We investigate the influence of an inter-chain coupling on the spiral ground state correlations of a spin-1/2 Heisenberg model consisting of a two-dimensional array of coupled chains with nearest (J1) and frustrating next-nearest neighbor (J2) in-chain exchange couplings. Using the coupled-cluster method we calculate the transition point between the commensurate and the incommensurate (spiral) ground state as well as the quantum pitch angle of the spiral ground state. In addition, we provide a simple empirical formula which describes the relation between the quantum pitch angle and the frustration parameter J2/J1.
The formation of coplanar spin spirals is a common motif in the magnetic ordering of many frustrated magnets. For classical antiferromagnets, geometric frustration can lead to a massively degenerate ground state manifold of spirals whose propagation vectors can be described, depending on the lattice geometry, by points (triangular), lines (fcc), surfaces (frustrated diamond) or completely flat bands (pyrochlore). Here we demonstrate an exact mathematical correspondence of these spiral manifolds of classical antiferromagnets with the Fermi surfaces of free-fermion band structures. We provide an…
The ground state phase diagram is determined for the frustrated classical Heisenberg chain with added nearest-neighbor biquadratic exchange interactions. There appear ferromagnetic, incommensurate-spiral, and up-up-down-down phases; a lock-in transition occurs at the spiral boundary. The model contains an isotropic version of the ANNNI model; it is also closely related to a model proposed for some manganites. The Luttinger-Tisza method is not obviously useful due to the non-linear weak-constraint problem; however the ground state is obtained analytically by the exact cluster method of Lyons an…
In this publication I discuss the phase diagram of a frustrated spin-1/2 Heisenberg model suggested in A. A. Nersesyan and A. M. Tsvelik, Phys. Rev. B{\bf 67}, 024422 (2003). The phase diagram contains $(π,0)$ and $(π,π)$ antiferromagnetic phases separated by the Valence Bond Crystal (VBC) state. I argue that the point of the phase diagram with deconfined spinons, predicted in the aforementioned work, is situated in the middle of VBC state, at the point where the dimerization order parameter changes sign.
Low-temperature magnetization curves and thermodynamics of a frustrated spin-1/2 Heisenberg triangular bilayer with the antiferromagnetic intradimer interaction and either ferromagnetic or antiferromagnetic interdimer interaction are investigated in a highly frustrated parameter region, where localized many-magnon eigenstates provide the most dominant contribution to magnetothermodynamics. Low-energy states of the highly frustrated spin-1/2 Heisenberg triangular bilayer can be accordingly found from a mapping correspondence with an effective triangular-lattice spin-1/2 Ising model in a field. …
We study the fate of spin-1/2 spiral-ordered two-dimensional quantum antiferromagnets that are disordered by quantum fluctuations. A crucial role is played by the topological point defects of the spiral phase, which are known to have a Z2 character. Previous works established that a nontrivial quantum spin-liquid phase results when the spiral is disordered without proliferating the Z2 vortices. Here, we show that when the spiral is disordered by proliferating and condensing these vortices, valence-bond solid ordering occurs due to quantum Berry phase effects. We develop a general theory for th…
In a recent letter [Phys. Rev. Lett. 89, 156603 (2002); cond-mat/0201300], Alvarez and Gros have numerically analyzed the Drude weight for thermal transport in spin ladders and frustrated chains of up to 14 sites and have proposed that it remains finite in the thermodynamic limit. In this comment, we argue that this conclusion cannot be sustained if the finite-size analysis is taken to larger system sizes.
We present the phase diagram of the frustrated ferromagnetic S=1/2 Heisenberg J_1-J_2 chain in a magnetic field, obtained by large scale exact diagonalizations and density matrix renormalization group simulations. A vector chirally ordered state, metamagnetic behavior and a sequence of spin-multipolar Luttinger liquid phases up to hexadecupolar kind are found. We provide numerical evidence for a locking mechanism, which can drive spiral states towards spin-multipolar phases, such as quadrupolar or octupolar phases. Our results also shed light on previously discovered spin-multipolar phases in …
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…
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.
