Two-dimensional Heisenberg Model Research Articles

Disordered phase of a two-dimensional Heisenberg model with [formula omitted

We use the two-step density-matrix renormalization group method to study an anisotropic version of the J 1 – J 2 model with S = 1 . We find a second order transition from a Néel Q = ( π , π ) phase to a disordered phase with a spin gap. This result which is contrasted to our previous finding on S = 1 2 systems suggests the importance of topological effects in the disordered phases of Heisenberg models.

Spin dynamics in the two-dimensional spin-12Heisenberg antiferromagnet

We present low-temperature dynamic properties of the quantum two-dimensional antiferromagnetic Heisenberg model with spin S=1/2. The calculation of the dynamic correlation function is performed by combining a projection operator formalism and the modified spin-wave theory (MSW), which gives a gap in the dispersion relation for finite temperatures. The so calculated dynamic correlation function shows a double peak structure.We also obtain the spin-wave damping and compare our results to experimental data and to theoretical results obtained by other authors using different approaches.

Monte Carlo study of the Kosterlitz-Thouless transition in the Heisenberg model with antisymmetric exchange interactions

We have studied the two-dimensional Heisenberg model with antisymmetric exchange interactions by employing a Monte Carlo simulation, which confirmed a Kosterlitz-Thouless transition. The Kosterlitz-Thouless transition temperature and the energy required to create a bound pair of vortices were calculated as a function of the magnitude of the antisymmetric exchange interaction and compared with the results of the supposedly equivalent two-dimensional easy-plane Heisenberg model.

Helicity modulus and vortex density in the two-dimensional easy-plane Heisenberg model on a square lattice

We have studied the two-dimensional easy-plane Heisenberg model by using a Monte Carlo simulation. The helicity modulus and the vortex density were calculated. The Kosterlitz–Thouless transition temperature obtained from the helicity modulus was consistent with previous results obtained using different methods. The energy required to create a bound pair of vortices shows an anisotropy dependence similar to that of the Kosterlitz–Thouless transition temperature.

Thermodynamics of a two-dimensional Heisenberg ferromagnet with dipolar interaction

Thermodynamics of quantum and classical two-dimensional (2D) Heisenberg models with long-range dipole--dipole interaction has been investigated using various forms of self-consistent spin-wave theory (SSWT). It has been found that SSWT gives a much lower transition temperature ${T}_{c}$ than the free-magnon (spin-wave) theory. For the classical spin, the ${T}_{c}$ from SSWT lies within 9% of the Monte Carlo value, making SSWT the best approximation among those considered. It is proven that the random phase approximation vertex corrections to SSWT are rather small. The results depend strongly on the value of the spin, emphasizing the importance of using the quantum and not the classical 2D Heisenberg model even for large spins such as $S=7∕2$.

Field-induced Magnetic Reorientation in Two-dimensional Anisotropic Quantum Ferromagnet

Field-induced magnetic reorientation of the two-dimensional (2D) Heisenberg model with arbitrary spin is treated by the many-body Green’s function theory. The orientation of the magnetization is determined by the expectation values (α = x,z;) of the spin components of different spins from which the orientation angle θ is obtained as a function of the temperature and of the transverse magnetic field for various parameters of the exchange anisotropy in the (x,y)-plane. Results obtained within the Green’s function theory are compared with the mean-field theory.

Two-dimensional Heisenberg model with nonlinear interactions: [formula omitted] corrections

We investigate a two-dimensional classical N-vector model with a generic nearest-neighbor interaction W ( σ i ⋅ σ j ) in the large- N limit, focusing on the finite-temperature transition point at which energy–energy correlations become critical. We show that this transition belongs to the Ising universality class. However, the width of the region in which Ising behavior is observed scales as 1 / N 3 / 2 along the magnetic direction and as 1 / N in the thermal direction; outside a crossover to mean-field behavior occurs. This explains why only mean-field behavior is observed for N = ∞ .

Magnetic properties of the two-dimensional Heisenberg model on a triangular lattice

The spin Green's function of the antiferromagnetic Heisenberg model on a triangular lattice is calculated using Mori's projection operator technique. At T = 0 the spin excitation spectrum is shown to have gaps at the wave vectors of the classical Néel ordering. This points to the absence of the antiferromagnetic long-range order in the ground state. The calculated spin correlation on the neighboring sites of the same sublattice is in good agreement with the value derived from exact diagonalization. The temperature dependencies of the spin correlations and the gaps are calculated.

