Spin-lattice model for cubic crystals

TL;DR

This paper introduces a Nél model-based methodology to construct classical spin-lattice Hamiltonians for cubic crystals, accurately capturing magnetic and magnetoelastic properties, including effects of pressure and volume changes.

Contribution

It develops a theoretical framework linking exchange integrals and multipole terms to magnetic properties, enabling accurate modeling of magnetoelastic phenomena in cubic crystals.

Findings

Accurately reproduces elastic tensor and magnetocrystalline anisotropy under pressure.

Models volume dependence of magnetic moments considering hydrostatic pressure effects.

Demonstrates applicability to BCC Fe and FCC Ni with realistic magnetic and elastic properties.

Abstract

We present a methodology based on the N\'{e}el model to build a classical spin-lattice Hamiltonian for cubic crystals capable of describing magnetic properties induced by the spin-orbit coupling like magnetocrystalline anisotropy and anisotropic magnetostriction, as well as exchange magnetostriction. Taking advantage of the analytical solutions of the N\'{e}el model, we derive theoretical expressions for the parameterization of the exchange integrals and N\'{e}el dipole and quadrupole terms that link them to the magnetic properties of the material. This approach allows to build accurate spin-lattice models with the desire magnetoelastic properties. We also explore a possible way to model the volume dependence of magnetic moment based on the Landau energy. This new feature can allow to consider the effects of hydrostatic pressure on the saturation magnetization. We apply this method to develop a spin-lattice model for BCC Fe and FCC Ni, and we show that it accurately reproduces the experimental elastic tensor, magnetocrystalline anisotropy under pressure, anisotropic magnetostrictive coefficients, volume magnetostriction and saturation magnetization under pressure at zero-temperature. This work could constitute a step towards large-scale modeling of magnetoelastic phenomena.