A Comparative Study of the Magnetization Process of Two-Dimensional Antiferromagnets

TL;DR

This paper investigates magnetization plateaux in two-dimensional antiferromagnets with different lattice geometries, using transfer matrix and series methods, and discusses their universality classes near saturation.

Contribution

It provides a comparative analysis of magnetization plateaux in various 2D antiferromagnets, combining transfer matrix, series expansions, and numerical methods.

Findings

Zero magnetization plateau on square and hexagonal lattices with Ising anisotropy.

One-third saturation plateau on triangular lattice persists with small easy-plane anisotropy.

Universal behavior of magnetization curves near saturation across different dimensions.

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 groundstates 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 to the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.