Quantum Monte Carlo methods are sophisticated numerical techniques for simulating interacting quantum systems. In some cases, however, they suffer from the notorious "sign problem" and become too inefficient to be useful. A recent publication [J. Wojtkiewicz, Phys. Rev. B 75, 174421 (2007)] claims to have solved the sign problem for a certain class of frustrated quantum spin systems through the use of a bipartite valence bond basis. We show in this Comment that the apparent positivity of the path integral is due to a misconception about the resolution of the identity operator in this basis, an…
We investigate two-dimensional frustrated Heisenberg magnets using non-perturbative renormalization group techniques. These magnets allow for point-like topological defects which are believed to unbind and drive either a crossover or a phase transition which separates a low temperature, spin-wave dominated regime from a high temperature regime where defects are abundant. Our approach can account for the crossover qualitatively and both the temperature dependence of the correlation length as well as a broad but well defined peak in the specific heat are reproduced. We find no signatures of a fi…
We consider the finite-temperature phase diagram of the $S = 1/2$ frustrated Heisenberg bilayer. Although this two-dimensional system may show magnetic order only at zero temperature, we demonstrate the presence of a line of finite-temperature critical points related to the line of first-order transitions between the dimer-singlet and -triplet regimes. We show by high-precision quantum Monte Carlo simulations, which are sign-free in the fully frustrated limit, that this critical point is in the Ising universality class. At zero temperature, the continuous transition between the ordered bilayer…
We study the thermal transport properties of several quantum spin chains and ladders. We find indications for a diverging thermal conductivity at finite temperatures for the models examined. The temperature at which the non-diverging prefactor κ^{(th)}(T) peaks is in general substantially lower than the temperature at which the corresponding specific heat c_V(T) is maximal. We show that this result of the microscopic approach leads to a substantial reduction for estimates of the magnetic mean-free path λextracted by analyzing recent experiments, as compared to similar analyses by phenomenologi…
We study formation of a periodical structure of quasiparticle-like magnetic configurations with non-trivial topological charge, known as a magnetic skyrmion phase, on a frustrated triangular lattice antiferromagnetic Heisenberg model with Dzyaloshinskii-Moriya interaction (DMI) by means of Monte Carlo simulations. The existence of such a phase, formed on the three interpenetrating sublattices, has been demonstrated for a sufficiently large strength of DMI. The goal of the present investigation is to establish the minimum values of both the DM interaction strength as well as the magnetic field …
We investigate the thermodynamic properties of the frustrated bilayer quantum Heisenberg antiferromagnet at low temperatures in the vicinity of the saturation magnetic field. The low-energy degrees of freedom of the spin model are mapped onto a hard-square gas on a square lattice. We use exact diagonalization data for finite spin systems to check the validity of such a description. Using a classical Monte Carlo method we give a quantitative description of the thermodynamics of the spin model at low temperatures around the saturation field. The main peculiarity of the considered two-dimensional…
The competition between quantum and classical magnetization plateaus of S=1/2 frustrated Heisenberg chains with modified exchange couplings is investigated. The conventional S=1/2 frustrated Heisenberg chains is known to exhibit a 3-fold degenerate udu-type classical plateau at 1/3 of the saturation magnetization accompanied by the spontaneous Z_3 translational symmetry breakdown. The stability of this plateau phase against period 3 exchange modulation which favors the 00u-type quantum plateau state (00= singlet dimer) is studied by bosonization, renormalization group and numerical diagonaliza…
The spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain with ferromagnetic next-nearest-neighbour (NNN) interaction is investigated. The ground state is the Haldane phase for weak NNN interaction, and is the ferromagnetic phase for weak antiferromagnetic interaction. We find a series of topologically distinct spin-gap phases with various magnitudes of edge spins for strong NNN interaction. The phase boundaries between these phases are determined on the basis of the DMRG calculation with additional spins that compensate the edge spins. It is found that each of the exact soluti…
We consider the spin-1/2 antiferromagnetic Heisenberg model on a bilayer honeycomb lattice including interlayer frustration in the presence of an external magnetic field. In the vicinity of the saturation field, we map the low-energy states of this quantum system onto the spatial configurations of hard hexagons on a honeycomb lattice. As a result, we can construct effective classical models (lattice-gas as well as Ising models) on the honeycomb lattice to calculate the properties of the frustrated quantum Heisenberg spin system in the low-temperature regime. We perform classical Monte Carlo si…
muSR and 7Li NMR relaxation measurements in frustrated two-dimensional S=1/2 Heisenberg antiferromagnets on a square lattice are presented. It is found that both in Li2VOSiO4 and Li2VOGeO4, spin dynamics at frequencies well below the Heisenberg exchange frequency are present. These dynamics are associated with the motions of walls separating coexisting collinear domains with a magnetic wave vector rotated by 90 degrees.
