Effects of frustration and cyclic exchange on the spin-1/2 Heisenberg antiferromagnet within the self-consistent spin-wave theory

TL;DR

This paper investigates how frustration and cyclic exchange interactions influence the magnetic properties of a spin-1/2 Heisenberg antiferromagnet using self-consistent spin-wave theory, providing detailed theoretical insights and applying findings to high-$T_c$ cuprates.

Contribution

It introduces a comprehensive self-consistent spin-wave analysis including multiple exchange interactions and applies it to experimental data on La2CuO4, improving understanding of magnetic excitations.

Findings

Detailed description of elementary spin excitations and ground-state energy.

Comparison of self-consistent spin-wave results with linear and perturbative theories.

Refined exchange parameters for La2CuO4 based on experimental dispersion data.

Abstract

The relevance of the quasi-two-dimensional spin-1/2 frustrated quantum antiferromagnet due to its possibility of modelling the high-temperature superconducting parent compounds has resulted in numerous theoretical and experimental studies. This paper presents a detailed research of the influence of the varying exchange interactions on the model magnetic properties within the framework of self-consistent spin-wave theory based on Dyson-Maleev representation. Beside the nearest neighbour interaction within the plane, the planar frustration up to the third nearest neighbours, cyclic interaction and the interlayer coupling are taken into account. The detailed description of the elementary spin excitations, staggered magnetization, spin-wave velocity renormalization factor and ground-state energy is given. The results are compared to the predictions of the linear spin-wave theory and when possible also to the second-order perturbative spin-wave expansion results. Finally, having at our disposal improved experimental results for the in-plane spin-wave dispersion in high-$T_c$ copper oxide $\mbox{La}_2\mbox{CuO}_4$, the self-consistent spin-wave theory is applied to that compound in order to correct earlier obtained set of exchange parameters and high temperature spin-wave dispersion.