Phase diagrams of a classical two-dimensional Heisenberg antiferromagnet with single-ion anisotropy

A classical variant of the two-dimensional anisotropic Heisenberg model reproducing inelastic neutron scattering experiments on La_5 Ca_9 Cu_24 O_41 [M. Matsuda et al., Phys.Rev. B 68, 060406(R) (2003)] is analysed using mostly Monte Carlo techniques. Phase diagrams with external fields parallel and perpendicular to the easy axis of the anisotropic interactions are determined, including antiferromagnetic and spin-flop phases. Mobile spinless defects, or holes, are found to form stripes which bunch, debunch and break up at a phase transition. A parallel field can lead to a spin-flop phase.

Auxiliary-fermion approach to critical fluctuations in the two-dimensional quantum antiferromagnetic Heisenberg model

The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge Q=1 on each lattice site, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low T. This drawback, which is caused by overdamping, is overcome in a `minimal self-consistent approximation' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths and in the short-range-order regime. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.

Out-of-plane vortex in a two-dimensional easy-plane ferromagnet with a magnetic field along the hard axis

In a two-dimensional easy-plane Heisenberg model with a magnetic field along the hard axis, switching between different vortex states (parallel and antiparallel to the field) was studied by means of a Monte Carlo simulation. The vortex-core magnetization appears to be conserved, whether a magnetic field is present or not. From conservation of the core magnetization, the switching field between the two vortex states were calculated, in good agreement with the Monte Carlo simulation.

Spin waves in striped phases

In many antiferromagnetic, quasi-two-dimensional materials, doping with holes leads to ``stripe'' phases, in which the holes congregate along antiphase domain walls in the otherwise antiferromagnetic texture. Using a suitably parametrized two-dimensional Heisenberg model on a square lattice, we study the spin wave spectra of well-ordered spin stripes, comparing bond-centered antiphase domain walls to site-centered antiphase domain walls for a range of spacings between the stripes and for stripes both aligned with the lattice (``vertical'') and oriented along the diagonals of the lattice (``diagonal''). Our results establish that there are qualitative differences between the expected neutron scattering responses for the bond-centered and site-centered cases. In particular, bond-centered stripes of odd spacing generically exhibit more elastic peaks than their site-centered counterparts. For inelastic scattering, we find that bond-centered stripes produce more spin wave bands than site-centered stripes of the same spacing and that bond-centered stripes produce rather isotropic low energy spin wave cones for a large range of parameters, despite local microscopic anisotropy. We find that extra scattering intensity due to the crossing of spin wave modes (which may be linked to the ``resonance peak'' in the cuprates) is more likely for diagonal stripes, whether site- or bond-centered, whereas spin wave bands generically repel, rather than cross, when stripes are vertical.

Instability of planar vortices in the two-dimensional easy-plane Heisenberg model with distance-dependent interactions

It is known that magnetic vortices in two-dimensional Heisenberg models with easy-plane anisotropy exhibit an instability depending on the anisotropy strength. In this paper, we study the statistic behavior of the two-dimensional easy-plane Heisenberg models with distance-dependent interactions ${J}_{xy}(r)$ and ${J}_{z}(r)$ for in-plane and out-of-plane components. We develop analytical and numerical methods for accurate determination of critical anisotropy, above which out-of-plane vortices become stable. In particular, we explore the vortex formation of the Gaussian-type interaction model and determine the critical anisotropy accurately for square, hexagonal, and triangular lattices.

Phase coherence in 2D XY and Heisenberg models*1

A high-precision Monte Carlo study has been made on the two-dimensional XY and Heisenberg models to make clear the nature of the low-temperature behavior of 2D classical spin models. A new type of order parameter is introduced to measure the phase coherence inherent in these models. It has been found that the phase coherence and its fluctuation can be expressed in terms of the characteristic scaling functions. The form of the scaling function in 2D XY model clearly indicate the existence of the Kosterlitz and Thouless transition. Several trials have been made to find the scaling function in 2D Heisenberg model; the most probable form is quite different from the KT form which renders some possibility that the coherent length is still finite at any nonzero temperatures.