We study here different regions in phase diagrams of the spin-1/2, spin-1 and spin-3/2 one dimensional antiferromagnetic Heisenberg systems with frustration (next-nearest-neighbor interaction $J_2$) and dimerization ($δ$). In particular, we analyze the behaviors of the bipartite entanglement entropy and fidelity at the gapless to gapped phase transitions and across the lines separating different phases in the $J_2-δ$ plane. All the calculations in this work are based on numerical exact diagonalizations of finite systems.
In a strongly frustrated square-lattice antiferromagnet with diagonal coupling J', for J/(2J') < 1, an incommensurate spiral state with propagation vector Q = (π+/- δ, π+/- δ) near (π,π) competes closely with the Neel collinear antiferromagnetic ground state. For classical Heisenberg spins the energy of the spiral state can be lowered as it adapts to the distortion of the crystal lattice. As a result, a weak superstructural modulation such as exist in doped cuprates might stabilize an incommensurate spiral phase for some range of the parameter J/(2J') close to 1.
Skyrmion crystal formation and temperature -- magnetic field phase diagram of the frustrated tirangular-lattice Heisenberg magnet with easy-axis masugnetic anisotropy
We discuss theoretically frustrated Heisenberg spiral magnets in magnetic field $\bf H$. We demonstrate that small anisotropic spin interactions (single-ion biaxial anisotropy or dipolar forces) select the plane in which spins rotate (spiral plane) and can lead to the spiral plane flop upon in-plane field increasing. Expressions for the critical fields $H_{flop}$ are derived. It is shown that measuring of $H_{flop}$ is an efficient and simple method of quantifying the anisotropy in the system (as the measurement of spin-flop fields in collinear magnets with axial anisotropy). Corresponding rec…
Ground state properties of the S=1/2 frustrated Heisenberg chain with period 3 exchange modulation are investigated using the numerical diagonalization and DMRG method. It is known that this model has a magnetization plateau at 1/3 of the saturation magnetization M_s. On the other hand, the ground state is ferrimagnetic even in the absence of frustration if one of the nearest neighbour bond is ferromagnetic and others are antiferromagnetic. In the present work, we show that this ferrimagnetic state continues to the region in which all bonds are antiferromagnetic if frustration is strong. This …
The ground state of the square lattice bilayer quantum antiferromagnet with nearest ($J_1$) and next-nearest ($J_2$) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling $J_3$. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Padé approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decrease…
For the frustrated two-dimensional $S=1/2$ antiferromagnetic Heisenberg model close to quantum phase transition we consider the singlet ground states retaining both translational and SU(2) symmetry. Besides usually discussed checkerboard, spin-liquid and stripe states an unconventional state with two coexisting long-range orders appears to be possible at sufficiently large damping of spin excitations. The problem is treated in the frames of self-consistent spherically symmetric approach.
