The Heisenberg antiferromagnet: an explicitly rotational invariant formulation

TL;DR

This paper presents a straightforward derivation of a rotationally invariant Lagrangian for antiferromagnetic spin systems, capable of describing both antiferromagnetic and ferromagnetic behaviors within a unified framework.

Contribution

It introduces a simple, explicitly rotational invariant Lagrangian for antiferromagnetic systems, extending its applicability across different magnetic regimes.

Findings

Lagrangian describes antiferromagnetic to ferromagnetic transition

Applicable to schematic models of spin systems

Provides a unified rotationally invariant formulation

Abstract

A simple derivation of an explicitly rotational invariant Lagrangian describing the dynamics of an antiferromagnetic spin system is presented. The scope of the derived Lagrangian is analysed in the context of schematic models. It is shown that the Lagrangian describes the behaviour of spin systems from the anti-ferromagnetic to the ferromagnetic regimes.