Magnetic materials play an important part in modern technology, appearing practically everywhere. Nonetheless, there is a need to discover new magnetic materials that can make devices faster, use less energy, and store more data. For this reason, computational modeling is an important tool. However, depending on the material and property, this can require a range of different complementary theoretical methods and modeling protocols, some of which are investigated in this thesis. Magnetic ordering and excitations are mainly governed by the so-called exchange interaction. This is well described within density functional theory (DFT), and we demonstrate that magnetism can emerge even in the non-magnetic anti-pervoskite Ba3SnO Dirac semimetal by introducing oxygen-vacancy defects. These results provide a path to realizing magnetic topological semi-metals, which so far has been very challenging.

To model dynamical and thermodynamic properties of magnetic systems, spin models are typically fitted to DFT total energy calculations. For this purpose, the magnetic force theorem (MFT) has been extensively used. The great advantage of the theorem is that the so-called inter-atomic exchange parameters can be determined from non-selfconsistent calculations. This approach allows for the modeling of complex and large systems. This is demonstrated for the ferrimagnetic insulator yttrium-iron garnet, for which we can model the entire magnon spectrum that agrees well with experimental results. A shortcoming of the conventional use of the MFT is the poor description of short-ranged interactions in itinerant systems. Hence, to improve on existing methods, a fully self-consistent method was developed to calculate exchange interactions from constraining fields. We demonstrate how the use of self-consistent computations can improve the accuracy of ferromagnetic 3d metals, as well as how it can be extended to include multi-spin interactions, which is shown to improve accuracy even further.

In addition to the 3d transition metals themselves, many ferromagnetic materials are alloys. From a modeling perspective, these pose additional complexity. Here, different alloy systems were investigated: the binary Fe–Ga alloy and the high-entropy alloy CrMnFeCoNi. Fe-Ga is known for its magneto-elastic properties. The true origin of these is still undetermined, but we show from a spin dynamics point of view that atomic ordering is essential when modeling these alloys. The high-entropy alloys have been of great interest since they were discovered due to their extraordinary mechanical properties. However, the Co-content in these materials represents an important sustainability issue. This study is focused on the reduction of Co-concentration which may lead to designing more ethical and environmentally friendly materials with good mechanical properties.

Alloy theory can also be used to investigate the adsorption of ions on a surface. This was used for two different SiC polymorphs which were found to be favorable to accommodate Na ions. Different descriptors were examined to assess their performance as anodes in Na-ion batteries and the results provide crucial information regarding the application of these systems as anode materials for next-generation Na-ion batteries.