Calorimetric investigation of phase transitions in the layered antiferromagnetic molecule-based material {N( n-C 5H 11) 4[Mn IIFe III(ox) 3]} ∞(ox=oxalato)

Heat capacity studies of the layered molecule-based magnetic material {N( n-C 5H 11) 4[Mn IIFe III(ox) 3]} ∞ (ox=oxalato) have been made in the 2–280 K range. Two distinct heat capacity anomalies were detected at 27.1 K ( T N) and 226 K corresponding to magnetic and structural phase transitions, respectively, along with a hump around 23 K. The magnetic heat capacities above T N can be well represented by S=5/2 two-dimensional antiferromagnetic Heisenberg model of a honeycomb lattice with intralayer exchange interaction J/ k B=−3.3 K. Application of spin-wave theory indicated the existence of a very weak interlayer magnetic interaction below T N. The anomaly at 27.1 K is due to the antiferromagnetic transition, in conformity with the magnetic results reported earlier. The hump around 23 K might be associated with the existing uncompensated magnetic moments. The estimated magnetic entropy (33.22 J K −1 mol −1) is close to the expected magnetic entropy ( R ln (6×6)=29.80 J K −1 mol −1) for the spin multiplicity of high spin Mn II and Fe III ions. The heat capacity anomaly at 226 K may be assigned to a structural phase transition of order–disorder type due to increasing conformational change of the n-C 5H 11 chains in the organic cation.

Comment on “Frustrating interactions and broadened magnetic interactions in the edge-sharingCuO2chains inLa5Ca9Cu24O41”

Using Monte Carlo techniques, we show that the two-dimensional anisotropic Heisenberg model reproducing nicely inelastic neutron scattering measurements on ${\mathrm{La}}_{5}{\mathrm{Ca}}_{9}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ [M. Matsuda et al., Phys. Rev. B 68, 060406(R) (2003)] seems to be insufficient to describe correctly measurements on thermodynamic quantities like the magnetization or the susceptibility. Possible reasons for the discrepancy are suggested.

Field‐induced magnetic reorientation of the 2D Heisenberg ferromagnet with S = 1: the influence of an exchange anisotropy

AbstractThe two‐dimensional (2D) Heisenberg model with spin S = 1, with the exchange anisotropy plus a second‐order uniaxial single‐site anisotropy and an external transverse magnetic field is treated by the Tyablikov (Random Phase Approximation: RPA) decoupling of the exchange interaction term and the Anderson‐Callen decoupling of the anisotropy term. The orientation of the magnetization is determined by the expectation values 〈Sα〉 (α = x, z) of the spin components from which the orientation angle θ is obtained as a function of the temperature and of the transverse magnetic field for various parameters of the exchange anisotropy in the (x,y)‐plane. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Phase coherence in 2D XY and Heisenberg models

A high-precision Monte Carlo study has been made on the two-dimensional XY and Heisenberg models to make clear the nature of the low-temperature behavior of 2D classical spin models. A new type of order parameter is introduced to measure the phase coherence inherent in these models. It has been found that the phase coherence and its fluctuation can be expressed in terms of the characteristic scaling functions. The form of the scaling function in 2D XY model clearly indicate the existence of the Kosterlitz and Thouless transition. Several trials have been made to find the scaling function in 2D Heisenberg model; the most probable form is quite different from the KT form which renders some possibility that the coherent length is still finite at any nonzero temperatures.

MAGNETIC EXCITATION OF ORTHOGONAL DIMER HEISENBERG SPIN SYSTEM FOR SrCu2(BO3)2

SrCu 2( BO 3)2 is a new two-dimensional spin gap system and the magnetic behaviour of this compound is explained well by the two-dimensional orthogonal dimer Heisenberg model. Recently several excitations have been observed by inelastic neutron scattering and other experiments. We study features of these excitations by Lanczos method and perturbation technique. A triplet excitation has an almost localised nature. This localised character is observed as an almost flat band in neutron scattering. On the other hand, bound states of two triplet excitations, which have dispersive character, are stable in contrast to ordinary magnetic systems. We calculate the dynamic structure factor by a Lanczos method in finite systems and compare our results with experiments.

Nonadiabatic interaction of acoustic phonons with spins S=1/2 in the two-dimensional Heisenberg model

The ground state of a two-dimensional antiferromagnet having spins S = 1/2 and interacting with acoustic phonons is investigated in the nonadiabatic approximation using the quantum-mechanical Monte Carlo method. The critical parameters of the spin-phonon coupling, corresponding to the formation of bound spin- phonon excitations, crystal symmetry lowering, and the emergence of a gap in the spin excitation spectrum, as well as the antiferromagnet-quantum spin liquid transition, are determined. The orthorhombicity parameter, the sublattice magnetization, the violation of the spherical symmetry of spin-spin correlation functions, and the magnetic moment in Gd 2 CuO 4 and Eu 2 CuO 4 are calculated. © 2003 MAIK "Nauka/Interperiodica".