We investigate the Heisenberg model on a decorated square (Fisher) lattice in the presence of first-neighbor $J_{1}$, second-neighbor $J_{2}$, and third-neighbor $J_{3}$ exchange couplings, with antiferromagnetic $J_{1}$. The classical ground-state phase diagram obtained within a Luttinger-Tisza framework is spanned by two antiferromagnetically ordered phases, and an infinitely degenerate antiferromagnetic chain phase. Employing classical Monte Carlo simulations we show that thermal fluctuations fail to lift the degeneracy of the antiferromagnetic chain phase. Interestingly, the spin-wave spectrum of the Néel state displays three Dirac nodal loops out of which two are symmetry protected while for the antiferromagnetic chain phase we find symmetry-protected Dirac lines. Furthermore, we investigate the spin $S=\frac{1}{2}$ limit employing a bond operator formalism which captures the singlet-triplet dynamics, and find a rich ground-state phase diagram host to a variety of valence bond solid orders in addition to antiferromagnetically ordered phases.
The magnetic susceptibility $χ(T)$ of spin-1/2 chains is widely used to quantify exchange interactions, even though $χ(T)$ is similar for different combinations of ferromagnetic $J_1$ between first neighbors and antiferromagnetic $J_2$ between second neighbors. We point out that the spin specific heat $C(T)$ directly determines the ratio $α= J_2/|J_1|$ of competing interactions. The $J_1-J_2$ model is used to fit the isothermal magnetization $M(T,H)$ and $C(T,H)$ of spin-1/2 Cu(II) chains in LiCuSbO$_4$. By fixing $α$, $C(T)$ resolves the offsetting $J_1$, $α$ combinations obtained from $M(T,H…
We investigate quantum phase transitions among the spin-gap phases and the magnetically ordered phases in a two-dimensional frustrated antiferromagnetic spin system, which interpolates several important models such as the orthogonal-dimer model as well as the model on the 1/5-depleted square lattice. By computing the ground state energy, the staggered susceptibility and the spin gap by means of the series expansion method, we determine the ground-state phase diagram and discuss the role of geometrical frustration. In particular, it is found that a RVB-type spin-gap phase proposed recently for …
We examine the ground-state phase diagram and thermal phase transitions in a plaquettized fully frustrated bilayer spin-1/2 Heisenberg model. Based on a combined analysis from sign-problem free quantum Monte Carlo simulations, perturbation theory and free-energy arguments, we identify a first-order quantum phase transition line that separates two competing quantum-disordered ground states with dominant singlet formations on inter-layer dimers and plaquettes, respectively. At finite temperatures, this line extends to form a wall of first-order thermal transitions, which terminates in a line of …
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.
Zero and longitudinal field $μ$SR measurements in Pb$_2$VO(PO$_4$)$_2$ and BaCdVO(PO$_4$)$_2$, two prototypes of the frustrated $S=1/2$ square lattice model with competing ferromagnetic and antiferromagnetic interactions, are presented. Both systems are observed to undergo a phase transition to a long-range magnetic order at $T_N\simeq 3.46$ K, for Pb$_2$VO(PO$_4$)$_2$, and at $T_N\simeq 0.99$ K, for BaCdVO(PO$_4$)$_2$. In Pb$_2$VO(PO$_4$)$_2$ both the temperature dependence of the order parameter and the longitudinal relaxation rate above $T_N$ are consistent with a two-dimensional XY model. …
Frustration in magnetic interactions can give rise to disordered ground states with subtle and beautiful properties. The spin ices Ho2Ti2O7 and Dy2Ti2O7 exemplify this phenomenon, displaying a classical spin liquid state, with fractionalized magnetic--monopole excitations. Recently there has been great interest in closely-related "quantum spin ice" materials, following the realization that anisotropic exchange interactions could convert spin ice into a massively-entangled, quantum, spin liquid, where magnetic monopoles become the charges of an emergent quantum electrodynamics. Here we show tha…
In frustrated spin-1/2 chains the competition between the nearest- and next-nearest-neighbor exchange interactions leads to a rich phase diagram that becomes even richer in the presence of perturbations in their material realizations. These effects are still largely unexplored, so that new insight into static and dynamic magnetism, in particular by sensitive local probes, is highly desired. Here we present a comprehensive $^{17}$O nuclear magnetic resonance study of $β$-TeVO$_4$, where the anisotropy of the main exchange interactions and additional weak interchain exchange interactions complem…
We study the spin-1 honeycomb lattice magnets with frustrated exchange interactions. The proposed microscopic spin model contains first and second neighbor Heisenberg interactions as well as the single-ion anisotropy. We establish a rich phase diagram that includes a featureless quantum paramagnet and various spin spiral states induced by the mechanism of order by quantum disorder. Although the quantum paramagnet is dubbed featureless, it is shown that, the magnetic excitations develop a contour degeneracy in the reciprocal space at the band minima. These contour degenerate excitations are res…
