We present a microscopic magnetic model for the spin-liquid candidate volborthite Cu3V2O7(OH)2(H2O)2. The essentials of this DFT-based model are (i) the orbital ordering of Cu(1) 3d 3z2-r2 and Cu(2) 3d 3x2-y2, (ii) three relevant couplings J_ic, J_1 and J_2, (iii) the ferromagnetic nature of J_1 and (iv) frustration governed by the next-nearest-neighbor exchange interaction J_2. Our model implies magnetism of frustrated coupled chains in contrast to the previously proposed anisotropic kagome model. Exact diagonalization studies reveal agreement with experiments.
Motivated by recent experiments on volborthite single crystals showing a wide 1/3-magnetization plateau, we perform microscopic modeling by means of density functional theory (DFT) with the single-crystal structural data as a starting point. Using DFT+U, we find four leading magnetic exchanges: antiferromagnetic J and J2, as well as ferromagnetic J' and J1. Simulations of the derived spin Hamiltonian show good agreement with the experimental low-field magnetic susceptibility and high-field magnetization data. The 1/3-plateau phase pertains to polarized magnetic trimers formed by strong J bonds…
Volborthite compound is one of the very few realizations of S=1/2 quantum spins on a highly frustrated kagome-like lattice. Low-T SQUID measurements reveal a broad magnetic transition below 2K which is further confirmed by a peak in the 51V nuclear spin relaxation rate (1/T1) at 1.4K$\pm$0.2K. Through 51V NMR, the ground state (GS) appears to be a mixture of different spin configurations, among which 20% correspond to a well defined short range order, possibly of the $\sqrt{3} \times \sqrt{3}$ type. While the freezing involve all the Cu$^{2+}$ spins, only 40% of the copper moment is actually f…
We determined the spin exchanges between the Cu2+ ions in the kagome layers of volborthite, Cu3V2O7(OH)2x2H2O, by performing the energy-mapping analysis based on DFT+U calculations, to find that the kagomé layers of Cu2+ ions are hardly spin-frustrated, and the magnetic properties of volborthite below ~75 K should be described by very weakly interacting antiferromagnetic uniform chains made up of effective S=1/2 pseudospin units. This conclusion was verified by synthesizing single crystals of not only Cu3V2O7(OH)2x2H2O but also its deuterated analogue Cu3V2O7(OD)2x2D2O and then by investigatin…
We have synthesized high-quality single crystals of volborthite, a seemingly distorted kagome antiferromagnet, and carried out high-field magnetization measurements up to 74 T and 51V NMR measurements up to 30 T. An extremely wide 1/3 magnetization plateau appears above 28 T and continues over 74 T at 1.4 K, which has not been observed in previous study using polycrystalline samples. NMR spectra reveal an incommensurate order (most likely a spin-density wave order) below 22 T and a simple spin structure in the plateau phase. Moreover, a novel intermediate phase is found between 23 and 26 T, wh…
We report single-crystal 51V NMR studies on volborthite Cu3V2O7(OH)2 2H2O, which is regarded as a quasi-two-dimensional frustrated magnet with competing ferromagnetic and antiferromagnetic interactions. In the 1/3 magnetization plateau above 28 T, the nuclear spin-lattice relaxation rate 1/T1 indicates an excitation gap with a large effective g factor in the range of 4.6-5.9, pointing to magnon bound states. Below 26 T where the gap has closed, the NMR spectra indicate small internal fields with a Gaussian-like distribution, whereas 1/T1 shows a power-law-like temperature dependence in the par…
Volborthite offers an interesting example of a highly frustrated quantum magnet in which ferromagnetic and antiferromagnetic interactions compete on anisotropic kagome lattices. A recent density functional theory calculation has provided a magnetic model based on coupled trimers, which is consistent with a broad 1/3-magnetization plateau observed experimentally. Here we study the effects of Dzyaloshinskii-Moriya (DM) interactions in volborthite. We derive an effective model in which pseudospin-1/2 moments emerging on trimers form a network of an anisotropic triangular lattice. Using the effect…
