The variational symmetries and conservation laws in classical theory of Heisenberg (anti)ferromagnet

TL;DR

This paper applies Lie symmetry analysis and Noether's theorem to derive conservation laws for the nonlinear spin dynamics equations in Heisenberg ferromagnets and antiferromagnets.

Contribution

It identifies variational symmetries and corresponding conservation laws for the classical Heisenberg (anti)ferromagnet equations using Lie group methods.

Findings

Derived generators of variational Lie symmetry groups.

Obtained conservation laws for the spin dynamics equations.

Enhanced understanding of symmetries in classical magnetic systems.

Abstract

The nonlinear partial differential equations describing the spin dynamics of Heisenberg ferro and antiferromagnet are studied by Lie transformation group method. The generators of the admitted variational Lie symmetry groups are derived and conservation laws for the conserved currents are found via Noether's theorem.