Effects of interlayer coupling and spatial anisotropy on spin-wave excitation spectra of a three-dimensional spatially anisotropic, frustrated spin-$\half$ Heisenberg antiferromagnet (HAFM) is investigated for the two ordered phases using second-order spin-wave expansion. We show that the second-order corrections to the spin-wave energies are significant and find that the energy spectra of the three-dimensional HAFM shares similar qualitative features with the energy spectra of the two-dimensional HAFM on a square lattice. We also discuss the features that can provide experimental measures for…
We use a recently proposed perturbative numerical renormalization group algorithm to investigate ground-state properties of a frustrated three dimensional Heisenberg model on an anisotropic lattice. We analyze the ground state energy, the finite size spin gap and the static magnetic structure factor. We find in two dimensions a frustration-induced gapless spin liquid state which separates two magnetically ordered phases. In the spin liquid state, the magnetic structure factor shows evidence that this state is made of nearly disconnected chains. This spin liquid state is unstable against unfrus…
Aiming to describe frustrated quantum magnets with non-magnetic singlet ground states, we have extended the Rokhsar-Kivelson (RK) loop-expansion to derive a generalized Quantum Dimer Model containing only connected terms up to arbitrary order. For the square lattice frustrated Heisenberg antiferromagnet (J1-J2-J3 model), an expansion up to 8th order shows that the leading correction to the original RK model comes from dimer moves on length-6 loops. This model free of the original sign problem is treated by advanced numerical techniques. The results suggest that a rotationally anisotropic plaqu…
We study the formation and growth of a skyrmion crystal (SkX) phase in a frustrated antiferromagnetic Heisenberg model on a triangular lattice with Dzyaloshinskii-Moriya interaction (DMI) in the presence of an external magnetic field. We build phase diagrams in the temperature-field parameter plane, featuring first-order phase transitions and tricritical points, and study their evolution with the increasing DMI strength. It is found that already relatively small DMI intensity can lead to the appearance of the SkX phase at low temperatures in the vicinity of the meeting point of the remaining h…
We study the dynamical response of frustrated, quasi-one-dimensional spin-1/2 Heisenberg antiferromagnets at finite temperatures. We allow for the presence of a Dzyaloshinskii-Moriya interaction. We concentrate on a model of weakly coupled planes of anisotropic triangular lattices. Combining exact results for the dynamical response of one dimensional Heisenberg chains with a Random Phase Approximation (RPA) in the frustrated interchain couplings, we calculate the dynamical susceptibility in the disordered phase. We investigate the instability of the disordered phase to the formation of collect…
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.
To clarify the instability of the ferrimagnetism which is the fundamental magnetism of ferrite, numerical-diagonalization study is carried out for the two-dimensional S=1/2 Heisenberg antiferromagnet with frustration. We find that the ferrimagnetic ground state has the spontaneous magnetization in small frustration; due to a frustrating interaction above a specific strength, the spontaneous magnetization discontinuously vanishes so that the ferrimagnetic state appears only under some magnetic fields. We also find that, when the interaction is increased further, the ferrimagnetism disappears ev…
We study a spin-5/2 antiferromagnetic trimerized chain substance SrMn3P4O14 using neutron powder diffraction experiments. The coplanar spiral magnetic structure appears below T_N1 = 2.2(1) K. Values of several magnetic structure parameters change rapidly at T_N2 = 1.75(5) K, indicating another phase transition, although the magnetic structures above and below T_N2 are the qualitatively same. The spiral magnetic structure can be explained by frustration between nearest-neighbor and next-nearest-neighbor exchange interactions in the trimerized chains.
We consider the spin-1/2 antiferromagnetic Heisenberg model on two one-dimensional frustrated lattices, double-tetrahedral chain and octahedral chain, with almost dispersionless (flat) lowest magnon band in a strong magnetic field. Using the localized magnons picture, we construct an effective description of the one-dimensional chains with triangle and square traps within the strong coupling approximation. We perform extensive exact diagonalization and density matrix renormalization group calculations to check the validity of the obtained effective Hamiltonians by comparison with the initial m…
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.