The interplay between Kondo screening, indirect magnetic interaction and geometrical frustration is studied in the two-dimensional Kondo-necklace model on the triangular lattice. Using infinite projected entangled pair states (iPEPS), we compute the ground state as a function of the antiferromagnetic local Kondo interaction $J_K$ and the Ising-type direct spin-spin interaction $I_z$ . As opposed to previous studies, we do not find partial Kondo screening (PKS) in the isotropic limit $I_z = 0$ but the same behavior as in the unfrustrated case, i.e. a direct phase transition between the paradigm…
We give a short review of our recent works on the first-order quantum phase transitions in frustrated spin chains with orthogonal-dimer structure. When the ratio of the competing antiferromagnetic exchange couplings is varied, a first-order transition occurs between the dimer phase and the plaquette phase, which is accompanied by the discontinuity in the spin excitation gap. We further show that strong frustration triggers the phase transitions in a magnetic field, which exhibit plateaus and jumps in the magnetization curve. The hole-doping effect is also addressed for the orthogonal-dimer cha…
The competing magnetic ground states of the itinerant magnet EuCuSb, which has a hexagonal layered structure, were studied via magnetization, resistivity, and neutron diffraction measurements on single-crystal samples. EuCuSb has a three-dimensional semimetallic band structure as confirmed by band calculation and angle-resolved photoelectron spectroscopy, consistent with the nearly isotropic metallic conductivity in the paramagnetic state. However, below the antiferromagnetic transition temperature of TN1 (8.5 K), the resistivity, especially along the hexagonal axis, increases significantly. T…
Frustrated systems exhibit remarkable properties due to the high degeneracy of their ground states. Stabilised by competing interactions, a rich diversity of typically nanometre-sized phase structures appear in polymer and colloidal systems, while the surface of ice pre-melts due to geometrically frustrated interactions. Atomic spin systems where magnetic interactions are frustrated by lattice geometry provide a fruitful source of emergent phenomena, such as fractionalised excitations analogous to magnetic monopoles. The degeneracy inherent in frustrated systems may prevail all the way down to…
We analyze the zero temperature phase diagrams of the spin S quantum antiferromagnet on square and triangular lattices with competing nearest and next-nearest exchange interactions as well as biquadratic couplings. We approach the problem from the large S limit. Our primary focus is on determining the extent to which the existence and character of any quantum disordered phases can be inferred from this approach.
We investigate quantum phase transitions for the $s=1/2$ antiferromagnetic Heisenberg model on a pyrochlore lattice. By means of a series expansion starting from isolated tetrahedra, the ground-state phase diagram is determined. When the ratio of the two competing exchange couplings is varied, the first-order (second-order) quantum phase transition occurs between the two spin gap phases (the spin-gap and the antiferromagnetic phases). We also discuss some properties expected for the s=1 pyrochlore spin system.
We present a model compound with a spin-1/2 spatially anisotropic frustrated square lattice, in which three antiferromagnetic interactions and one ferromagnetic interaction are competing. We observe an unconventional gradual increase in the low-temperature magnetization curve reminiscent of the quantum critical behavior between gapped and gapless phases. In addition, the specific heat and electron spin resonance signals indicate one-dimensional characteristics. These results demonstrate quantum critical behavior associated with one dimensionalization caused by frustrated interactions in the sp…
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…
The applied magnetic field and temperature phase diagram of the archetypal frustrated magnet, Gd3Ga5O12, has been reinvestigated using single crystal magnetometry and polarised neutron diffraction. The updated phase diagram is substantially more complicated than previously reported and can be understood in terms of competing interactions with loops of spins, trimers and decagons, in addition to competition and interplay between antiferromagnetic, incommensurate and ferromagnetic order. Several additional distinct phase boundaries are presented. The phase diagram centers around a multiphase con…
We investigate the dynamical quadrupole structure factor of a spin-1/2 $J_{1}$-$J_{2}$ Heisenberg chain with competing ferromagnetic $J_{1}$ and antiferromagnetic $J_{2}$ in a magnetic field by exploiting density-matrix renormalization group techniques. In a field-induced spin nematic regime, we observe gapless excitations at $q=π$ according to quasi-long-range antiferro-quadrupole correlations. The gapless excitation mode has a quadratic form at the saturation, while it changes into a linear dispersion as the magnetization decreases.
