XY Antiferromagnet Research Articles

Vortex dynamics in the classical two-dimensional antiferromagnetic XY model

We investigate the dynamics of the two-dimensional antiferromagnetic Heisenberg model with easy-plane exchange symmetry by explicitly calculating the dynamic correlation functions S αα( q , w), α = x, y, z. In addition to the spin waves we find also topological excitations, namely vortices which cause a Kosterlitz-Thouless phase transition at T KT. Our main interest is focused on the free vortices just above T KT where we developed a phenomenology based on a dilute gas of noninteracting vortices. With this ansatz we find central peaks in S αα( q , w) which are at different positions in q-space depending on whether the static vortex structure or the deviations from it due to a finite velocity dominates the correlations. We compare these results with a combined Monte Carlo Molecular Dynamics simulation on a 100 × 100 square lattice. We find a good agreement between our theory and the simulations and we obtain from this comparison explicit values for the vortex correlation length and the vortex average velocity.

Zero-temperature properties of quantum spin systems in two dimensions

We consider the zero-temperature properties of four different spin 1/2 models on two-dimensional lattices: the XY ferromagnet, the XY antiferromagnet, the Heisenberg antiferromagnet, and the Dzyaloshinsky–Moriya models. Most of this article is a review of previously published work, but a few previously unpublished results are included. The relation between three of the models on bipartite lattices is described. The properties of the XY ferromagnet in two dimensions, especially those derived from extrapolation of finite lattice results, are reviewed. A numerical factor by which spin-wave and finite-lattice estimates of the long-range order parameter differ is discussed. For frustrated models on the triangular lattice the possibility of a chirality phase transition instead of, or in addition to, a magnetic phase transition is considered.

Monte Carlo simulations of CsMnBr3

Monte Carlo simulations of the magnetic Hamiltonian of CsMnBr3, an XY antiferromagnet on a simple-hexagonal lattice, have been carried in order to examine the phase diagram in an applied magnetic field and the recently discovered tetracritical point. Results on a 12×12×12 lattice reproduce the observed phase diagram. Application of a magnetic field in the ab plane splits the zero-field transition into two transitions. The structures of the two phases are also in agreement with the measurements. Simulations of lattices with a larger number of spins along the c axis reveal a substantial renormalization of the Néel temperature due to the quasi-one-dimensional nature of the Hamiltonian.

Low Temperature Properties of One-Dimensional ClassicalXYModel with Frustration

An antiferromagnetic classical XY model with the nearest-neighbor interaction 2 J and the next-nearest-neighbor interaction δ J on a one-dimensional lattice is investigated in the low temperature limit. We obtain the asymptotic behaviors at long distances, of the two-spin correlation function for δ>1/2 and of the chirality-chirality correlation function for δ=1. The behavior of the latter correlation function is shown to be similar to the one of the two-spin correlation function for the Ising model with the nearest-neighbor interaction J /2 on a one-dimensional lattice.

Pairing of holes via vortex/antivortex attraction in doped La 2-x(Sr)xCuO4

The consequences of delocalised magnetic frustration in the pure antiferromagnetic XY (n=2) spin system are studied numerically. This frustration is found to enhance significantly the formation of vortex excitations, which tend to bind antivortices below the Kosterlitz-Thouless transition temperature. We find a net attraction between frustrated plaquettes mediated by the attraction between the vortices. Applied to the understanding of high temperature superconducting materials, like La 2−x (Sr) x CuO 4 , this can serve as a real space pairing mechanism with a high binding energy between the holes, induced by doping. There are common features between this pairing model and the «spinon-holon» picture, which may provide a link between these different approaches

Mean field theory of superconductivity in frustrated 2D-XY magnets

We consider the two-dimensional antiferromagnetic classical XY model on a square lattice with frustrated plaquettes introduced by dilute doping of ferromagnetic bonds. These ferromagnetic bonds carry positive electronic charges of the holes. A pairing potential is derived and the energy spectrum of a hole pair is discussed for the possibility of bound states. In the long distance approximation, the dipolar interaction between canted local states is derived and discussed in the mean field in both reciprocal space and real space. BCS type calculation of the pairing potential is formulated for the lowest angular momentum gap function. The odd parity gap yields higher transition temperature then the corresponding even parity one. Application to La 2CuO 4 yields critical temperature in the order of 40 K. Implications of this effective attraction mediated by the frustrated plaquettes in the XY model are suggested for other types of two-dimensional magnets. Possible extensions of the model to incorporate Ising anisotropy and interplanar coupling are discussed.

