We study the influence of the spin lattice distortion on the properties of frustrated magnetic systems and consider the applicability of the spin-1/2 frustrated square lattice model to materials lacking tetragonal symmetry. We focus on the case of layered vanadium phosphates AA'VO(PO4)2 (AA' = Pb2, SrZn, BaZn, and BaCd). To provide a proper microscopic description of these compounds, we use extensive band structure calculations for real materials and model structures and supplement this analysis with simulations of thermodynamic properties, thus facilitating a direct comparison with the experimental data. Due to the reduced symmetry, the realistic spin model of layered vanadium phosphates AA'VO(PO4)2 includes four inequivalent exchange couplings: J1 and J1' between nearest-neighbors and J2 and J2' between next-nearest-neighbors. The estimates of individual exchange couplings suggest different regimes, from J1'/J1 and J2'/J2 close to 1 in BaCdVO(PO4)2, a nearly regular frustrated square lattice, to J1'/J1 ~ 0.7 and J2'/J2 ~ 0.4 in SrZnVO(PO4)2, a frustrated square lattice with sizable distortion. The underlying structural differences are analyzed, and the key factors causing the distortion of the spin lattice in layered vanadium compounds are discussed. We propose possible routes for finding new frustrated square lattice materials among complex vanadium oxides. Full diagonalization simulations of thermodynamic properties indicate the similarity of the extended model to the regular one with averaged couplings. In case of moderate frustration and moderate distortion, valid for all the AA'VO(PO4)2 compounds reported so far, the distorted spin lattice can be considered as a regular square lattice with the couplings (J1+J1')/2 between nearest-neighbors and (J2+J2')/2 between next-nearest-neighbors.
Magnetic properties of the silver vanadium phosphate Ag(2)VOP(2)O(7) are studied by means of magnetic susceptibility measurements and electronic structure calculations. In spite of the layered crystal structure suggesting 1D or 2D magnetic behavior, this compound can be understood as a spin dimer system. The fit of the magnetic susceptibility indicates an intradimer interaction of about 30 K in perfect agreement with the computational results. Our study emphasizes the possible pitfalls in interpreting experimental data on structural basis only and points out the importance of microscopic model…
Crystal structure and magnetic properties of the layered vanadium phosphate PbZnVO(PO4)2 are studied using x-ray powder diffraction, magnetization and specific heat measurements, as well as band structure calculations. The compound resembles AA'VO(PO4)2 vanadium phosphates and fits to the extended frustrated square lattice model with the couplings J(1), J(1)' between nearest-neighbors and J(2), J(2)' between next-nearest-neighbors. The temperature dependence of the magnetization yields estimates of averaged nearest-neighbor and next-nearest-neighbor couplings, J(1) ~ -5.2 K and J(2) ~ 10.0 K, …
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…
We report on high-field magnetization measurements for a number of layered vanadium phosphates that were recently recognized as spin-1/2 frustrated square lattice compounds with ferromagnetic nearest-neighbor couplings (J_1) and antiferromagnetic next-nearest-neighbor couplings (J_2). The saturation fields of the materials lie in the range from 4 to 24 T and show excellent agreement with the previous estimates of the exchange couplings deduced from low-field thermodynamic measurements. The consistency of the high-field data with the regular frustrated square lattice model provides experimental…
We report the synthesis and characterization of Li2ZnV3O8, which is a new Zn-doped LiV2O4 system containing only tetravalent vanadium. A Curie-Weiss susceptibility with a Curie-Weiss temperature of <theta>CW ~214 K suggests the presence of strong antiferromagnetic correlations in this system. We have observed a splitting between the zero-field cooled ZFC and field cooled FC susceptibility curves below 6 K. A peak is present in the ZFC curve around 3.5 K suggestive of spin-freezing . Similarly, a broad hump is also seen in the inferred magnetic heat capacity around 9 K. The consequent entropy c…
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 …
We report on the magnetic properties of the layered perovskite PbVO(3). The results of magnetic susceptibility and specific heat measurements as well as band structure calculations consistently suggest that the S=1/2 square lattice of vanadium atoms in PbVO(3) is strongly frustrated due to next-nearest-neighbor antiferromagnetic interactions. The ratio of next-nearest-neighbor (J(2)) to nearest-neighbor (J(1)) exchange integrals is estimated to be J(2)/J(1)\approx 0.2-0.4. Thus, PbVO(3) is within or close to the critical region of the J(1)-J(2) frustrated square lattice. Supporting this, no si…
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 …
Motivated by the intriguing properties of the vanadium spin tube Na2V3O7, we show that an effective spin-chirality model similar to that of standard Heisenberg odd-legged S=1/2 spin tubes can be derived for frustrated inter-ring couplings, but with a spin-chirality coupling constant alpha that can be arbitrarily small. Using density matrix renormalization group and analytical arguments, we show that, while spontaneous dimerization is always present, solitons become bound into low-lying singlets as alpha is reduced. Experimental implications for strongly frustrated tubes are discussed.
