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arXiv:cond-mat/0205227 · Physical review. B, Condensed matter

Spin-dynamics simulations of the triangular antiferromagneticXYmodel

Kwangsik T. Nho, D. P. Landau

Published Nov 4, 2002• 11 citations
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Abstract

Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes $L<~300.$ The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor $S(\mathbf{q},w)$ for momentum $\mathbf{q}$ and frequency $\ensuremath{\omega}.$ Below ${T}_{\mathrm{KT}}$ (Kosterlitz-Thouless transition), both the in-plane ${(S}^{\mathrm{xx}})$ and out-of-plane ${(S}^{\mathrm{zz}})$ components of $S(\mathbf{q},\ensuremath{\omega})$ exhibit very strong and sharp spin-wave peaks. Well above ${T}_{\mathrm{KT}},$ ${S}^{\mathrm{xx}}$ and ${S}^{\mathrm{zz}}$ apparently display a central peak, and spin-wave signatures are still seen in ${S}^{\mathrm{zz}}.$ In addition, we also observed an almost dispersionless domain-wall peak at high $\ensuremath{\omega}$ below ${T}_{c}$ (Ising transition), where long-range order appears in the staggered chirality. Above ${T}_{c},$ the domain-wall peak disappears for all q. The line shape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent $z=1.002(3).$ We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequency ${\ensuremath{\omega}}_{m}$ and the dynamic structure factor $S(\mathbf{q},\ensuremath{\omega})$ itself.

DOI
10.1103/physrevb.66.174403

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International Journal of Modern Physics C•Apr 1, 2006•1 citation
Using Monte Carlo and spin-dynamics methods, we have investigated the dynamic behavior of the classical, antiferromagnetic XY model on a triangular lattice with linear sizes L< 300.L<~300.L< 300. The temporal evolutions of spin configurations were obtained by solving numerically the coupled equations of motion for each spin using fourth-order Suzuki-Trotter decompositions of exponential operators. From space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms we obtained the dynamic structure factor S(q,w)S(\mathbf{q},w)S(q,w) for momentum q\mathbf{q}q and frequency \ensuremathω.\ensuremath{\omega}.\ensuremathω. Below TKT{T}_{\mathrm{KT}}TKT​ (Kosterlitz-Thouless transition), both the in-plane (Sxx){(S}^{\mathrm{xx}})(Sxx) and out-of-plane (Szz){(S}^{\mathrm{zz}})(Szz) components of S(q,\ensuremathω)S(\mathbf{q},\ensuremath{\omega})S(q,\ensuremathω) exhibit very strong and sharp spin-wave peaks. Well above TKT,{T}_{\mathrm{KT}},TKT​, Sxx{S}^{\mathrm{xx}}Sxx and Szz{S}^{\mathrm{zz}}Szz apparently display a central peak, and spin-wave signatures are still seen in Szz.{S}^{\mathrm{zz}}.Szz. In addition, we also observed an almost dispersionless domain-wall peak at high \ensuremathω\ensuremath{\omega}\ensuremathω below Tc{T}_{c}Tc​ (Ising transition), where long-range order appears in the staggered chirality. Above Tc,{T}_{c},Tc​, the domain-wall peak disappears for all q. The line shape of these peaks is captured reasonably well by a Lorentzian form. Using a dynamic finite-size scaling theory, we determined the dynamic critical exponent z=1.002(3).z=1.002(3).z=1.002(3). We found that our results demonstrate the consistency of the dynamic finite-size scaling theory for the characteristic frequency \ensuremathωm{\ensuremath{\omega}}_{m}\ensuremathωm​ and the dynamic structure factor S(q,\ensuremathω)S(\mathbf{q},\ensuremath{\omega})S(q,\ensuremathω) itself.
Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the classical three component XY model (i.e., the anisotropic limit of an easy-plane Heisenberg ferromagnet), on square lattices of size up to 1922{192}^{2}1922, for several temperatures below, at, and above TKT{\mathit{T}}_{\mathrm{KT}}TKT​. The temporal evolution of spin configurations was determined numerically from coupled equations of motion for individual spins by a fourth-order predictor-corrector method, with initial spin configurations generated by a hybrid Monte Carlo algorithm. The neutron-scattering function S(q,\ensuremath{\omega}) was calculated from the resultant space-time displaced spin-spin correlation function. Pronounced spin-wave peaks were found both in the in-plane and the out-of-plane scattering function over a wide range of temperatures. The in-plane scattering function Sxx{\mathit{S}}^{\mathit{xx}}Sxx also has a large number of clear but weak additional peaks, which we interpret to come from two-spin-wave scattering. In addition, we observed a small central peak in Sxx{\mathit{S}}^{\mathit{xx}}Sxx, even at temperatures well below the phase transition. We used dynamic finite-size scaling theory to extract the dynamic critical exponent z. We find z=1.00(4) for all T\ensuremath{\le}TKT{\mathit{T}}_{\mathrm{KT}}TKT​, in excellent agreement with theoretical predictions, although the shape of S(q,\ensuremath{\omega}) is not well described by current theory. \textcopyright{} 1996 The American Physical Society.
Spin-dynamics techniques have been used to perform large-scale simulations of the dynamic behavior of the classical Heisenberg antiferromagnet in simple cubic lattices with linear sizes L< 60.L<~60.L< 60. This system is widely recognized as an appropriate model for the magnetic properties of RbMnF3.{\mathrm{RbMnF}}_{3}.RbMnF3​. Time evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using an algorithm implemented by Krech et al., which is based on fourth-order Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical temperature. The dynamic critical exponent was estimated to be $z=(1.43\ifmmode\pm\else\textpm\fi{}0.03),$ which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Direct, quantitative comparisons of both the dispersion curve and the line shapes obtained from our simulations with very recent experimental results for RbMnF3{\mathrm{RbMnF}}_{3}RbMnF3​ are presented.
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Using spin-dynamics techniques we have performed large-scale computer simulations of the dynamic behavior of the L\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}L body-centered-cubic classical Heisenberg ferromagnet with L\ensuremath{\le}40 in the vicinity of the critical point Tc{\mathit{T}}_{\mathit{c}}Tc​. The temporal evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins by a fourth-order predictor-corrector method with initial spin configurations generated by Monte Carlo methods. The space- and time-displaced spin-spin correlation functions and their space-time Fourier transforms were calculated to determine the neutron-scattering functions. We developed a dynamic finite-size scaling theory for the neutron-scattering function at Tc{\mathit{T}}_{\mathit{c}}Tc​ and used it to extract the dynamic critical exponent z. Within our resolution limit, the value of z was estimated to be 2.478(28), in excellent agreement with the dynamic scaling prediction, and dynamic scaling was found to be valid for momentum transfer q up to 0.4\ensuremath{\pi} in the (1,0,0) direction.
Spin-dynamics simulations have been used to investigate the dynamic behavior of RbMnF_3, treating it as a classical Heisenberg antiferromagnet on a simple cubic lattice. Time-evolutions of spin configurations were determined numerically from coupled equations of motion for individual spins using a new algorithm which is based on Suzuki-Trotter decompositions of exponential operators. The dynamic structure factor was calculated from the space- and time-displaced spin-spin correlation function. The crossover from hydrodynamic to critical behavior of the dispersion curve and spin-wave half-width was studied as the temperature was increased towards the critical value. The dynamic critical exponent was estimated to be z=(1.43\pm 0.03), which is slightly lower than the dynamic scaling prediction, but in good agreement with a recent experimental value. Comparisons are made of both the dispersion curve and the lineshapes obtained from our simulations with very recent experimental results for RbMnF_3 are presented.
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