Quantum spin ice materials, pyrochlore magnets with competing Ising and transverse exchange interactions, have been widely discussed as candidates for a quantum spin-liquid ground state. Here, motivated by quantum chemical calculations for Pr pyrochlores, we present the results of a study for frustrated transverse exchange. Using a combination of variational calculations, exact diagonalisation, numerical linked-cluster and series expansions, we find that the previously-studied U(1) quantum spin liquid, in its pi-flux phase, transforms into a nematic quantum spin liquid at a high-symmetry, SU(2…
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.
Ordering of frustrated S=1/2 and 1 XY and Heisenberg spin chains with the competing nearest- and next-nearest-neighbor antiferromagnetic couplings is studied by exact diagonalization and density-matrix renormalization-group methods. It is found that the S=1 XY chain exhibits both gapless and gapped `chiral' phases characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, $κ_i = S_i^xS_{i+1}^y-S_i^yS_{i+1}^x$, whereas the spin correlation decays either algebraically or exponentially. Such chiral phases are not realized in the S=1/2 XY chain nor…
We explore the phase diagram and the low-energy physics of three Heisenberg antiferromagnets which, like the kagome lattice, are networks of corner-sharing triangles but contain two sets of inequivalent short-distance resonance loops. We use a combination of exact diagonalization, analytical strong-coupling theories, and resonating valence bond approaches, and scan through the ratio of the two inequivalent exchange couplings. In one limit, the lattices effectively become bipartite, while at the opposite limit heavily frustrated nets emerge. In between, competing tunneling processes result in s…
We consider the effects of local impurities in highly frustrated diamond lattice antiferromagnets, which exhibit large but non-extensive ground state degeneracies. Such models are appropriate to many A-site magnetic spinels. We argue very generally that sufficiently dilute impurities induce an ordered magnetic ground state, and provide a mechanism of degeneracy breaking. The states which are selected can be determined by a "swiss cheese model" analysis, which we demonstrate numerically for a particular impurity model in this case. Moreover, we present criteria for estimating the stability of t…
Based on the Chern-Simons fermionization of spin-1/2 operators, we propose a systematic framework to investigate the competition between emergent phases in frustrated two-dimensional XY quantum magnets. Application of the method to the antiferromagnetic honeycomb spin-1/2 $J_1$-$J_2$ XY model reveals an unconventional phase transition between two Chern-Simons orders: the Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions. We show that in the spin language, this transition translates to the transition from the planar Néel state to the non-uniform chiral spin-liquid t…
The description and detection of unconventional magnetic states such as spin liquids is a recurring topic in condensed matter physics. While much of the efforts have traditionally been directed at geometrically frustrated antiferromagnets, recent studies reveal that systems featuring competing antiferromagnetic and ferromagnetic interactions are also promising candidate materials. We find that this competition leads to the notion of special temperatures, analogous to those of gases, at which the competing interactions balance, and the system is quasi-ideal. Although induced by weak perturbing …
By exploiting density-matrix renormalization group techniques, we investigate the spin dynamics of a spin-1/2 one-dimensional J1-J2 XXZ model with competing ferromagnetic J1 and antiferromagnetic J2 exchange couplings under applied magnetic fields. Numerical results of spin excitation spectra show that in the field-induced spin quadrupole regime, the longitudinal component has a gapless mode and the transverse component has a gapped mode irrespective of the exchange anisotropy. The excitation gap of the transverse spin excitation increases as the exchange anisotropy increases over the XY-like …
We show that a system with competing interactions on different length scales, as relevant for the formation of stripes in doped Mott insulators, undergoes a self-generated glass transition which is caused by the frustrated nature of the interactions and not related to the presence of quenched disorder. An exponentially large number of metastable configurations is found, leading to a slow, landscape dominated long time relaxation and a break up of the system into a disordered inhomogeneous state.