We propose a scenario for the two phase transitions in $A$V$_2$O$_4$ ($A$=Zn, Mg, Cd), based on an effective spin-orbital model on the pyrochlore lattice. At high temperatures, spin correlations are strongly frustrated due to the lattice structure, and the transition at $\sim$50 [K] is an orbital order, supported by Jahn-Teller lattice distortion. This orbital order introduces spatial modulation of spin exchange couplings depending on the bond direction. This partially releases the frustration, and leads to a spin order at $\sim$40 [K]. We also study the stable spin configuration by taking acc…
The J1-J2 model on a square lattice exhibits a rich variety of different forms of magnetic order that depend sensitively on the ratio of exchange constants J2/J1. We use bulk magnetometry and polarized neutron scattering to determine J1 and J2 unambiguously for two materials in a new family of vanadium phosphates, Pb2VO(PO4)2 and SrZnVO(PO4)2, and we find that they have ferromagnetic J1. The ordered moment in the collinear antiferromagnetic ground state is reduced, and the diffuse magnetic scattering is enhanced, as the predicted bond-nematic region of the phase diagram is approached.
The vanadium oxyfluoride [NH4]2[C7H14N][V7O6F18] (DQVOF) is a geometrically frustrated magnetic bilayer material. The structure consists of S=1/2 kagome planes of V4+ d1 ions with S=1 V3+ d2 ions located between the kagome layers. Muon spin relaxation measurements demonstrate the absence of spin freezing down to 40 mK despite an energy scale of 60 K for antiferromagnetic exchange interactions. From magnetization and heat capacity measurements we conclude that the S=1 spins of the interplane V3+ ions are weakly coupled to the kagome layers, such that DQVOF can be viewed as an experimental model…
We develop a general framework, which combines exact diagonalization in small clusters with a density matrix variational principle, to study frustrated magnets at finite temperature. This thermodynamic hierarchical mean-field technique is used to determine the phase diagram and magnetization process of the three-dimensional spin-1/2 $J_1$-$J_2$ antiferromagnet on a stacked square lattice. Its non-magnetic phase exhibits a thermal crossover from a quantum to a classical paramagnet at a temperature $T=T_0$ which can be extracted from thermodynamic measurements. At low temperature an applied magn…
We present our theoretical results on the mechanism of two transitions in vanadium spinel oxides $A$V$_2$O$_4$ ($A$=Zn, Mg, or Cd) in which magnetic V cations constitute a geometrically-frustrated pyrochlore structure. We have derived an effective spin-orbital-lattice coupled model in the strong correlation limit of the multiorbital Hubbard model, and applied Monte Carlo simulation to the model. The results reveal that the higher-temperature transition is a layered antiferro-type orbital ordering accompanied by tetragonal Jahn-Teller distortion, and the lower-temperature transition is an antif…
LiVO$_2$ is a model system of the valence bond solid (VBS) in $3d^2$ triangular lattice. The origin of the VBS formation has remained controversial. We investigate the microscopic mechanism by elucidating the $d$ orbital character via on-site $^{51}$V NMR measurements in a single crystal up to 550 K across a structural transition temperature $T_c$. The Knight shift, $K$, and nuclear quadrupole frequency, $δν$, show that the 3d orbital with local trigonal symmetry are reconstructed into a $d_{yz}d_{zx}$ orbital order below $T_c$. Together with the NMR spectra with three-fold rotational symmetry…
We present a unique study of the frustrated spinel MgV2O4 which possesses highly coupled spin, lattice and orbital degrees of freedom. Using large single-crystal and powder samples, we find a distortion from spinel at room temperature (space group F-43m) which allows for a greater trigonal distortion of the VO6 octahedra and a low temperature space group (I-4m2) that maintains the mirror plane symmetry. The magnetic structure that develops below 42 K consists of antiferromagnetic chains with a strongly reduced moment while inelastic neutron scattering reveals one-dimensional behavior and a sin…
We discuss new high-field magnetization data recently obtained by Tsirlin et al. for layered vanadium phosphates in the framework of the square-lattice model. Our predictions for the saturation fields compare exceptionally well to the experimental findings, and the strong bending of the curves below saturation agrees very well with the experimental field dependence. Furthermore we discuss the remarkably good agreement of the frustrated Heisenberg model on the square lattice in spite of the fact that the compounds described with this model actually have a lower crystallographic symmetry. We pre…
The magnetic properties and spin dynamics of the spin frustrated polyoxometalate {W72V30}, where 30 V^{4+} ions (s = 1/2) occupy the sites of an icosidodecahedron, have been investigated by low temperature magnetization, magnetic susceptibility, proton and vanadium nuclear magnetic resonance, and theoretical studies. The field-dependent magnetization at 0.5 K increases monotonically up to 50 T without any sign of staircase behavior. This low-temperature behavior cannot be explained by a Heisenberg model based on a single value of the nearest-neighbor exchange coupling. We analyze this behavior…
