Accurate simulation of magnetic materials using computational methods is essential for under-standing their fundamental behavior and enabling their use in technological applications. In this work, I use first-principles calculations to investigate systems with magnetic properties and to develop new methods for predicting the behavior of these materials. The systems studied are characterized by magnetic moments that are localized near the atomic sites. The paramagnetic state, at which these magnetic moments are disordered, and the magnetic order-disorder transition are of specific interest in this work.

To better capture finite-temperature magnetic behavior, a machine learning (ML) model is developed to predict the magnitudes of the magnetic moments at finite temperatures. This enables the inclusion of longitudinal spin fluctuations in coupled spin-lattice dynamics simulations, which would otherwise be computationally prohibitive. The ML model is applied to Fe at both the magnetic transition temperature, 1043 K, and at a pressure and temperature comparable to the conditions of the Earth’s inner core.

Evidently, the magnetic order-disorder transition temperature of ferromagnetic materials, known as the Curie temperature, is a fundamental property, since these materials lose their macroscopic magnetization above this point. Predicting this temperature is therefore crucial for the discovery and design of new magnetic materials. An approach is proposed which is based on the energy difference between magnetically ordered and disordered states, obtained from density functional theory (DFT) calculations. This method offers a balance between accuracy and computational efficiency, allowing its application to a wide variety of systems and making it suitable for high-throughput screening. The approach is fitted to and benchmarked against several known ferro- and ferrimagnetic materials and further evaluated on a particularly challenging class of systems: substitutionally disordered alloys. Finally, this approach enables a high-throughput exploration of Fe-, Mn-, and Co-containing systems to identify promising candidates for magnetic applications.

In addition, the debated role of constraining fields in DFT calculations for constrained non-collinear magnetism is investigated. The study shows that these fields can be used to propagate the transverse dynamics of magnetic moments, thereby providing a theoretical foundation for their use in adiabatic spin dynamics simulations.