We investigate the nature of a $Z_2$-invariant XY ring-exchange interaction with a frustrated Ising coupling on the triangular lattice. In the limit of pure XY ring-exchange interaction, we show that the classical ground state is degenerate resulting from the $Z_2$-invariance of the Hamiltonian. Quantum fluctuations lift these classical degenerate ground states and produce an unusual state whose excitation spectrum exhibits a gapped maximum quadratic dispersion near ${\bf k}=0$ and vanishes at the midpoints of each side of the Brillouin zone. This result is in contrast to a gapless quadratic d…
The Faraday rotation technique is used to map out the finite-temperature phase diagram of the prototypical frustrated magnet ZnCr2O4, in magnetic fields of up to 190 T generated by the single-turn coil method. We find evidence for a number of magnetic phase transitions, which are well-described by the theory based on spin-lattice coupling. In addition to the 1/2 plateau and a 3:1 canted phase, a 2:1:1 canted phase is found for the first time in chromium spinel oxides, which has been predicted by a theory of Penc et al. to realize in a small spin-lattice coupling limit. Both the new 2:1:1 and t…
We study the ground state properties of the spin-1/2 frustrated ferromagnetic J1-J2 Heisenberg model on the square lattice, employing projected BCS wavefunctions with spin-triplet pairings of the spinon fields as trial wavefunctions. Based on the variational Monte Carlo analysis, we argue that, in the competing coupling regime, a certain type of the projected BCS wavefunction, dubbed the projected Z2 planar state, achieves the best optimal energy among the other competing states such as the ferromagnetic state and collinear antiferromagnetic state. Like in quantum spin liquids, the projected Z…
We solve a model of phase separation among two competing phases frustrated by the long-range Coulomb interaction in two and three dimensions (2D/3D) taking into account finite compressibility effects. In the limit of strong frustration in 2D, we recover the results of R. Jamei, S. Kivelson, and B. Spivak, Phys. Rev. Lett. 94, 056805 (2005) and the system always breaks into domains in a narrow range of densities, no matter how big is the frustration. For weak frustration in 2D and for arbitrary frustration in 3D the finite compressibility of the phases is shown to play a fundamental role. Our r…
Motivated by recent experiments on low-dimensional frustrated quantum magnets with competing nearest-neighbor exchange coupling J1 and next nearest-neighbor exchange coupling J2 we investigate the magnetic susceptibility of two-dimensional J1-J2 Heisenberg models with arbitrary spin quantum number s. We use exact diagonalization and high-temperature expansion up to order 10 to analyze the influence of the frustration strength J2/J1 and the spin quantum number s on the position and the height of the maximum of the susceptibility. The derived theoretical data can be used to get information on th…
We re-visit the phase diagram of the frustrated spin-1/2 ladder with two competing inter-chain antiferromagnetic exchanges, rung coupling J_\perp and diagonal coupling J_\times. We suggest, based on the accurate renormalization group analysis of the low-energy Hamiltonian of the ladder, that marginal inter-chain current-current interaction plays central role in destabilizing previously predicted intermediate columnar dimer phase in the vicinity of classical degeneracy line J_\perp = 2J_\times. Following this insight we then suggest that changing these competing inter-chain exchanges from the p…
We investigate quantum phase transitions in the frustrated orthogonal-dimer chain with an arbitrary spin $S \geq 1/2$. When the ratio of the competing exchange couplings is varied, first-order phase transitions occur 2S times among distinct spin-gap phases. The introduction of single-ion anisotropy further enriches the phase diagram. The phase transitions described by the present model possess most of the essential properties inherent in frustrated quantum spin systems.