Tetracritical behavior of CsMnBr3.

We have used elastic neutron scattering to determine the magnetic phase diagram of ${\mathrm{CsMnBr}}_{3}$, an XY antiferromagnet on a stacked triangular lattice. The application of a field along (100) splits the antiferromagnetic transition and results in an intermediate phase of spin-flop character. This phase is extremely narrow near the zero-field transition at ${\mathrm{T}}_{\mathrm{N}}$=8.32 K which is shown to be a tetracritical point. This suggests that the unusual critical properties of the zero-field phase transition may be due to its tetracriticality as opposed to belonging to a new universality class.

MAGNETIC PAIRING IN TWO-DIMENSIONAL ANTIFERROMAGNETIC XY MODEL

A two-dimensional Ising Coulomb gas is introduced to describe the frustrated plaquettes of the two-dimensional antiferromagnetic XY model with Coulomb repulsion. The Ising spin variable corresponds to the two possible chiralities of the frustrated plaquettes, which repel each other with a screened Coulomb potential. Using the self-consistent screening analysis, the Ising Coulomb gas is shown to have a Kosterlitz-Thouless transition from a pairing phase at low temperature to a plasma phase at high temperature. The phase diagram is obtained numerically as a function of density and relative strength of the attraction between particles of opposite chiralities and the Coulomb repulsion. Possible applications to the magnetic pairing mechanism of high temperature superconductors is discussed in the context of Li doped La 2 CuO 4. It is also argued that the Aharony et al. model of magnetic pairing with the dipolar attraction can be derived as a special case of the Ising Coulomb gas model and is superceded by a stronger attractive interaction in magnetic pairing mechanism in the self-consistent analysis.

New Universality Class of Antiferromagnetic Phase Transition in CsMnBr3

The critical exponents γ and ν of an XY antiferromagnet on a layered-triangular lattice, CsMnBr 3 , have been measured by neutron scattering. They are γ=1.10±0.05 and ν=0.57±0.03 in the reduced temperature range 0.015< e < 0.1 above the Neel temperature. These and the previously measured β show that this phase transition belongs to the universality class characterized by the O(2) symmetry order-parameter in three dimensions, as calculated by Kawamura.

New Critical Exponent β of the XY Antiferromagnet on Stacked Triangular Lattice, CsMnBr3

The phase transition of the XY antiferromagnet on a stacked triangular lattice, CsMnBr 3 is studied by neutron diffraction. The critical exponent β is found to be β=0.25±0.01. The value is in excellent agreement with the predicted value by Kawamura for a new universality class, giving convincing experimental support to the phase transition characterized by the Z 2 ×S 1 or O(2) symmetry.

Statistical Mechanical Theory of Cooperative Phenomena. II. Super-Effective-Field Theory with Applications to Exotic Phase Transitions

A new scheme to study exotic phase transitions is formulated by introducing the concept of a super-effective field. A general mechanism of phase transitions is elucidated and a general criterion of order parameters is proposed on the basis of the newly formulated super-effective-field theory. An alternative formulation based on a decoupled density matrix is also given. It is easily shown using these formulations that a quantum chiral order appears in the antiferromagnetic XY model on the triangular lattice. A super-effective-field theory of spin glasses is also presented.

Zero-temperature ordering in the two-dimensional quantum XY model

We have calculated the probability distribution for the staggered magnetization at T=0 for the 2D antiferromagnetic quantum XY model on finite lattices. For the ground state, the distribution shows evidence of isotropic magnetization ordering on the xy-plane. Based on data on seven lattices up to 26 sites, the extrapolated value of the staggered magnetization is 0.448±0.003 in the thermodynamic limit.

Local canting in a dilute triangular XY antiferromagnet

Computer simulations are used to show how diamagnetic impurities induce the formation of 'canted local states' in a triangular lattice of antiferromagnetically coupled XY spins, through relief of the magnetic frustration inherent in the lattice. The canted local states are shown to interact with each other through polarisation of the intervening medium. At low concentration of impurities the exchange energy of some of the remaining moments is found to increase, in contrast to the usual effect of impurities on the exchange energy of the moments in a non-frustrated lattice.

