glass-forming ability of $X$ $=$ TlCo(…
The spin dynamics of the geometrically frustrated triangular antiferromagnet multiferroic CuCrO2 have been mapped out using inelastic neutron scattering. The relevant spin Hamiltonian parameters modelling the incommensurate modulated helicoid have been determined, and correspond to antiferromagnetic nearest and next-nearest neighbour interactions in the ab plane, with a strong planar anisotropy. The weakly dispersive excitation along c reflects the essentially two-dimensional character of the magnetic interactions and according to classical energy calculations it is weakly ferromagnetic. Our r…
We measured two magnetic modes with finite and discrete energies in an antiferromagnetic ordered phase of a geometrically frustrated magnet MgCr2O4 by single-crystal inelastic neutron scattering, and clarified the spatial spin correlations of the two levels: one is an antiferromagnetic hexamer and the other is an antiferromagnetic heptamer. Since these correlation types are emblematic of quasielastic scattering with geometric frustration, our results indicate instantaneous suppression of lattice distortion in an ordered phase by spin-lattice coupling, probably also supported by orbital and cha…
We have investigated the magnetic, dielectric and magnetodielectric (MDE) behavior of a geometrically frustrated spin-chain system, Ca3Co1.4Rh0.6O6, in the single crystalline form for different orientations. The results bring out that the magnetic behavior of this compound is by itself interesting in the sense that this compound exhibits an anisotropic glassy-like magnetic behavior with a huge frequency dependence of ac susceptibility peak for an orientation along the spin-chain in the range 30-60 K; this behavior is robust to applications of large external magnetic fields (H) unlike in canoni…
Using Monte Carlo simulations, we study the critical behavior of two models of frustrated XY antiferromagnets with a collinear spin ordering and with an additional twofold degeneracy of the ground state. We consider a classic antiferromagnet on a body-centered cubic lattice with an additional antiferromagnetic exchange interaction between next-nearest spins, and a ferromagnet with an extra antiferromagnetic intralayer exchange. In both models, a single first-order transition on the discrete and continuous order parameters is found. Observed critical pseudo-exponents are in agreement with expon…
We use a Monte Carlo simulation to study the diluted antiferromagnetic Ising model on the frustrated lattices including the pyrochlore lattice to show the dilution effects. Using the Wang-Landau algorithm, which directly calculates the energy density of states, we accurately calculate the entropy of the system. We discuss the nonmonotonic dilution concentration dependence of residual entropy for the antiferromagnetic Ising model on the pyrochlore lattice, and compare it to the generalized Pauling approximation proposed by Ke et al. [Phys. Rev. Lett. 99, 137203 (2007)]. We also investigate othe…
Effects of Fe-substitution on the crystal structure and magnetic correlations of the geometrically frustrated antiferromagnets YBaCo4-xFexO7+δ (x = 0, 0.2, 0.4, 0.5, 0.6, and 0.8) have been studied by neutron diffraction, Mössbauer spectroscopy, and ac susceptibility. The compounds YBaCo4-xFexO7+δ have a special layered-type crystal structure with an alternating Kagomé (6c site) and triangular (2a site) layers along the c axis. Fe3+ ions are found to be substituted at both the crystallographic 2a and 6c sites of Co ions. Mössbauer results show a high spin state of Fe3+ ions in a tetrahedral co…
