Spin Rotation Technique for Non-Collinear Magnetic Systems: Application to the Generalized Villain Model

TL;DR

This paper introduces a generalized spin rotation technique for analyzing non-collinear magnetic systems, demonstrated on the generalized Villain model, revealing new phase behaviors and spin dynamics.

Contribution

A novel generalized spin rotation method using Holstein-Primakoff expansion and Green's functions for non-collinear magnetic systems.

Findings

Expanded phase diagram with new canted spin configurations

Analytical and numerical results for spin-wave dynamics

Identification of distinct spin structure factors

Abstract

This work develops a new generalized technique for determining the static and dynamic properties of any non-collinear magnetic system. By rotating the spin operators into the local spin reference frame, we evaluate the zeroth, first, and second order terms in a Holstein-Primakoff expansion, and through a Green's functions approach, we determine the structure factor intensities for the spin-wave frequencies. To demonstrate this technique, we examine the spin-wave dynamics of the generalized Villain model with a varying interchain interaction. The new interchain coupling expands the overall phase diagram with the realization of two non-equivalent canted spin configurations. The rotational Holstein-Primakoff expansion provides both analytical and numerical results for the spin dynamics and intensities of these phases.