The Kagome-lattice-based material, Volborthite, $\mathrm{Cu_3 V_2 O_7 (OH)_2 \cdot 2 H_2 O}$, has been considered as a promising platform for discovery of unusual quantum ground states due to the frustrated nature of spin interactions. Here we explore possible quantum spin liquid and magnetically ordered phases in a two-dimensional non-symmorphic lattice described by $p2gg$ layer space group, which is consistent with the spatial anisotropy of the spin model derived from density functional theory (DFT) for Volborthite. Using the projective symmetry group (PSG) analysis and Schwinger boson mean …
When quantum fluctuations destroy underlying long-range ordered states, novel quantum states emerge. Spin-liquid (SL) states of frustrated quantum antiferromagnets, in which highly-correlated spins keep to fluctuate down to very low temperatures, are prominent examples of such quantum states. SL states often exhibit exotic physical properties, but the precise nature of the elementary excitations behind such phenomena remains entirely elusive. Here we utilize thermal Hall measurements that can capture the unexplored property of the elementary excitations in SL states, and report on the observat…
We use a semiclassical large-$S$ expansion to study a plateau at $1/3$ saturation in the magnetization curve of a frustrated ferrimagnet on a spatially anisotropic kagomé lattice. The spins have both ferromagnetic and antiferromagnetic nearest-neighbor Heisenberg couplings, and a frustrating next-nearest-neighbor coupling in one lattice direction. The magnetization plateau appears at the classical level for a certain range of couplings, and quantum fluctuations significantly broaden it at both ends. Near the region of the phase diagram where the classical plateau destabilizes, we find an exoti…
Ultrasound velocity measurements of the orbitally-frustrated GeCo$_2$O$_4$ reveal unusual elastic instabilities due to the phonon-spin coupling within the antiferromagnetic phase. Shear moduli exhibit anomalies arising from the coupling to short-range ferromagnetic excitations. Diplike anomalies in the magnetic-field dependence of elastic moduli reveal magnetic-field-induced orbital order-order transitions. These results strongly suggest the presence of geometrical orbital frustration which causes novel orbital phenomena within the antiferromagnetic phase.
Motivated by recent interest in quasi-one-dimensional compound CaV2O4, we study the ground states of a spin-orbital chain characterized by an Ising-like orbital Hamiltonian and frustrated interactions between S=1 spins. The on-site spin-orbit interaction and Jahn-Teller effect compete with inter-site superexchange leading to a rich phase diagram in which an antiferro-orbital phase is separated from the orbital paramagnet by a continuous Ising transition. Two distinct spin liquids depending on the underlying orbital order are found in the limit of small spin-orbit coupling. In the opposite limi…
We consider the superexchange in `frustrated' Jahn-Teller systems, such as the transition metal oxides NaNiO_2, LiNiO_2, and ZnMn_2O_4, in which transition metal ions with doubly degenerate orbitals form a triangular or pyrochlore lattice and are connected by the 90-degree metal-oxygen-metal bonds. We show that this interaction is much different from a more familiar exchange in systems with the 180-degree bonds, e.g. perovskites. In contrast to the strong interplay between the orbital and spin degrees of freedom in perovskites, in the 90-degree exchange systems spins and orbitals are decoupled…
Ultrasound velocity measurements of the orbital-degenerate frustrated spinel MgV$_2$O$_4$ are performed in the high-purity single crystal which exhibits successive structural and antiferromagnetic phase transitions, and in the disorder-introduced single crystal which exhibits spin-glass-like behavior. The measurements reveal that two-types of unusual temperature dependence of the elastic moduli coexist in the cubic paramagnetic phase, which are resolved by magnetic-field and disorder sensitivities: huge Curie-type softening with decreasing temperature, and concave temperature dependence with a…
A layered iron oxide \rfeo ($R$: rare-earth elements) is an exotic dielectric material with charge-order (CO) driven electric polarization and magnetoelectric effect caused by spin-charge coupling. In this paper, a theory of electronic structure and dielectric property in \rfeo is presented. Charge frustration in paired-triangular lattices allows a charge imbalance without inversion symmetry. Spin frustration induces reinforcement of this polar CO by a magnetic ordering. We also analyze an orbital model for the Fe ion which does not show a conventional long-range order.
