24 research outputs found
The Heisenberg antiferromagnet on a triangular lattice: topological excitations
We study the topological defects in the classical Heisenberg antiferromagnet
in two dimensions on a triangular lattice (HAFT). While the topological
analysis of the order parameter space indicates that the defects are of
type, consideration of the energy leads us to a description of the low--energy
stationary points of the action in terms of vortices, as in the planar XY
model. Starting with the continuum description of the HAFT, we show
analytically that its partition function can be reduced to that of a
2--dimensional Coulomb gas with logarithmic interaction. Thus, at low
temperatures, the correlation length is determined by the spinwaves, while at
higher temperatures we expect a crossover to a Kosterlitz--Thouless type
behaviour. The results of recent Monte Carlo calculations of the correlation
length are consistent with such a crossover.Comment: 9 pages, revtex, preprint: ITP-UH 03/9
Dynamics of topological defects in a spiral: a scenario for the spin-glass phase of cuprates
We propose that the dissipative dynamics of topological defects in a spiral
state is responsible for the transport properties in the spin-glass phase of
cuprates. Using the collective-coordinate method, we show that topological
defects are coupled to a bath of magnetic excitations. By integrating out the
bath degrees of freedom, we find that the dynamical properties of the
topological defects are dissipative. The calculated damping matrix is related
to the in-plane resistivity, which exhibits an anisotropy and linear
temperature dependence in agreement with experimental data.Comment: 4 pages, as publishe
Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations
We have simulated the classical Heisenberg antiferromagnet on a triangular
lattice using a local Monte Carlo algorithm. The behavior of the correlation
length , the susceptibility at the ordering wavevector , and
the spin stiffness clearly reflects the existence of two temperature
regimes -- a high temperature regime , in which the disordering
effect of vortices is dominant, and a low temperature regime ,
where correlations are controlled by small amplitude spin fluctuations. As has
previously been shown, in the last regime, the behavior of the above quantities
agrees well with the predictions of a renormalization group treatment of the
appropriate nonlinear sigma model. For , a satisfactory fit of the
data is achieved, if the temperature dependence of and is
assumed to be of the form predicted by the Kosterlitz--Thouless theory.
Surprisingly, the crossover between the two regimes appears to happen in a very
narrow temperature interval around .Comment: 13 pages, 8 Postscript figure
Topological Defects and the Spin Glass Phase of Cuprates
We propose that the spin glass phase of cuprates is due to the proliferation
of topological defects of a spiral distortion of the antiferromagnet order. Our
theory explains straightforwardly the simultaneous existence of short range
incommensurate magnetic correlations and complete a-b symmetry breaking in this
phase. We show via a renormalization group calculation that the collinear
O(3)/O(2) symmetry is unstable towards the formation of local non-collinear
correlations. A critical disorder strength is identified beyond which
topological defects proliferate already at zero temperature.Comment: 7 pages, 2 figures. Final version with some changes and one replaced
figur
Vortex-induced topological transition of the bilinear-biquadratic Heisenberg antiferromagnet on the triangular lattice
The ordering of the classical Heisenberg antiferromagnet on the triangular
lattice with the the bilinear-biquadratic interaction is studied by Monte Carlo
simulations. It is shown that the model exhibits a topological phase transition
at a finite-temperature driven by topologically stable vortices, while the spin
correlation length remains finite even at and below the transition point. The
relevant vortices could be of three different types, depending on the value of
the biquadratic coupling. Implications to recent experiments on the triangular
antiferromagnet NiGaS is discussed
Z_2-vortex ordering of the triangular-lattice Heisenberg antiferromagnet
Ordering of the classical Heisenberg antiferromagnet on the triangular
lattice is studied by means of a mean-field calculation, a scaling argument and
a Monte Carlo simulation, with special attention to its vortex degree of
freedom. The model exhibits a thermodynamic transition driven by the Z_2-vortex
binding-unbinding, at which various thermodynamic quantities exhibit an
essential singularity. The low-temperature state is a "spin-gel" state with a
long but finite spin correlation length where the ergodicity is broken
topologically. Implications to recent experiments on triangular-lattice
Heisenberg antiferromagnets are discussed
Spin-stiffness and topological defects in two-dimensional frustrated spin systems
Using a {\it collective} Monte Carlo algorithm we study the low-temperature
and long-distance properties of two systems of two-dimensional classical tops.