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 magnetocaloric properties of the two-dimensional frustrated J1-J2 model on a square lattice. This model describes well the magnetic behavior of two classes of quasi-two-dimensional S = 1/2 vanadates, namely the Li2VOXO4 (X = Si, Ge) and AA'VO(PO4)2 (A, A' = Pb, Zn, Sr, Ba) compounds. The magnetocaloric effect (MCE) consists in the adiabatic temperature change upon changing the external magnetic field. In frustrated systems, the MCE can be enhanced close to the saturation field because of massive degeneracies among low lying excitations. We discuss results for the MCE in the …
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…
Crystal structure, electronic structure, and magnetic behavior of the spin-1/2 quantum magnet Na1.5VOPO4F0.5 are reported. The disorder of Na atoms leads to a sequence of structural phase transitions revealed by synchrotron x-ray powder diffraction and electron diffraction. The high-temperature second-order alpha <--> beta transition at 500 K is of the order-disorder type, whereas the low-temperature beta <--> gamma+gamma' transition around 250 K is of the first order and leads to a phase separation toward the polymorphs with long-range (gamma) and short-range (gamma') order of Na. Despite the…
We report the bulk magnetic properties of a yet unexplored vanadium-based multivalued spinel system, Zn3V3O8. A Curie-Weiss fit of our dc magnetic susceptibility data in the temperature region from 140 to 300 K yields a Curie constant C = 0.75cm3K/mole V, theta CW = -370 K. We have observed a splitting between the zero field cooled ZFC and field cooled FC susceptibility curves below a temperature Tirr of about 6.3 K. The value of the 'frustration parameter' nearly equals to 100 suggests that the system is strongly frustrated. From the ac susceptibility measurements we find a logarithmic variat…
We present a detailed investigation of the magnetic properties of complex vanadium phosphates M(VO)2(PO4)2 (M = Ca, Sr) by means of magnetization, specific heat, 31P NMR measurements, and band structure calculations. Experimental data evidence the presence of ferro- and antiferromagnetic interactions in M(VO)2(PO4)2 resulting in a nearly vanishing Curie-Weiss temperature θ_{CW} < 1 K that contrasts with the maximum of magnetic susceptibility at 3 K. Specific heat and NMR measurements also reveal weak exchange couplings with the thermodynamic energy scale J_c = 10-15 K. Additionally, the reduce…
LiV2O4, a frustrated mixed valent metal (d^1 <-> d^2), is argued to undergo two spin-screening processes. The first quenches the effective spin to produce the spin 1/2 behavior seen below room temperature[1], while the second produces the heavy fermi liquid character seen at low temperatures[2]. We present here a preliminary discussion of a t-J model with strong Hund's coupling of the strongly correlated d-electrons. Valence fluctuations of the Hubbard operators (S = {1/2} <-> 1) combined with the frustration of the underlying corner-shared tetrahedral vanadium lattice are the essential compon…
We have investigated the structural and magnetic properties of a new cubic spinel LiZn$_{2}$V$_{3}$O$_{8}$ (LZVO) through x-ray diffraction, dc and ac susceptibility, magnetic relaxation, aging, memory effect, heat capacity and $^{7}$Li nuclear magnetic resonance (NMR) measurements. A Curie-Weiss fit of the dc susceptibility $χ_{\mathrm{dc}}$($\mathit{T}$) yields a Curie-Weiss temperature $\mathrmθ_{\mathrm{CW}}$ = -185 K. This suggests strong antiferromagnetic (AFM) interactions among the magnetic vanadium ions. The dc and ac susceptibility data indicate the spin-glass behavior below a freezi…
The spinel vanadates have become a model family for exploring orbital order on the frustrated pyrochlore lattice, and recent debate has focused on the symmetry of local crystal fields at the cation sites. Here, we present neutron scattering measurements of the magnetic excitation spectrum in $\mathrm{FeV_2O_4}$, a recent example of a ferrimagnetic spinel vanadate which is available in single crystal form. We report the existence of two emergent magnon modes at low temperatures, which draw strong parallels with the closely related material, $\mathrm{MnV_2O_4}$. We were able to reproduce the ess…
A Kagome-Derived Mosaic Lattice Family A3V9Te13 (A = Cs, Rb) with Tunable Strong Electronic Correlations
Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）；School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology（南方科技大学量子科学工程学院）；International Quantum Academy（国际量子科学院）
In the vanadium oxyfluoride compound (NH$_4$)$_2$[C$_7$H$_{14}$N][V$_7$O$_6$F$_{18}$] (DQVOF), the V$^{4+}$ (3d$^1$, $S=1/2$) ions realize a unique, highly frustrated breathing kagome lattice composed of alternately-sized, corner-sharing equilateral triangles. Here we present an $^{17}$O NMR study of DQVOF, which isolates the local susceptibility of the breathing kagome network. By a fit to series expansion we extract the ratio of the interactions within the breathing kagome plane, $J_\triangledown / J_\vartriangle = 0.55(4)$, and the mean antiferromagnetic interaction $\bar{J}=60(7)$~K. Spin …