Experimental confirmation of the existence of a new universality class for stacked triangular lattices

Neutron scattering studies of CsMnBr3, a three-dimensional XY antiferromagnet on a stacked triangular lattice, have been carried out in the critical region. Measurements of three magnetic Bragg peak intensities as a function of temperature have shown that the transition to an antiferromagnetically ordered state at TN=8.3 K takes place with critical exponent beta =0.22+or-0.02. This value of beta does not correspond to any standard model of a universality class characterised by the real-space dimensionality and the dimensionality of the order parameters. It does, however, agree well with the predictions of Kawamura (1986, 1988) for a universality class described by the symmetry of the order parameter rather than just the dimensionality. For CsMnBr3 this symmetry is V=Z2*S1, and Kawamura has predicted beta =0.25+or-0.02, in agreement with the experimental data.

Magnetic susceptibilities of the random-site diluted XY antiferromagnet

The magnetic dilution problem has been studied in a series of compounds of formula [${\mathrm{Co}}_{\mathit{p}}$${\mathrm{Zn}}_{1\mathrm{\ensuremath{-}}\mathit{p}}$(${\mathrm{C}}_{5}$${\mathrm{H}}_{5}$No${)}_{6}$](${\mathrm{NO}}_{3}$${)}_{2}$, with p between 0.17 and 1, by means of low-temperature zero-field susceptibility measurements over the temperature interval 40 mK--4.2 K. The pure compound (p=1) is a good example of the simple-cubic (sc), XY antiferromagnet. The measurements have been recorded primarily on single crystals, although some polycrystalline samples have also been included. The magnetic ordering temperature ${T}_{c}$(p) decreases with diminishing concentration p of the magnetic component. The ${T}_{c}$(p) curve follows the theoretical prediction for the sc XY model, being compatible with the percolation limit ${p}_{c}$=0.31 for this lattice. The transverse susceptibility increases with decreasing p and diverges for p\ensuremath{\rightarrow}${p}_{c}$. The predictions for the quenched-site, diluted XY antiferromagnet for S=(1/2, ${J}_{\mathrm{XY}}$/${k}_{B}$=-0.22 K, and ${g}_{\mathrm{XY}}$=4.99 have been compared with the experimental transverse susceptibility. Near the critical concentration, the system susceptibility can be described remarkably well by the predictions for the XY linear chain with the same exchange constant as for the pure material.

Zero-temperature properties of quantum spin models on the triangular lattice III: the Heisenberg antiferromagnet

The calculation of two- and four-spin correlations of the [Formula: see text] Heisenberg antiferromagnet has been extended to an N = 21 site triangular lattice. The infinite-lattice ground state energy per bond is estimated to be E0/3NJ = −0.3678 ± 0.005 by fitting a quadratic in 1/N to the finite N data. The plaquette chirality order is slightly greater than in the XY antiferromagnet. The two-spin correlation is conjectured to decay as [Formula: see text].

Renormalization group approach to antiferromagnetic quantum XY model on a triangular lattice

Renormalization group approach to antiferromagnetic quantum XY model on a triangular lattice

Exact real space renormalisation group transformation for the dimerised XY chain

An analytical real space renormalisation group transformation is obtained for the one-dimensional spin-1/2 antiferromagnetic dimerised XY model. Using the method of Sarker (1984) the recursion relations for the parameters are derived from the mapping between blocks of sizes L and L/b, for arbitrary size L and scale factor b. The results for the gap and for the critical exponent are shown to converge rapidly toward their exact values. The dynamical exponent has 1/L corrections (b approximately 1) instead of the usual 1/ln L ones (b=L). The differential renormalisation group equations are obtained explicitly. The authors show that the non-analyticity of the scaling function (for the density of energy) stems from a dangerous irrelevant variable, the antiferromagnetic coupling.

Phase diagram of the antiferromagnetic XY model with a triangular lattice in an external magnetic field

The ordered states of a planar antiferromagnet with a triangular lattice are investigated in the presence of a magnetic field. The spin wave free energy is taken into account and proved to be important for determining the properties of the system. The phase diagram is constructed. It contains four different phases with rigorous long-range order. Three of them are characterised by different configurations of mean magnetic moments for the three substances. The existence of one or more non-trivial phase with an algebraic decay of the correlation functions is very probable.

Ground-state properties of the Heisenberg antiferromagnet-numerical study

The ground states of the spin-1/2 antiferromagnetic Heisenberg and XY models are investigated on the fully-frustrated triangular lattice. We extrapolate numerically exact properties of finite size systems (up to 21 spins) to the infinite lattice to estimate the energy and spin state.