Layered kagome-lattice 3d transition metals are emerging as an exciting platform to explore the frustrated lattice geometry and quantum topology. However, the typical kagome electronic bands, characterized by sets of the Dirac-like band capped by a phase-destructive flat band, have not been clearly observed, and their orbital physics are even less well investigated. Here, we present close-to-textbook kagome bands with orbital differentiation physics in CoSn, which can be well described by a minimal tight-binding model with single-orbital hopping in Co kagome lattice. The capping flat bands wit…
We have measured extremely large coercive magnetic fields of up to 55~T in Sr$_3$NiIrO$_6$, with a switched magnetic moment $\approx 0.8~μ_{\rm B}$ per formula unit. As far as we are aware, this is the largest coercive field observed thus far. This extraordinarily hard magnetism has a completely different origin from that found in conventional ferromagnets. Instead, it is due to the evolution of a frustrated antiferromagnetic state in the presence of strong magnetocrystalline anisotropy due to the overlap of spatially-extended Ir$^{4+}$ 5$d$ orbitals with oxygen 2$p$ and Ni$^{2+}$ 3$d$ orbital…
We study the $3d$ substitution in $4d$ transition metal oxides in the cases of $3d^3$ doping at either $3d^2$ or $4d^4$ sites which realize orbital dilution. We derive the effective $3d-4d$ (or $3d-3d$) superexchange in a Mott insulator with different ionic valencies, underlining the emerging structure of the spin-orbital coupling between the impurity and the host sites and demonstrate that it is qualitatively different from that encountered in the host itself. This derivation shows that the interaction between the host and the impurity depends in a crucial way on the type of doubly occupied $…
CuAl2O4 is a normal spinel oxide having quantum spin, S=1/2 for Cu2+. It is a rather unique feature that the Cu2+ ions of CuAl2O4 sit at a tetrahedral position, not like the usual octahedral position for many oxides. At low temperatures, it exhibits all the thermodynamic evidence of a quantum spin glass. For example, the polycrystalline CuAl2O4 shows a cusp centered at ~2 K in the low-field dc magnetization data and a clear frequency dependence in the ac magnetic susceptibility while it displays logarithmic relaxation behavior in a time dependence of the magnetization. At the same time, there …
The $A$-site spinel NiRh$_2$O$_4$ is the only known realization of a spin-1 diamond lattice magnet and is predicted to host unconventional magnetic phenomena driven by frustrated nearest and next-nearest neighbor exchange as well as orbital degeneracy. Previous works found no sign of magnetic order but found a gapped dispersive magnetic excitation indicating a possible valence bond magnetic ground state. However, the presence of many competing low energy degrees of freedom and limited empirical microscopic constraints complicates further analysis. Here, we carry out resonant inelastic x-ray sc…
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.
The emergence of complex electronic behaviour from simple ingredients has resulted in the discovery of numerous states of matter. Many examples are found in systems exhibiting geometric magnetic frustration, which prevents simultaneous satisfaction of all magnetic interactions. This frustration gives rise to complex magnetic properties such as chiral spin structures orbitally-driven magnetism, spin-ice behavior exhibiting Dirac strings with magnetic monopoles, valence bond solids, and spin liquids. Here we report the synthesis and characterization of LiZn2Mo3O8, a geometrically frustrated anti…
The interplay of non-local Coulomb repulsion and Hund's coupling in the d-orbital manifold in frustrated triangular lattices is analyzed by a mutliband extended Hubbard model. We find a rich phase diagram with several competing phases, including a robust pinball liquid phase, which is an unconventional metal characterized by threefold charge order, bad metallic behavior and the emergence of high spin local moments. Our results naturally explain the anomalous charge-ordered metallic state observed in the triangular layered compound AgNiO2. The potential relevance to other triangular transition …
