Quantitative Multiscale Modelling of Magnetic Materials: From First Principles to Atomic and Continuum Models

In recent years, antiferromagnets have become one of the the primary classes of magnetic materials studied for spintronic device applications. The development of new experimental techniques has made these materials easier to study, though challenges remain as the compensated order makes it difficult to resolve the dynamics of individual sublattices, and their multi-sublattice structure means the magnetic symmetry is typically lower than their ferromagnetic counterparts, permitting more complicated Hamiltonians and making the development of physical models difficult. As a result, computational techniques are playing an increasing role in advancing research on antiferromagnets. Proper parameterisation of these computational models is vital for realistic and reproducible research.

This work aimed to better understand the thermodynamics of the prototypical easy-plane antiferromagnet NiO. NiO is considered to be a simple antiferromagnet, yet there are several conflicting models which have been used to explain different phenomena in this material. No model thus far has been able to describe all aspects of this material. In order to understand complex antiferromagnetic materials, it is vital that we have a complete understanding of the simplest examples.

In this work, a combination of analytic and numerical calculations are used which are compared to the best available experimental measurements throughout. Analytic calculations of the finite temperature behaviour of antiferromagnets are primarily based on Linear Spin Wave Theory (LSWT). Numerical simulations are a combination of spin dynamics calculations using the Landau-Lifshitz-Gilbert (LLG) equation and Monte Carlo methods applied to atomistic models of magnetic materials. A stochastic Langevin term is used to augment the LLG equation which allows modelling at finite temperatures.

In Chapter 4 of this work, we develop a framework of tools to create an atomistic model of NiO which hasn't been used previously in the literature and is consistent with both neutron scattering experiments and advanced ab-initio calculations, has the correct ground state, and is consistent with the magnetic symmetry of the crystal. In Chapter 5, we use constrained Monte Carlo and analytic calculations to show that the temperature dependence of the easy-plane anisotropy in NiO--from magnetic dipole-dipole interactions--deviates from the Callen-Zenner scaling for a uniaxial magnetocrystalline anisotropy. Further, we derive new expressions for the temperature dependence of the sublattice magnetisation and spin wave stiffness using linear spin wave theory, then compare this to atomistic simulations implemented with a thermal Langevin field which is consistent with Bose-Einstein statistics, as well as experimental measurements. From this, we are able to quantify at which temperature the first order expansion of Holstein-Primakoff operators breaks down, and we show that the temperature dependence of the Kittel mode is approximately the same as the sublattice magnetisation. Using atomistic simulations, we calculate the temperature dependence of the magnetic damping (magnon scattering) and, by comparing with experimental measurements, we show that damping due to magnon-electron and magnon-phonon scattering is negligible at low temperatures. In Chapter 6, we show that all experimentally observed resonant modes in NiO appear using our model but that many of these modes are non-linear in origin so cannot be understood using the linear spin wave approximations which have been used previously. This gives new insight into the physics of NiO which helps the interpretation of dynamical experiments, and resolves the discrepancies between previous models and the observed phenomena in NiO. In the final chapter, we develops a new method for calculating the finite temperature value of macroscopic parameters in any magnetic material. This leverages the fundamentals of thermodynamics and statistical mechanics, and has broad applications for the multiscale modelling of magnetic materials.