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arXiv:1908.06630 · Physical review. B./Physical review. B

Effects of magnetic anisotropy on spin and thermal transport in classical antiferromagnets on the square lattice

Kazushi Aoyama, Hikaru Kawamura

Published Oct 9, 2019• 18 citations
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Abstract

Transport properties of the classical antiferromagnetic XXZ model on the square lattice have been theoretically investigated, putting emphasis on how the occurrence of a phase transition is reflected in spin and thermal transports. As is well known, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}\ensuremath{\equiv}{J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition of the model, i.e., either a second-order transition at ${T}_{N}$ into a magnetically ordered state or the Kosterlitz-Thouless (KT) transition at ${T}_{\text{KT}}$, which respectively occur for the Ising-type ($\mathrm{\ensuremath{\Delta}}>1$) and XY-type ($\mathrm{\ensuremath{\Delta}}<1$) anisotropies, while for the isotropic Heisenberg case of $\mathrm{\ensuremath{\Delta}}=1$, a phase transition does not occur at any finite temperature. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that the spin current probes the difference in the ordering properties, while the thermal current does not. For the XY-type anisotropy, the longitudinal spin-current conductivity ${\ensuremath{\sigma}}_{xx}^{s}$ ($={\ensuremath{\sigma}}_{yy}^{s}$) exhibits a divergence at ${T}_{\text{KT}}$ of the exponential form ${\ensuremath{\sigma}}_{xx}^{s}\ensuremath{\propto}exp\left[B/\sqrt{T/{T}_{\text{KT}}\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}\right]$ with $B=O(1)$, while for the Ising-type anisotropy, the temperature dependence of ${\ensuremath{\sigma}}_{xx}^{s}$ is almost monotonic without showing a clear anomaly at ${T}_{N}$ and such a monotonic behavior is also the case in the Heisenberg-type spin system. The significant enhancement of ${\ensuremath{\sigma}}_{xx}^{s}$ at ${T}_{\text{KT}}$ is found to be due to the exponential rapid growth of the spin-current relaxation time toward ${T}_{\text{KT}}$, which can be understood as a manifestation of the topological nature of a vortex whose lifetime is expected to get longer toward ${T}_{\text{KT}}$. Possible experimental platforms for the spin-transport phenomena associated with the KT topological transition are discussed.

DOI
10.1103/physrevb.100.144416

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We investigate spin and thermal transport near the N\'eel transition temperature TN{T}_{N}TN​ in three dimensions by numerically analyzing the classical antiferromagnetic XXZXXZXXZ model on the cubic lattice, where in the model, the anisotropy of the exchange interaction $\mathrm{\ensuremath{\Delta}}={J}_{z}/{J}_{x}$ plays a role to control the universality class of the transition. It is found by means of the hybrid Monte Carlo and spin-dynamics simulations that in the XYXYXY and Heisenberg cases of $\mathrm{\ensuremath{\Delta}}\ensuremath{\le}1$, the longitudinal spin conductivity ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ exhibits a divergent enhancement on cooling toward TN{T}_{N}TN​ while not in the Ising case of $\mathrm{\ensuremath{\Delta}}>1$. In all three cases, the temperature dependence of the thermal conductivity ${\ensuremath{\kappa}}_{\ensuremath{\mu}\ensuremath{\mu}}$ is featureless at TN{T}_{N}TN​, being consistent with experimental results. The divergent enhancement of ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ toward TN{T}_{N}TN​ is attributed to the spin-current relaxation time which gets longer toward TN{T}_{N}TN​, showing a power-law divergence characteristic of critical phenomena. It is also found that in contrast to the XYXYXY case where the divergence in ${\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ is rapidly suppressed below ${T}_{N}, {\ensuremath{\sigma}}_{\ensuremath{\mu}\ensuremath{\mu}}^{s}$ likely remains divergent even below TN{T}_{N}TN​ in the Heisenberg case, which might experimentally be observed in the ideally isotropic antiferromagnet RbMnF3{\mathrm{RbMnF}}_{3}RbMnF3​.
The critical behavior of 2D magnetic easy-plane systems has mainly been studied by the classical XY model. However, the z components of the spins have to be considered in order to describe real systems, and their fluctuations cannot positively be neglected when quantum effects are to be included, quantum spins being intrinsically three-component objects. Therefore, Monte Carlo simulations are performed for the Heisenberg ferromagnet with easy-plane anisotropy (XXZ model) on a two-dimensional square lattice with a twofold aim: first, to obtain accurate quantitative results about the critical behavior of the classical model, showing the relevant role played by the out-of-plane fluctuations; second, to open the way for approaching the quantum thermodynamics by means of the effective Hamiltonian method that reduces the quantum thermodynamics of the XXZ ferromagnet to the investigation of an effective classical model with temperature-dependent renormalized interaction parameters. Specific heat, magnetic susceptibility, and correlation length are calculated in the critical region for lattice sizes up to 128×128. These quantities preserve the Kosterlitz–Thouless behavior of the XY model. For the transition temperature of the classical XX0 model we obtain the estimate kBTc/(JS̃2)=0.69±0.01.
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We study the thermal transition between the paramagnetic and antiferromagnetic phases of interacting magnetic dipoles on square lattices in two dimensions. By Monte Carlo simulations, we find strong long-range order in the low temperature phase and a critical behavior that is, as in the fourfold anisotropic XY model, nonuniversal, in that the single-site quadrupolar anisotropy h4{h}_{4}h4​ is a relevant variable. However, the critical indices differ markedly from the ones for the anisotropic XY model. They vary from Ising type, within errors, for h4=0{h}_{4}=0h4​=0, to a critical behavior in the ${h}_{4}\ensuremath{\rightarrow}\ensuremath{\infty}$ limit that is nearly as abrupt as a first-order transition.
Spontaneous symmetry breaking of 2D isotropic Heisenberg magnet is restricted by Mermin-Wagner theorem at any finite temperature in presence of short-range exchange interaction.Kosterlitz and Thouless using XY spin model showed that how an order state could developed in 2D spin system in presence of short range isotropic interaction.Very recent discovery of several van der waals magnet revised and redefined our understanding on 2D Heisenberg magnet and its ground state properties.After a rigorous and careful study of several 2D magnetic material we have realized from both experimentally and numerically that the finite size of a 2D system has great impact on the ground state symmetry breaking.Because of that finite size effect more often an anisotropic residual magnetic moment is generated and trigger the spontaneous symmetry breaking at finite temperature(T) and even only presence of short-range interaction we observed the phase transition of that Heisenberg spin system.In this present work we have shown the basic role of finite size,anisotropy during the symmetry breaking of 2D Heisenberg XY magnet.Here we have simulated Kosterlitz-Thouless transition using classical Monte-carlo simulation and study the effect of anisotropy during the phase transition.We presented the behaviour of different thermodynamic properties of 2D XY spin model system during the Kosterlitz-Thouless(KT) transition.The generic characteristic of KT transition which make it distinct from other critical phenomena is that the peak of heat capacity is not diverging with increase of system size rather peak is decreasing with the increasing of system size near at transition temperature.Here we are observing that behaviour in our present simulation and that specific behaviour help us for classifying the present transition as Kosterlitz-Thouless(KT) transition.
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