Since the discovery of two-dimensional magnetic materials in 2017, an uncharted territory has opened within the field of spintronics, drawing intense interest from both experimental and computational research. From a computational perspective, studying magnetic materials requires addressing several challenges: achieving accurate simulations of localized electrons, identifying the ground state magnetic ordering, determining the parameters of effective Hamiltonians, such as Hubbard parameters or exchange interactions for Heisenberg models used to compute spin-wave spectra, and estimating magnetic transition temperatures. This thesis addresses several of these aspects.

First, we investigate two well-known case studies with available experimental data, monolayer CrI3 and FePS3, and compute their Hubbard parameters (U and V) using linear-response theory within density-functional perturbation theory (DFPT). For antiferromagnetic FePS3, Hubbard corrections are essential to recover the experimentally observed insulating phase, the correct crystal symmetry, and vibrational spectra in quantitative agreement with Raman data. In contrast, applying a conventional Hubbard U to ferromagnetic CrI3 leads to a spurious splitting of the conduction bands, a problem that can be resolved by promoting U to a spin-resolved quantity. With this modification, a remarkable agreement with experiments for the character of the valence bands and the phonon frequencies is achieved.

Next, we introduce an automated framework capable of systematically exploring the complex energy landscapes of magnetic monolayers, including the effect of Hubbard corrections. By controlling and sampling orbital occupation matrices, the workflow efficiently identifies multiple self-consistent metastable states and determines the global magnetic ground state of 194 magnetic monolayers from the Materials Cloud 2D database. Using this approach, we identify 109 ferromagnets, 83 antiferromagnets, 2 altermagnets, and 12 novel ferromagnetic half-metals with promising spintronics potential. Using the energy-mapping method, we then compute the effective exchange parameters of the insulating magnetic monolayers identified through this workflow and exploit these parameters as a proxy to rank the materials according to their estimated transition temperatures.

Finally, we investigate the robustness of calculations of exchange parameters within the so-called Liechtensteinâ Katsnelsonâ Antropovâ Gubanov (LKAG) formalism, which requires plane-wave first-principles results to be mapped onto a tight-binding Hamiltonian using, e.g., Wannier functions. Focusing on the paradigmatic case of monolayer CrI3 and performing the calculations using the TB2J package, we show that the standard Wannierization approach can break the symmetry of the computed exchange parameters and, when fully occupied semicore states that should not contribute to magnetism are included, may even lead to an incorrect prediction of an antiferromagnetic ground state. These issues are resolved by implementing a Wannierization procedure that constrains both the Wannier centers and the overlap between spin-up/spin-down Wannier functions.