We present a computational study of the layered copper oxychloride [CuCl]LaNb(2)O(7) that has been recently proposed as a spin-1/2 frustrated square lattice compound. Our results evidence an orbitally degenerate ground state for the reported tetragonal crystal structure and reveal a Jahn-Teller-type structural distortion. This distortion heavily changes the local environment of copper -- CuO(2)Cl(2) plaquettes are formed instead of CuO(2)Cl(4) octahedra -- and restores the single-orbital scenario typical for copper oxides and oxyhalides. The calculated distortion is consistent with the availab…
The candidate magnetoelectric Pb3Mn7O15 has a structure consisting of 1/3 filled Kagome layers linked by ribbons of edge-sharing octahedra in the stacking direction. Previous reports have indicated a complex hexagonal-orthorhombic structural transition upon cooling to room temperature, although its origins are uncertain. Here both structures are revisited using a combination of neutron and synchrotron X-ray diffraction data. Large shifts of oxygen positions are detected which show that the interlayer sites and those which occupy voids in the kagome lattice are trivially charge ordered in both …
Dielectric and magnetic phenomena in spin and charge frustrated system RFe2O4 (R is a rare-earth metal ion) are studied. An electronic model for charge, spin and orbital degrees in a pair of triangular-lattice planes is derived. We analyze this model by utilizing the mean-field approximation and the Monte-Carlo simulation in a finite size cluster. A three fold-type charge ordered structure with charge imbalance between the planes is stabilized in finite temperatures. This polar charge order is reinforced by spin ordering of Fe ions. This novel magneto-dielectric phenomenon is caused by spin fr…
FeF$_3$, with its half-filled Fe$^{3+}$ $3d$ orbital, hence zero orbital angular momentum and $S=5/2$, is often put forward as a prototypical highly-frustrated classical Heisenberg pyrochlore antiferromagnet. By employing {\it ab initio} density functional theory (DFT), we obtain an effective spin Hamiltonian for this material. This Hamiltonian contains nearest-neighbor antiferromagnetic Heisenberg, bi-quadratic and Dzyaloshinskii-Moriya interactions as dominant terms and we use Monte Carlo simulations to investigate the nonzero temperature properties of this minimal model. We find that upon d…
The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the $e_{g}$ Mott insulator Ba$_{3}$CuSb$_{2}$O$_{9}$ and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantu…
In the light of recent interesting experimental work on MgV$_2$O$_4$ we employ the density functional theory to investigate the crucial role played by different interaction parameters in deciding its electronic and magnetic properties. The strong Coulomb correlation in presence of antiferromagnetic (AFM) coupling is responsible for the insulating ground state. In the ground state the $d_{xz}$ and $d_{yz}$ orbitals are ordered and intra-chain vanadium ions are antiferromagnetically coupled. The calculation gives small spin-orbit coupling (SOC), which provides a tilt of $\sim11.3^0$ to the magne…
We investigate the frustrated magnetic interactions in cubic transition metal oxides with orbital degeneracy. The $e_g$ orbitals order easier and their ordering explains the $A$-type antiferromagnetic phase in KCuF$_3$ and LaMnO$_3$. In $t_{2g}$ systems the magnetic order changes at a transition from an orbital liquid to orbital ordered states. The fluctuations of $t_{2g}$ orbitals play a prominent role in LaVO$_3$ and YVO$_3$, where they compete with the Jahn-Teller effect and trigger the C-type antiferromagnetic order.
