Heisenberg model with Dzyaloshinskii-Moriya interaction: A Schwinger boson study

TL;DR

This paper develops a Schwinger-boson approach to study the Heisenberg model with Dzyaloshinskii-Moriya interaction, capturing magnon interactions and noncollinear phases, and applies it to La_2CuO_4 and related compounds.

Contribution

It introduces a conserving mean-field Schwinger-boson method that accounts for magnon-magnon interactions and noncollinear phases in the Dzyaloshinskii-Moriya Heisenberg model, extending previous linear spin-wave analyses.

Findings

Reproduces linear spin-wave predictions in the large-S limit.

Shows small renormalization effects at S=1/2.

Provides detailed analysis of ground-state energy, anisotropy gap, and ferromagnetic moment in La_2CuO_4.

Abstract

We present a Schwinger-boson approach to the Heisenberg model with Dzyaloshinskii-Moriya interaction. We write the anisotropic interactions in terms of Schwinger bosons keeping the correct symmetries present in the spin representation, which allows us to perform a conserving mean-field approximation. Unlike previous studies of this model by linear spin-wave theory, our approach takes into account magnon-magnon interactions and includes the effects of three-boson terms characteristic of noncollinear phases. The results reproduce the linear spin-wave predictions in the semiclassical large-S limit, and show a small renormalization in the strong quantum limit S=1/2. For the sake of definiteness, we specialize the calculations for the pattern of Moriya vectors corresponding to the orthorhombic phase in La_2CuO_4, and give a fairly detailed account of the behavior of ground-state energy, anisotropy gap, and net ferromagnetic moment. In the last part of this work we generalize our approach to describe the geometry of the intermediate phase in La_{2-x}Nd_xCuO_4, and discuss the effects of including nondegenerate 2p_z oxygen orbitals in the calculations.