Semiclassical theory of the magnetization process of the triangular lattice Heisenberg model

TL;DR

This paper presents a semiclassical method using linear spin-wave theory to accurately compute the full magnetization curve, including quantum corrections and the 1/3 plateau, for the triangular lattice Heisenberg antiferromagnet.

Contribution

It introduces a simple semiclassical approach to calculate the entire magnetization curve with quantum corrections, improving upon previous methods that only identified critical fields.

Findings

Magnetization curves agree with experimental data for spins 1/2, 1, and 5/2.

The method accurately predicts critical fields for the 1/3 plateau.

The approach captures quantum effects within linear spin-wave theory.

Abstract

Motivated by the numerous examples of 1/3 magnetization plateaux in the triangular lattice Heisenberg an- tiferromagnet with spins ranging from 1/2 to 5/2, we revisit the semiclassical calculation of the magnetization curve of that model, with the aim of coming up with a simple method that allows one to calculate the full mag- netization curve, and not just the critical fields of the 1/3 plateau. We show that it is actually possible to calculate the magnetization curve including the first quantum corrections and the appearance of the 1/3 plateau entirely within linear spin-wave theory, with predictions for the critical fields that agree to order 1/S with those derived a long-time ago on the basis of arguments that required to go beyond linear spin-wave theory. This calculation relies on the central observation that there is a kink in the semiclassical energy at the field where the classical ground state is the collinear up-up-down structure, and that this kink gives rise to a locally linear behavior of the energy with the field when all semiclassical ground states are compared to each other for all fields. The magnetization curves calculated in this way for spin 1/2, 1 and 5/2 are shown to be in good agreement with available experimental data.