31P nuclear and muon spin-lattice relaxation rate measurements in SrZnVO(PO4)2, a S=1/2 frustrated magnet on a square lattice, are presented. The temperature (T) dependence of the in-plane correlation length ξ(T) is derived and it is shown that the overall behaviour is analogous to the one found for non-frustrated systems but with a reduced spin stiffness. The temperature dependence of ξ(T) in SrZnVO(PO4)2 is compared to the one of other frustrated magnets on a square lattice with competing nearest neighbour (J1) and next-nearest neighbour (J2) exchange couplings and it is shown that ξ(T) prog…
Spin waves in the type-III ordered antiferromagnetic state of the frustrated $t$-$t'$ Hubbard model on the fcc lattice are calculated to investigate finite-$U$-induced competing interaction and frustration effects on magnetic excitations and instabilities. Particularly strong competing interactions generated due to interplay of fcc lattice geometry and magnetic order result in significant spin wave softening. The calculated spin wave dispersion is found to be in qualitative agreement with the measured spin wave dispersion in the pyrite mineral $\rm Mn S_2$ obtained from inelastic neutron scatt…
A quantum magnet, LiCuSbO4, with chains of edge-sharing S = 1/2 CuO6 octahedra is reported. While the Curie-Weiss constant is ferromagnetic, θ= 30 K, no phase transition or spin freezing occurs down to 100 mK. Specific heat indicates a distinct high field phase near the 12 T saturation field. Neutron scattering shows incommensurate spin correlations with q = 0.47\pm0.01π/a and places an upper limit of 70 \mueV on a potential spin gap. Exact diagonalization of easy plane S = 1/2 chains with competing ferro- and antiferromagnetic interactions (J1 = - 75 K, J2 = 34 K) accounts for the T > 2 K dat…
We present a brief survey of the recent theoretical work related to generic Heisenberg spin models describing quasi-one-dimensional quantum ferrimagnets. The emphasis is on quantum chains and ladders with strong competing interactions, such as the frustrated $J_1-J_2$ chain with alternating (1,1/2) spins, the spin-1/2 diamond chain with four-spin cyclic couplings, and some generic types of mixed-spin ladders with geometric frustration. As a rule, discussed models exhibit rich quantum phase diagrams and provide some interesting examples of one-dimensional magnetic-paramagnetic quantum phase tra…
Thermodynamic properties of cubic Heisenberg ferromagnets with competing exchange interactions are considered near the frustration point where the coefficient $D$ in the spin-wave spectrum $E_{\mathbf{k}}\sim D k^{2}$ vanishes. Within the Dyson-Maleev formalism it is found that at low temperatures thermal fluctuations stabilize ferromagnetism by increasing the value of $D$. For not too strong frustration this leads to an unusual "concave" shape of the temperature dependence of magnetization, which is in agreement with experimental data on the europium chalcogenides. Anomalous temperature behav…
We present a new scenario for the breakdown of ferromagnetic order in a two-dimensional quantum magnet with competing ferromagnetic and antiferromagnetic interactions. In this, dynamical effects lead to the formation of two-magnon bound states, which undergo Bose-Einstein condensation, giving rise to bond-centered nematic order. This scenario is explored in some detail for an extended Heisenberg model on a square lattice. In particular, we present numerical evidence confirming the existence of a state with d-wave nematic correlations but no long range magnetic order, lying between the saturate…
The phase diagram of the one-dimensional Su-Schrieffer-Heeger model of spinless fermions coupled to quantum phonons is determined by quantum Monte Carlo simulations. It differs significantly from previous work. In addition to Luttinger liquid and bond-order-wave (BOW) phases, we find an extended charge-density-wave (CDW) phase. Because of different broken symmetries, BOW and CDW phases are connected by a retardation-driven phase transition. Our results are consistent with the theory of the frustrated $XXZ$ chain, including unconventional power-law exponents at criticality, and an interpretatio…
Using both exact diagonalizations and diagonalizations in a subset of short-range valence bond singlets, we address the nature of the groundstate of the Heisenberg spin-1/2 antiferromagnet on the square lattice with competing next-nearest and next-next-nearest neighbor antiferromagnetic couplings (J1-J2-J3 model). A detailed comparison of the two approaches reveals a region along the line (J2+J3)/J1=1/2, where the description in terms of nearest-neighbor singlet coverings is excellent, therefore providing evidence for a magnetically disordered region. Furthermore a careful analysis of dimer-di…
In this paper, we demonstrate that in frustrated magnets when several conventional (i.e., symmetry-breaking) orders compete, and are "intertwined" by a Wess-Zumino-Witten (WZW) term, the possibility of spin liquid arises. The resulting spin liquid could have excitations which carry fractional spins and obey non-trivial self/mutual statistics. As a concrete example, we consider the case where the competing orders are the Néel and valence-bond solid (VBS) order on square lattice. Examining different scenarios of vortex condensation from the VBS side, we show that the intermediate phases, includi…