The pronounced enhancement of the effective mass is the primary phenomenon associated with strongly correlated electrons. In the presence of local moments, the large effective mass is thought to arise from Kondo coupling, the interaction between itinerant and localised electrons. However, in d electron systems, the origin is not clear because of the competing Hund's rule coupling. Here we experimentally address the microscopic origin for the heaviest d fermion in a vanadium spinel LiV2O4 having geometrical frustration. Utilising orbital-selective 51V NMR, we elucidate the orbital-dependent loc…
The crossover from localized- to itinerant-electron behavior is associated with many intriguing phenomena in condensed-matter physics. In this paper, we investigate the crossover from localized to itinerant regimes in the spinel system Mn$_{1-x}$Co$_x$V$_2$O$_4$. At low Co doping, orbital order (OO) of the localized electrons on the V3+ ions suppresses magnetic frustration by triggering a tetragonal distortion. With Co doping, electronic itinerancy melts the OO and suppresses the structural phase transition while the reduced spin-lattice coupling produces magnetic frustration. Neutron scatteri…
In this work, we study a biquadratic Heisenberg model with coupled orbital degree of freedom using Monte Carlo simulation in order to investigate the phase transitions in iron-based superconductors. The antiferro-quadrupolar state, which may be related to the magnetism of FeSe [Phys. Rev. Lett. 115, 116401 (2015)], is stabilized by the anisotropic biquadratic interaction induced by a ferro-orbital-ordered state. It is revealed that the orbital and nematic transitions occur at the same temperature for all the cases, supporting the mechanism of the orbital-driven nematicity as revealed in most r…
We investigate the electronic structure of Cs$_2$CuCl$_4$, a material discussed in the framework of a frustrated quantum antiferromagnet, by means of resonant inelastic x-ray scattering (RIXS) and Density Functional Theory (DFT). From the non-dispersive highly localized dd excitations, we resolve the crystal field splitting of the Cu$^{2+}$ ions in a strongly distorted tetrahedral coordination. This allows us to model the RIXS spectrum within the Crystal Field Theory (CFT), assign the dd orbital excitations and retrieve experimentally the values of the crystal field splitting parameters D$_q$,…
We show theoretically that spin and orbital degrees of freedom in the pyrochlore oxide Y2Mo2O7, which is free of quenched disorder, can exhibit a simultaneous glass transition, working as dynamical randomness to each other. The interplay of spins and orbitals is mediated by the Jahn-Teller lattice distortion that selects the choice of orbitals, which then generates variant spin exchange interactions ranging from ferromagnetic to antiferromagnetic ones. Our Monte Carlo simulations detect the power-law divergence of the relaxation times and the negative divergence of both the magnetic and dielec…
Mn$_3$O$_4$ is a spin frustrated magnet that adopts a tetragonally distorted spinel structure at ambient conditions and a CaMn$_2$O$_4$-type postspinel structure at high pressure. We conducted both optical measurements and \emph{ab} \emph{initio} calculations, and systematically studied the electronic band structures of both the spinel and postspinel Mn$_3$O$_4$ phases. For both phases, theoretical electronic structures are consistent with the optical absorption spectra, and display characteristic band-splitting of the conduction band. The band gap obtained from the absorption spectra is 1.91(…
The evolution of spin- and orbital-ordered states has been systematically investigated for a series of insulating perovskites $R$MnO$_3$ ($R$=La,Pr,Nd,...). $R$MnO$_3$ with a large GdFeO$_3$-type distortion is regarded as a frustrated spin system having ferromagnetic nearest-neighbor and antiferromagnetic (AF) next-nearest-neighbor (NNN) interactions within a MnO$_2$ plane. The staggered orbital order associated with the GdFeO$_3$-type distortion induces the anisotropic NNN interaction, and yields the unique sinusoidal and $E$-type ("up-up-down-down") AF ordered states in the distorted perovsk…
The formation of a spin glass usually requires both structural disorder and frustrated magnetic interactions. Consequently, the origin of spin-glass behaviour in Y$_2$Mo$_2$O$_7$ $-$ in which magnetic Mo$^{4+}$ ions occupy a frustrated pyrochlore lattice with minimal compositional disorder $-$ has been a longstanding question. Here, we use neutron and X-ray pair-distribution function (PDF) analysis to develop a disorder model that resolves apparent incompatibilities between previously-reported PDF, EXAFS and NMR studies and provides a new and physical mechanism for spin-glass formation. We sho…
