Antiferromagnetic (AF) materials possess resonance frequencies reaching the THz range, which is two orders of magnitude higher than those of ferromagnets. Many antiferromagnets, such as the prototypical AF Nickel Oxide NiO, are insulating oxides in which the energy dissipation of the spin dynamics is low due to the localized nature of electrons. Their high resonance frequency and low energy dissipation have triggered considerable interest as the modern electronics industry is hitting the walls of frequency and dissipation, and is reaching size limits. Moreover, due to their antiparallel arrangement, the spin structures in AFs are robust and not easily affected by external fields. Because they do not produce stray fields outside the sample, these magnetic materials bring challenges to probe and manipulate, especially at this early stage of their development. Consequently, modelling and numerical simulations of their spin dynamics are crucial in understanding the relevant microscopic processes at the picosecond time scale and in predicting the critical conditions for some interesting physical phenomena. Besides their magnetic order, some materials are also multiferroic, i.e. they possess more than one ferroic order simultaneously. As an archetype of such materials, Bismuth Ferrite BiFeO3 (BFO) is at ambient conditions a ferroelectric antiferromagnet. The AF spin orientation in BFO is modulated by an incommensurate cycloidal order, which is induced by the magneto-electric interaction. This interaction couples the magnetic and ferroelectric orders, providing an extra handle to manipulate the spin structure, as well as the possibility of creating topological entities. 

In my PhD, we focused our study on NiO and BiFeO3. We based our modelling of the spin dynamics on the experimentally measured parameters and conducted theoretical and numerical studies. We studied the spin wave propagation in NiO starting from trivial geometries to more complex ones, as well as the interaction between spin waves in a junction. In order to model BFO, we developed a new code from scratch to efficiently simulate its spin dynamics with GPU acceleration. This code vastly boosted the computational speed and made possible a series of studies. We then addressed the phase transition of its spin texture under a strong magnetic field of different orientations. We simulated its spin dynamics under the effect of a spin-transfer torque pulse. We also modelled spin textures in ferroelectric domain walls and more exotic polarization configurations. In the end, we uncovered the critical conditions for the existence and stability of AF skyrmions in BFO, studied their dynamical properties, and the possible conditions for their nucleation. This work aims to provide a useful reference for future experimental studies in the new field of antiferromagnetic spintronics.