The antiferromagnetic Heisenberg two-leg ladder in the presence of frustration and an external magnetic field is a system that is characterized by two sorts of quantum criticalities, not only one. One criticality is the consequence of intrinsic frustration, and the other one is a result of the external magnetic field. So the behaviour of each of them in the presence of the other deserves to be studied. Using the Jordan-Wigner transformation in dimensions higher than one and bond-mean-field theory we examine the interplay between the field-induced and frustration-induced quantum criticalities i…
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 …
The ground state of the frustrated A-site magnetic spinel CoAl2O4 has been a controversial issue whether it is a collinear antiferromagnetic ordering or a spiral spin - liquid state, as the ratio of the two competing interactions, J2/J1 lies close to the boundary between these two ground states. Here, we address the magnetic ground state in CoAl2O4 with different amount of Co2+/Al3+ site disorder from the study of magnetoelectric effect and Monte Carlo simulations. CoAl2O4 with low site disorder exhibits linear magnetoelectric effect below the magnetic ordering temperature. With increasing dis…
$^7$Li and $^{29}$Si NMR, $μ$SR and magnetization measurements in Li$_2$V$_{1-x}$OTi$_x$SiO$_4$, for $0 \leq x \leq 0.2$, are presented. The $x=0$ compound is a prototype of frustrated two-dimensional Heisenberg antiferromagnet on a square-lattice with competing nearest ($J_1$) and next-nearest ($J_2$) neighbour exchange interactions. Ti$^{4+}$ (S=0) for V$^{4+}$ (S=1/2) substitution yields the spin dilution of the antiferromagnetic layers. The analysis of the magnetization and of the nuclear spin-lattice relaxation rate shows that spin dilution not only reduces the spin-stiffness by a factor …
The phase diagram of the quasi-one-dimensional magnet NaCuMoO$_4$(OH) is established through single-crystal NMR and heat-capacity measurements. The $^{23}$Na and $^1$H NMR experiments indicate a spiral and a collinear spin-density-wave (SDW) order below and above $B_c$ = 1.5-1.8 T, respectively. Moreover, in the paramagnetic state above the SDW transition temperature, the nuclear spin-lattice relaxation rate $1/T_1$ indicates anisotropic spin fluctuations that have gapped excitations in the transverse spectrum but gapless ones in the longitudinal spectrum. These static and dynamic properties a…
The antiferromagnetic (AF) compound MnBi$_{2}$Te$_{4}$ is suggested to be the first realization of an antiferromagnetic (AF) topological insulator. Here we report on inelastic neutron scattering studies of the magnetic interactions in MnBi$_{2}$Te$_{4}$ that possess ferromagnetic (FM) triangular layers with AF interlayer coupling. The spin waves display a large spin gap and pairwise exchange interactions within the triangular layer are frustrated due to large next-nearest neighbor AF exchange. The degree of frustration suggests proximity to a variety of magnetic phases, potentially including s…
We investigate the ground-state phase diagram of an anisotropic Heisenberg model on the honeycomb lattice with competing interactions. We use quantum Monte Carlo simulations, as well as linear spin-wave and Ising series expansions, to determine the phase boundaries of the ordered magnetic phases. We find a region without any classical order in the vicinity of a highly frustrated point. Higher-order correlation functions in this region give no signal for long-range valence-bond order. The low-energy spectrum is derived via exact diagonalization to check for topological order on small-size perio…
We study a square-lattice spin-half Heisenberg model where frustration is introduced by competing nearest-neighbor bonds of different signs. We discuss the influence of quantum fluctuations on the nature of the zero-temperature phase transitions from phases with collinear magnetic order at small frustration to phases with noncollinear spiral order at large frustration. We use the coupled cluster method (CCM) for high orders of approximation (up to LSUB6) and the exact diagonalization of finite systems (up to 32 sites) to calculate ground-state properties. The role of quantum fluctuations is ex…
We outline the recent results on the ground state for a class of one- and two-dimensional frustrated quantum spin models with competing ferro(F)- and antiferromagnetic (AF) interactions. Frustrated spin systems are known to have many interesting properties due to large quantum fluctuations. As a result of these fluctuations usual mean-field approach gives quite crude (if not false) description of these systems. Therefore, exactly solvable models are very instructive at investigations of such systems. The exact ground state wave function of proposed models has a structure of the valence-bond st…