Quantum spin-1/2 kagome Heisenberg antiferromagnet is the representative frustrated system possibly hosting a spin liquid. Clarifying the nature of this elusive topological phase is a key challenge in condensed matter, however, even identifying it still remains unsettled. Here, we apply a magnetic field and discover a series of spin gapped phases appearing at five different fractions of magnetization by means of grand canonical density matrix renormalization group, an unbiased state-of-art numerical technique. The magnetic field dopes magnons and first gives rise to a possible Z3 spin liquid p…
We report a high-resolution neutron diffraction study of the crystal and magnetic structure of the orbitally-degenerate frustrated metallic magnet AgNiO2. At high temperatures the structure is hexagonal with a single crystallographic Ni site, low-spin Ni3+ with spin-1/2 and two-fold orbital degeneracy, arranged in an antiferromagnetic triangular lattice with frustrated spin and orbital order. A structural transition occurs upon cooling below 365 K to a tripled hexagonal unit cell containing three crystallographically-distinct Ni sites with expanded and contracted NiO6 octahedra, naturally expl…
In order to clarify a crucial role of orbital degree of freedom in geometrically frustrated systems, we investigate both ground- and excited-state properties of the e_g-orbital degenerate Hubbard model on two kinds of lattices, ladder and zigzag chain, by using numerical techniques. In the ladder, spin correlation extends on the whole system, while the zigzag chain is decoupled to a double chain and spin excitation is confined in one side of the double chain due to the selection of a specific orbital. We envision a kind of self-organization phenomenon that the geometrically frustrated multi-or…
Frustrated spin systems on Kagome lattices have long been considered to be a promising candidate for realizing exotic spin liquid phases. Recently, there has been a lot of renewed interest in these systems with the discovery of materials such as Volborthite and Herbertsmithite that have Kagome like structures. In the presence of an external magnetic field, these frustrated systems can give rise to magnetization plateaus of which the plateau at $m=\frac{1}{3}$ is considered to be the most prominent. Here we study the problem of the antiferromagnetic spin-1/2 quantum XXZ Heisenberg model on a Ka…
In the present work, we investigate the applicability of the LSDA+$U$ method in understanding the electronic and magnetic properties of a geometrically frustrated ZnV$_2$O$_4$ compound, where the delicate balance of electrons, lattice, orbital and spin interactions play an important role in deciding its physical properties. In the ferromagnetic solution of the compound, only one type of orbital solution is found to exist in all ranges of $U$ studied here. However, in antiferromagnetic (AFM) phase, two types of orbital solutions, AFM(OS1) and AFM(OS2), exist for $U >$3 eV. If the difference of …
We present our theoretical and numerical results on thermodynamic properties and the microscopic mechanism of two successive transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) obtained by Monte Carlo calculations of an effective spin-orbital-lattice model in the strong correlation limit. Geometrical frustration in the pyrochlore lattice structure of V cations suppresses development of spin and orbital correlations, however, we find that the model exhibits two transitions at low temperatures. First, a discontinuous transition occurs with an orbital ordering assisted by the …
The question of the existence of a spin liquid state in the half-filled Hubbard model on the honeycomb (aka graphene) lattice is revisited. The Variational Cluster Approximation (VCA), the Cluster Dynamical Mean Field Theory (CDMFT) and the Cluster Dynamical Impurity Approximation (CDIA) are applied to various cluster systems. Assuming that the spin liquid phase coincides with the Mott insulating phase in this non-frustrated system, we find that the Mott transition is pre-empted by a magnetic transition occuring at a lower value of the interaction $U$, and therefore the spin liquid phase does …
We have theoretically studied successive transitions in vanadium spinel oxides with (t_2g)^2 electron configuration. These compounds show a structural transition at ~ 50K and an antiferromagnetic transition at ~ 40K. Since threefold t_2g orbitals of vanadium cations are occupied partially and vanadiums constitute a geometrically-frustrated pyrochlore lattice, the system provides a particular example to investigate the interplay among spin, orbital and lattice degrees of freedom on frustrated lattice. We examine the models with the Jahn-Teller coupling and/or the spin-orbital superexchange inte…
Crystal structure, magnetic susceptibility, and specific heat were measured in the normal cubic spinel compounds MnSc_2S_4 and FeSc_2S_4. Down to the lowest temperatures, both compounds remain cubic and reveal strong magnetic frustration. Specifically the Fe compound is characterized by a Curie-Weiss temperature Θ_{CW}= -45 K and does not show any indications of order down to 50 mK. In addition, the Jahn-Teller ion Fe^{2+} is orbitally frustrated. Hence, FeSc_2S_4 belongs to the rare class of spin-orbital liquids. MnSc_2S_4 is a spin liquid for temperatures T > T_N \approx 2 K.
