The understanding of finite temperature behavior of magnetic materials is of vital importance for spintronic applications. In this dissertation different theoretical techniques for studying magnetic thermodynamics of various materials are discussed.

Cr₂O₃ is an antiferromagnetic insulator that was proposed to be a key component of new spintronic devices. The magnetic properties of Cr₂O₃ were studied using the LDA+U method. Magnetism was found to be very well described by the Heisenberg model. Subsequently, magnetic thermodynamics was explored using quantum pair cluster approximation. Overall, very good agreement with experiment was found for the ground state and thermodynamics properties.

The magnetism at the (0001) surface of Cr₂O₃ was investigated using first principles. The description of magnetic properties required a detailed knowledge of the surface structure that was found to be very nontrivial. In particular, an order-disorder structural phase transition was shown to exist at the surface. In addition, the existence of the reentrant phase transition due to a magneto-structural coupling was hypothesized. The magnetic properties of the Cr₂O₃ (0001) surface were found to be very unique; an uncompensated magnetic moment exists at the surface and persists even with surface roughness. The finite temperature behavior of this surface magnetism was studied using the Heisenberg model and the mean-field approximation. The surface magnetization was found to exist up to almost room temperature. This effect makes Cr₂O₃ a very promising material for exchange bias applications.

In itinerant magnets both transverse and longitudinal spin fluctuations are very important for thermodynamics. A classical model containing both types of fluctuations was introduced with a single parameter controlling the degree of itinerancy, i.e., relative importance of longitudinal and transverse spin fluctuations. The thermodynamics was studied using the Monte Carlo method, mean-field approximation, and Onsager method. In general, magnetic short-range order was found to be weak even for strongly itinerant systems and Monte Carlo was in a good agreement with mean-field approximation. The Onsager cavity field method was extended to models with longitudinal spin fluctuations and was shown to be in excellent agreement with Monte Carlo. The ambiguity of the choice of the phase space measure for longitudinal spin fluctuations for classical models was emphasized.

In magnetic metals the resistivity has an additional contribution due to scattering on the thermally induced spin fluctuations. This spin-disorder resistivity was studied from first principles for Fe and Ni. Various models of thermal spin disorder were considered, including the mean-field approximation and the nearest-neighbor Heisenberg model. In general, spin-disorder resistivity was found to depend very weakly on magnetic short-range order. For local moments frozen to their zero-temperature values, a good agreement with experiment was obtained for Fe, but for Ni the resistivity at elevated temperatures was significantly overestimated. This overestimation of spin-disorder resistivity for Ni was attributed to the reduction of the local moment due to longitudinal spin fluctuations.