Exact and rigorous solutions of the ground-state problem for the classical Heisenberg model with nearest-neighbor interactions on two- and three-dimensional lattices composed of zigzag (triangular) ladders are obtained in a very simple way, with the use of a cluster method. It is shown how the geometrical frustration due to the presence of triangles as structural units leads to the emergence of incommensurate spiral orderings and their collinear limits. Interestingly, these orderings are determined by a single angle (along with the signs of the interactions between neighboring spins); therefor…
We investigate non-equilibrium properties of the frustrated Heisenberg antiferromagnets on the triangular lattice. Nonequilibrium critical relaxation of frustrated Heisenberg antiferromagnets shows a dynamic transition (or, at least, sharp crossover) at the same temperature $T_{\rm u}=0.282 J$ as for static properties due to unbinding of $\mathbb{Z}_2$-vortices. We show that starting from the high-temperature initial state, due to presence of $\mathbb{Z}_2$-vortices in the considering system, in a broad temperature range $T<T_{\rm u}$ the dynamic properties in the intermediate time range are s…
We use bosonization and renormalization group methods to determine the ground state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-1/2 Luttinger liquid coupled by a Kondo exchange interaction $J_K$ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling $J_1$ and a next-nearest-neighbor (frustrating) exchange interaction $J_2$. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling $J_K$ with the Luttinger liquid. We discuss the stru…
Frustration refers to competition between different interactions that cannot be simultaneously satisfied, a familiar feature in many magnetic solids. Strong frustration results in highly degenerate ground states, and a large suppression of ordering by fluctuations. Key challenges in frustrated magnetism are characterizing the fluctuating spin-liquid regime and determining the mechanism of eventual order at lower temperature. Here, we study a model of a diamond lattice antiferromagnet appropriate for numerous spinel materials. With sufficiently strong frustration a massive ground state degenera…
Using a lattice-gas description of the low-energy degrees of freedom of the quantum Heisenberg antiferromagnet on the frustrated two-leg ladder and bilayer lattices we examine the magnetization process at low temperatures for these spin models. In both cases the emergent discrete degrees of freedom implicate a close relation of the frustrated quantum Heisenberg antiferromagnet to the classical lattice gas with finite nearest-neighbor repulsion or, equivalently, to the Ising antiferromagnet in a uniform magnetic field. Using this relation we obtain analytical results for thermodynamically large…
We studied the thermodynamics of the one-dimensional J1-J2 spin-1/2 Heisenberg chain for ferromagnetic nearest-neighbor bonds J1 < 0 and frustrating antiferromagnetic next-nearest-neighbor bonds J1 > 0 using full diagonalization of finite rings and a second-order Green-function formalism. Thereby we focus on J2 < |J1|/4 where the ground state is still ferromagnetic, but the frustration influences the thermodynamic properties. We found that their critical indices are not changed by J2. The analysis of the low-temperature behavior of the susceptibility chi leads to the conclusion that this behav…
Using the Bond Operator Technique (BOT), we have studied the low energy excitationspectrum of a frustrated dimerized antiferromagnetic Heisenberg chain. In particular, we have compared our analytical results with previous Exact Diagonalizations (ED) data. Qualitatively, the BOT results are in good agreement with the ED data. And even a very good quantitative agreement is obtained in some parameter region. It is clearly shown that there is only one elementary excitation branch (lowest triplet branch) and that the two other well defined excitations which appear below the continuum, one singlet a…
Using the spin-rotation-invariant Green's function method we calculate the thermodynamic quantities (correlation functions <S_0 S_R>, uniform static spin susceptibility χ, correlation length ξ, and specific heat C_V) of the two-dimensional spin-1/2 J1-J2 Heisenberg ferromagnet for J2 < J2^c \approx 0.44|J1|, where J2^c is the critical frustrating antiferromagnetic next-nearest neighbor coupling at which the ferromagnetic ground state gives way for a ground-state phase with zero magnetization. Examining the low-temperature behavior of χand ξ, in the limit T \to 0 both quantities diverge exponen…
Using the density-matrix renormalization group, we determine the phase diagram of the spin 1/2 Heisenberg antiferromagnet on a honeycomb lattice with a nearest neighbor interaction J1 and a frustrating, next-neighbor exchange J2. As frustration increases, the ground state exhibits Neel, plaquette and dimer orders, with critical points at J2/J1 = 0.22 and 0.35. We observe that both the spin gap and the corresponding order parameters vanish continuously at both the critical points, indicating the presence of deconfined quantum criticality.