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…
The inconsistency about the degree of geometrical frustration has been a long issue in AV$_{2}$O$_{4}$ (A $\equiv$ Zn, Cd and Mg) compounds, which arises from the two experimental results: (i) frustration indices and (ii) magnetic moments. In the present study, we try to understand such inconsistency by using {\it ab initio} electronic structure calculations. The orbital degrees of freedom are found to play an important role in understanding the geometrically frustrated magnetic behaviour of these compounds. The inclusion of the orbital and spin angular momenta for calculating the frustration …
Ultracold Fermi gases with synthetic gauge field represent an excellent platform to study the combined effect of lattice frustration and an effective magnetic flux close to one flux quantum per particle. The minimal theoretical model to accomplish this task is a system of spinless noninteracting fermions on a triangular two-chain flux ladder. In this paper we consider this model close to half-filling, with interchain hopping amplitudes alternating along the zigzag bonds of the ladder and being small. In such setting qualitative changes in the ground state properties of the model, most notably …
A class of the symmetrically frustrated SU(N) models is constructed for quantum magnets based on the generators of SU(N) group. The total Hamiltonian lacks SU(N) symmtry. A mean field theory in the quasi-particle representation is developed for spin liquid states. Numerical solutions in two dimension indicate that the ground states are gapless and the quasi-particles are Dirac particles. The mechanism may be helpful in exploring the spin liquid phases in the spin-1 bilinear-biquadratic model and the spin-orbital model in higher dimensions.
The interplay between spin and orbital degrees of freedom in the Mott-Hubbard insulator is studied by considering an orbitally degenerate superexchange model. We argue that orbital order and the orbital excitation gap in this model are generated through the order-from-disorder mechanism known previously from frustrated spin models. We propose that the orbital gap should show up indirectly in the dynamical spin structure factor; it can therefore be measured using the conventional inelastic neutron scattering method.
Competing interactions in Quantum Materials induce novel states of matter such as frustrated magnets, an extensive field of research both from the theoretical and experimental perspectives. Here, we show that competing energy scales present in the low-dimensional orbital-selective Mott phase (OSMP) induce an exotic magnetic order, never reported before. Earlier neutron scattering experiments on iron-based 123 ladder materials, where OSMP is relevant, already confirmed our previous theoretical prediction of block-magnetism (magnetic order of the form $\uparrow\uparrow\downarrow\downarrow$). Now…
Isotropic and anisotropic magnetic behavior of the frustrated spin chain compound $β$-TeVO$_4$ is reported. Three magnetic transitions observed in zero magnetic field are tracked in fields applied along different crystallographic directions using magnetization, heat capacity, and magnetostriction measurements. Qualitatively different temperature-field diagrams are obtained below 10 T for the field applied along $a$ or $b$ and along $c$, respectively. In contrast, a nearly isotropic high-field phase emerges above 18 T and persists up to the saturation that occurs around 22.5 T. Upon cooling in …
Spin fluctuations were studied over a wide momentum ($\hbar Q$) and energy ($E$) space in the frustrated $d$-electron heavy-fermion metal LiV$_2$O$_4$ by time-of-flight inelastic neutron scattering. We observed the overall $Q$$-$$E$ evolutions near the characteristic $Q=0.6$ Å$^{-1}$ peak and found another weak broad magnetic peak around 2.4 Å$^{-1}$. The data are described by a simple response function, a highly itinerant magnetic form factor, and antiferromagnetic short-range spatial correlations, indicating that heavy-fermion formation is attributable to spin-orbit fluctuations with orbital…
We propose a model for the multi-orbital material Sr$_2$CrOsO$_6$ (SCOO), an insulator with remarkable magnetic properties and the highest $T_c \simeq 725$ K among {\em all} perovskites with a net moment. We derive a new criterion for the Mott transition $(\widetilde{U}_{1} \widetilde{U}_{2})^{1/2}>2.5W$ using slave rotor mean field theory, where $W$ is the bandwidth and $\widetilde{U}_{1(2)}$ are the effective Coulomb interactions on Cr(Os) including Hund's coupling. We show that SCOO is a Mott insulator, where the large Cr $\widetilde{U}_{1}$ compensates for the small Os $\widetilde{U}_{2}$.…
