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arXiv:cond-mat/9902163 · Journal of Physics Condensed Matter

A comparative study of the magnetization process of two-dimensional antiferromagnets

A. Honecker

Published Jan 1, 1999• 81 citations

Abstract

Plateaux in the magnetization curves of the square-, triangular- and hexagonal-lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero-magnetization plateau (corresponding to a spin gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one-third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer-matrix computations for the Ising limit and continue with series in the XXZ anisotropy for plateau boundaries using the ground states of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated with the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.

DOI: 10.1088/0953-8984/11/24/311

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Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagomé lattices using exact diagonalization (ED) for up to N = 40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagomé lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.

Using mainly numerical methods, we investigate the ground-state magnetization curve of a mixed spin chain with uniaxial single-ion anisotropies, where S = 1 and S = 2 spins are alternating and coupled antiferromagnetically. Special attention is paid to the magnetization plateau, the 1/3-plateau, which appears at one third of the saturation magnetization in the magnetization curve. It is found that there appear three kinds of 1/3-plateaux, one of which has a quantum nature, while the remaining two have a classical (Ising) nature.

The magnetization process of theantiferromagnetic chain with coupling and single-ion anisotropies is investigated using numerical diagonalization of finite-size clusters and level spectroscopy analysis. Various magnetization plateaux are found at 1/5, 2/5, 3/5, and 4/5 of the saturation magnetization. plateaux without translational symmetry breaking are predicted to occur at 1/5 and 3/5 magnetization. A symmetry-protected topological plateau phase is found at 3/5 magnetization, but not at 1/5. In addition translational-symmetry-broken plateaux induced by large coupling anisotropy are found at 1/5, 2/5, 3/5, and 4/5 magnetization. Phase diagrams at 1/5, 2/5, 3/5, and 4/5 of the saturation magnetization are obtained. Magnetization curves for several representative anisotropies are also presented, together with the corresponding magnetic phase diagrams.

We study the breakdown of the magnetization plateau at the magnetization M = M S /3 ( M S is the saturation magnetization) of the S = 1/2 anisotropic spin chain with ferromagnetic-ferromagnetic-antiferromagnetic interactions. We consider the model with the isotropic ferromagnetic (trimer) coupling J F , and anisotropic antiferromagnetic coupling ( J x = J y = J AF and J z = J AF ). For the limit of large J F / J AF , the model is equivalent to the S = 3/2 XXZ chain with the exchange anisotropy . There is a phase transition between the plateau (small- ) and the no-plateau (large- ) regions. This phase transition is of the Berezinskii-Kosterlitz-Thouless type, and we determine the phase boundary from the numerical diagonalization data. For = 1, in particular, the phase transition between the plateau and the no-plateau regions occurs at the point c = 15.4.

The magnetization process of the spin-1/2 antiferromagnetic

\mathrm{XXZ}

models with Ising-like anisotropy in the ground state is investigated. We show numerically that the Ising-like

\mathrm{XXZ}

models on square and cubic lattices show a first-order phase transition at some critical magnetic field. We estimate the value of the critical field and the magnetization jump on the basis of the Maxwell construction. The magnetization jump in the Ising limit is investigated by means of perturbation theory. Based on our numerical results, we briefly discuss the phase diagram of the extended Bose-Hubbard model in the hard-core limit.