Development of a magnetic interatomic potential for cubic anti-ferromagnets: the case of NiO

TL;DR

This work addresses the challenge of embedding magnetic interactions into empirical interatomic potentials for cubic antiferromagnets, using NiO as a case study. It develops a spin-lattice MD framework with a Hamiltonian $\mathcal{H}_{sl}(\mathbf{r},\mathbf{p},\mathbf{s})$ that combines elasticity and magnetism, including a two-ion Néel term and a Bethe-Slater parameterization. It constructs two NiO potentials (Born-type and RF-MEAM) and validates them against DFT at zero temperature, reproducing volume magnetostriction, magnetocrystalline anisotropy, and anisotropic magnetostriction. This approach enables large-scale simulations of magnetoelastic phenomena and paves the way for studying magnetoelectric coupling and magnon–phonon dynamics in oxide antiferromagnets.

Abstract

Interatomic potentials are essential for molecular dynamics simulations of magnetic materials, yet incorporating magnetic features into potentials for complex antiferromagnets remains challenging. Nickel oxide (NiO), a prototypical cubic antiferromagnet, exemplifies this difficulty. Here we develop a methodology to integrate magnetic properties into interatomic potentials for cubic antiferromagnets by adding a magnetic Hamiltonian which includes both the Heisenberg exchange and Néel model. We apply this approach to NiO by constructing two potentials: one based on the Born model of ionic solids and another using a reference-free modified embedded atom method. Both potentials include magnetoelastic interactions and are validated against Density Functional Theory calculations, showing excellent agreement in mechanical and magnetic properties at zero temperature. These models enable large-scale simulations of magnetoelastic phenomena in antiferromagnets and open avenues for molecular dynamics studies involving coupled electric and magnetic fields in metal oxides.

Figures (8)

• Figure 1: (a) Crystal and magnetic structure of NiO. (b) The exchange interactions between nearest neighbor and next-nearest-neighbor Ni sites.
• Figure 2: Total energy and pressure as a function of the cell volume changes. The red dots depict the results obtained from the MD simulation in LAMMPS by just including the interionic potential modeled by Fisher and MatsubaraFisher-potential and the dashed line corresponds to the EOS fit. The blue line shows the pressure.
• Figure 3: Total energy as a function of the cell volume changes fitted by EOS for the case of NiO MD simulations performed with the RF-MEAM potential. The green line shows the pressure.
• Figure 4: Definition of the SC Ni$^{2+}$ sublattices in NiO. Each of the 4 SC sublattices, in turn, consists of two sublattices with spin up and spin down.
• Figure 5: Volume magnetostriction in SD-MD models. Equilibrium volumes for AFM and PM states were derived from fitting simulation data by EOS giving the volume magnetostriction constant $\omega_s=-0.00149$ in (a) SD-MD 1 and $\omega_s=-0.00136$ in (b) SD-MD 2. The dotted lines show the equilibrium volumes of the corresponding AFM and PM states. The energy difference between the PM and AFM ordered equilibrium states is $E(V_0^{PM})-E(V_0^{AFM})=0.03378$ (eV/f.u.) in both SD-MD models.