Both systems have the same spin-wave dynamics (low-temperature behavior) as a
large class of Heisenberg frustrated spin systems. They are constructed so that
to differ only by their topological properties. The spin-stiffnesses for the
two systems of tops are calculated for different temperatures and different
sizes of the sample. This allows to investigate the role of topological defects
in frustrated spin systems. Comparisons with Renormalization Group results
based on a Non Linear Sigma model approach and with the predictions of some
simple phenomenological model taking into account the topological excitations
are done.Comment: RevTex, 25 pages, 14 figures, Minor changes, final version. To appear
in Phys.Rev.
Phase-transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: a Monte Carlo simulation
We present the results of Monte Carlo simulations for the antiferromagnetic
classical XXZ model with easy-plane exchange anisotropy on the triangular
lattice, which causes frustration of the spin alignment. The behaviour of this
system is similar to that of the antiferromagnetic XY model on the same
lattice, showing the signature of a Berezinskii-Kosterlitz-Thouless transition,
associated to vortex-antivortex unbinding, and of an Ising-like one due to the
chirality, the latter occurring at a slightly higher temperature. Data for
internal energy, specific heat, magnetic susceptibility, correlation length,
and some properties associated with the chirality are reported in a broad
temperature range, for lattice sizes ranging from 24x24 to 120x120; four values
of the easy-plane anisotropy are considered. Moving from the strongest towards
the weakest anisotropy (1%) the thermodynamic quantities tend to the isotropic
model behaviour, and the two transition temperatures decrease by about 25% and
22%, respectively.Comment: 11 pages, 13 figures (embedded by psfig), 3 table
Nonequilibrium relaxation study of the anisotropic antiferromagnetic Heisenberg model on the triangular lattice
Effect of exchange anisotropy on the relaxation time of spin and vector
chirality is studied for the antiferromagnetic classical Heisenberg model on
the triangular lattice by using the nonequilibrium relaxation Monte Carlo
method. We identify the Berezinskii-Kosterlitz-Thouless (BKT) transition and
the chiral transition in a wide range of the anisotropy, even for very small
anisotropy of 0.01%. As the anisotropy decreases, both the critical
temperatures steeply decrease, while the BKT critical region becomes
divergently wide. We elucidate a sharp "V shape" of the phase diagram around
the isotropic Heisenberg point, which suggests that the isotropic case is
exceptionally singular and the associated Z vortex transition will be isolated
from the BKT and chiral transitions. We discuss the relevance of our results to
peculiar behavior of the spin relaxation time observed experimentally in
triangular antiferromagnets.Comment: 5 pages, 4 figures, accepted for publication in J. Phys. Soc. Jp
First-Order Phase Transition with Breaking of Lattice Rotation Symmetry in Continuous-Spin Model on Triangular Lattice
Using a Monte Carlo method, we study the finite-temperature phase transition
in the two-dimensional classical Heisenberg model on a triangular lattice with
or without easy-plane anisotropy. The model takes account of competing
interactions: a ferromagnetic nearest-neighbor interaction and an
antiferromagnetic third nearest-neighbor interaction . As a result, the
ground state is a spiral spin configuration for . In this
structure, global spin rotation cannot compensate for the effect of 120-degree
lattice rotation, in contrast to the conventional 120-degree structure of the
nearest-neighbor interaction model. We find that this model exhibits a
first-order phase transition with breaking of the lattice rotation symmetry at
a finite temperature. The transition is characterized as a vortex
dissociation in the isotropic case, whereas it can be viewed as a vortex
dissociation in the anisotropic case. Remarkably, the latter is continuously
connected to the former as the magnitude of anisotropy decreases, in contrast
to the recent work by Misawa and Motome [J. Phys. Soc. Jpn. \textbf{79} (2010)
073001.] in which both the transitions were found to be continuous.Comment: 11pages, 16figures, accepted to JPS