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Title: Dynamic correlations in the classical two-dimensional antiferromagnetic Heisenberg model with easy-plane symmetry

Abstract

We investigate the dynamics of the two-dimensional antiferromagnetic Heisenberg model with easy-plane exchange symmetry. We develop a phenomenology of spin-wave and vortex excitations and calculate their contributions to the dynamical correlation functions {ital S}{sup {alpha}{alpha}}({bold q},{omega}), {alpha}={ital x},{ital y},{ital z}. The vortex shape depends explicitly on an exchange anisotropy parameter {lambda} and changes from a mainly in-plane structure below a critical {lambda}{sub {ital c}} to a shape with well-established {ital z} components around the vortex center above {lambda}{sub {ital c}}. In this paper we will discuss only the case {lambda}{lt}{lambda}{sub {ital c}}, where the system behaves almost like the pure {ital XY} model. The general properties of the dynamical behavior of the spin waves and vortices below the Kosterlitz-Thouless transition temperature {ital T}{sub KT} have been widely examined for the ferromagnetic {ital XY} model, and do not change much in the antiferromagnet (although here we have two magnon branches according to the two different spin sublattices). Our main interest is focused on the unbound vortices just above {ital T}{sub KT}. Assuming a dilute gas of ballistically moving vortices, we obtain central peaks in {ital S}{sup {alpha}{alpha}}({bold q},{omega}) similar to the ferromagnetic case, but in some cases at different positions inmore » {bold q} space depending on whether the static vortex structure or the deviation from it due to a finite velocity dominates the correlations. These results are compared with a combined Monte Carlo--molecular-dynamics simulation on a 100{times}100 square lattice.« less

Authors:
; ; ;  [1]
  1. Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico (USA)
Publication Date:
OSTI Identifier:
6218804
Resource Type:
Journal Article
Journal Name:
Physical Review, B: Condensed Matter; (United States)
Additional Journal Information:
Journal Volume: 44:18; Journal ID: ISSN 0163-1829
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ANTIFERROMAGNETIC MATERIALS; CORRELATION FUNCTIONS; SPIN WAVES; ARSENATES; CHROMIUM CHLORIDES; CHROMIUM COMPLEXES; CLATHRATES; COPPER CHLORIDES; COPPER COMPLEXES; COPPER FLUORIDES; GRAPHITE; HEISENBERG MODEL; POTASSIUM COMPOUNDS; RUBIDIUM COMPOUNDS; TWO-DIMENSIONAL CALCULATIONS; ALKALI METAL COMPOUNDS; ARSENIC COMPOUNDS; CARBON; CHLORIDES; CHLORINE COMPOUNDS; CHROMIUM COMPOUNDS; COMPLEXES; COPPER COMPOUNDS; COPPER HALIDES; CRYSTAL MODELS; ELEMENTAL MINERALS; ELEMENTS; FLUORIDES; FLUORINE COMPOUNDS; FUNCTIONS; HALIDES; HALOGEN COMPOUNDS; MAGNETIC MATERIALS; MATERIALS; MATHEMATICAL MODELS; MINERALS; NONMETALS; OXYGEN COMPOUNDS; TRANSITION ELEMENT COMPLEXES; TRANSITION ELEMENT COMPOUNDS; 360606* - Other Materials- Physical Properties- (1992-)

Citation Formats

Voelkel, A R, Wysin, G M, Bishop, A R, and Mertens, F G. Dynamic correlations in the classical two-dimensional antiferromagnetic Heisenberg model with easy-plane symmetry. United States: N. p., 1991. Web. doi:10.1103/PhysRevB.44.10066.
Voelkel, A R, Wysin, G M, Bishop, A R, & Mertens, F G. Dynamic correlations in the classical two-dimensional antiferromagnetic Heisenberg model with easy-plane symmetry. United States. doi:10.1103/PhysRevB.44.10066.
Voelkel, A R, Wysin, G M, Bishop, A R, and Mertens, F G. Fri . "Dynamic correlations in the classical two-dimensional antiferromagnetic Heisenberg model with easy-plane symmetry". United States. doi:10.1103/PhysRevB.44.10066.
@article{osti_6218804,
title = {Dynamic correlations in the classical two-dimensional antiferromagnetic Heisenberg model with easy-plane symmetry},
author = {Voelkel, A R and Wysin, G M and Bishop, A R and Mertens, F G},
abstractNote = {We investigate the dynamics of the two-dimensional antiferromagnetic Heisenberg model with easy-plane exchange symmetry. We develop a phenomenology of spin-wave and vortex excitations and calculate their contributions to the dynamical correlation functions {ital S}{sup {alpha}{alpha}}({bold q},{omega}), {alpha}={ital x},{ital y},{ital z}. The vortex shape depends explicitly on an exchange anisotropy parameter {lambda} and changes from a mainly in-plane structure below a critical {lambda}{sub {ital c}} to a shape with well-established {ital z} components around the vortex center above {lambda}{sub {ital c}}. In this paper we will discuss only the case {lambda}{lt}{lambda}{sub {ital c}}, where the system behaves almost like the pure {ital XY} model. The general properties of the dynamical behavior of the spin waves and vortices below the Kosterlitz-Thouless transition temperature {ital T}{sub KT} have been widely examined for the ferromagnetic {ital XY} model, and do not change much in the antiferromagnet (although here we have two magnon branches according to the two different spin sublattices). Our main interest is focused on the unbound vortices just above {ital T}{sub KT}. Assuming a dilute gas of ballistically moving vortices, we obtain central peaks in {ital S}{sup {alpha}{alpha}}({bold q},{omega}) similar to the ferromagnetic case, but in some cases at different positions in {bold q} space depending on whether the static vortex structure or the deviation from it due to a finite velocity dominates the correlations. These results are compared with a combined Monte Carlo--molecular-dynamics simulation on a 100{times}100 square lattice.},
doi = {10.1103/PhysRevB.44.10066},
journal = {Physical Review, B: Condensed Matter; (United States)},
issn = {0163-1829},
number = ,
volume = 44:18,
place = {United States},
year = {1991},
month = {11}
}