We calculate the low-temperature thermodynamic quantities (magnetization, correlation functions, transverse and longitudinal correlation lengths, spin susceptibility, and specific heat) of the frustrated one-dimensional spin-half J1-J2 Heisenberg ferromagnet, i.e. for J2< 0.25|J1|, in an external magnetic field using a second-order Green-function formalism and full diagonalization of finite systems. We determine power-law relations for the field dependence of the position and the height of the maximum of the uniform susceptibility. Considering the specific heat at low magnetic fields, two maxi…
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.
We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest and next-nearest neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S_1 > S_2, using 1/S spin-wave expansions, density-matrix renormalization group, and exact- diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate- incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of…
We present a detailed numerical analysis of the low energy excitation spectrum of a frustrated and dimerized spin $S=1/2$ Heisenberg chain. In particular, we show that in the commensurate spin--Peierls phase the ratio of the singlet and triplet excitation gap is a universal function which depends on the frustration parameter only. We identify the conditions for which a second elementary triplet branch in the excitation spectrum splits from the continuum. We compare our results with predictions from the continuum limit field theory . We discuss the relevance of our data in connection with recen…
Based on exact diagonalization data for finite quantum Heisenberg antiferromagnets on two frustrated lattices (two-leg ladder and bilayer) and analytical arguments we map low-energy degrees of freedom of the spin models in a magnetic field on classical lattice-gas models. Further we use transfer-matrix calculations and classical Monte Carlo simulations to give a quantitative description of low-temperature thermodynamics of the quantum spin models. The classical lattice-gas model yields an excellent description of the quantum spin models up to quite large temperatures. The main peculiarity of t…
Within Dyson-Maleev (DM) transformation and self-consistent mean-field treatment, the Néel order/disorder transition is studied for an antiferromagnetic Heisenberg model which is defined on a square lattice with a nearest neighbour exchange $J_1$ and a next-nearest neighbour exchange $J_2$ along only one of the diagonals. It is found that the Néel order may exist up to $J_2/J_1=0.572$, beyond its classically stable regime. This result qualitatively improves that from linear spin-wave theory based on Holstein-Primakoff transformation.
We consider the antiferromagnetic spin-1/2 $XXZ$ Heisenberg model on a frustrated diamond-chain lattice in a $z$- or $x$-aligned external magnetic field. We use the strong-coupling approach to elaborate an effective description in the low-temperature strong-field regime. The obtained effective models are spin-1/2 $XY$ chains which are exactly solvable through the Jordan-Wigner fermionization. We perform exact-diagonalization studies of the magnetization curves to test the quality of the effective description. The results may have relevance for the description of the azurite spin-chain compound…
Motivated by recent experimental work on FeCrAs, we study the magnetic properties of classical spin models on the hexagonal Fe$_2$P/ZrNiAl structure (space group $P{\bar{6}}2m$). When both transition metal/rare earth sites carry magnetic moments, one has alternating distorted kagome and triangular lattice layers. Each point of the triangular lattice lies at the centre of a distorted hexagon and actually corresponds to three isolated magnetic atoms: a "trimer". We show that a simple model consisting of antiferromagnetically correlated Heisenberg spins on the frustrated distorted kagome lattice …
We discuss theoretically phase transitions in frustrated antiferromagnets with biaxial anisotropy or dipolar forces in magnetic field applied along the easy axis at $T=0$. There are well-known sequences of phase transitions upon the field increasing: the conventional spin-flop transition and the flop of the spiral plane at strong and weak easy-axis anisotropy, respectively. We argue that much less studied scenarios can appear at moderate anisotropy in which the magnetic field induces transitions of the first order from the collinear state to phases with spiral orderings. Critical fields of the…
We present a Density Matrix Renormalization Group (DMRG) study of the ground-state properties of spin-1/2 frustrated $J_1-J_3$ Heisenberg $n_l$-leg ladders (with $n_l$ up to 8). For strong frustration ($J_3/J_1\simeq 0.5$), both even- and odd-leg ladders display a finite gap to spin excitations, which we argue remains finite in the two-dimensional limit. In this regime, on odd-leg ladders the ground state is spontaneously dimerized, in agreement with the Lieb-Schultz-Mattis prediction, while on even-leg ladders the dimer correlations decay exponentially. The magnitude of the dimer order parame…
Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear Néel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the Néel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critica…
