Modification of the classical Heisenberg helimagnet by weak uniaxial anisotropy and magnetic field

TL;DR

This paper investigates how weak uniaxial anisotropy and magnetic fields modify the classical ground state of the Heisenberg helimagnet, revealing higher-order Fourier harmonics and providing a microscopic approach beyond traditional methods.

Contribution

It introduces an alternative microscopic method to accurately determine the classical ground state of the Heisenberg helimagnet under anisotropy and magnetic field effects.

Findings

Higher-order Fourier harmonics appear in the spin structure.

The classical ground state energy and magnetization are calculated.

The approach surpasses the limitations of the Luttinger-Tisza method.

Abstract

Classical ground state of the isotropic Heisenberg spin Hamiltonian on a primitive Bravais lattice is known to be a single-Q planar spin spiral. A uniaxial anisotropy and external magnetic field distort this structure by generating the higher-order Fourier harmonics at wave-vectors nQ in the spatial spin configuration. These features are not captured in the formalism based on the Luttinger-Tisza theorem, where the classical ground state energy is minimized under the ``weak'' condition on the length of the spins. We discuss why the correct solution is lost in that approach and present an alternative microscopic treatment of the problem. It allows to find the classical ground state for general Q for both easy-axis and easy-plane uniaxial second-order anisotropy, and for any orientation of the magnetic field, by treating the effect of anisotropy (but not the field) as a perturbation to the exchange structure. As a result, the classical ground state energy, the uniform magnetization, and the magnetic Bragg peak intensities that are measured in experiment, are calculated.