We study the metastability of magnetic nanoparticles with size distributions. We simulate an array of magnetic nanoparticles with a spin S = 1 ferromagnetic Blume-Capel model on a square lattice. Studying decays of the metastable state in the Blume-Capel model at low temperatures requires an extremely long computational time in kinetic Monte Carlo simulations. Therefore, we use an advanced algorithm adapted from the Monte Carlo with absorbing Markov chain algorithm for the Ising model in order to study the Blume-Capel model with size distributions. We modeled the particle size distributions as distributions of magnetic anisotropy. We compute the low-temperature average lifetime of the magnetization relaxation using kinetic Monte Carlo simulations with the advanced algorithms. We also calculate the lifetime using the absorbing Markov chains method for analytical results. Our results show that the lifetime of the metastable state follows a modified-Arrhenius law where the energy barrier has a dependency on temperature and standard deviation of the distributions in addition to magnetic field and magnetic anisotropy. The magnetic anisotropy barrier is determined by the smallest particle within a given distribution. We also study magnetization relaxation in different single critical droplet regions using different dynamics: Glauber and phonon-assisted dynamics. We find that the lifetime follows the modified-Arrhenius law for both dynamics, and an explicit form of the lifetime differs in different regions for different dynamics. For the Glauber dynamics, the Arrhenius prefactor does not depend on the standard deviation of the distribution of the magnetic anisotropy. For the phonon-assisted dynamics, however, even the prefactor of the lifetime depends on the standard deviation and is significantly reduced for a wide distribution of magnetic anisotropy. Furthermore, the phonon-assisted dynamics forbids transitions between degenerate energy states and results in an increase of the energy barrier at the single critical droplet region boundary compared to that for the Glauber dynamics. We find that the spin system with a distribution of magnetic anisotropy finds lower-energy relaxation pathways to avoid degenerate state, and the energy barrier becomes the same for both dynamics. / Ph. D.

Research on spintronics has galvanized the design of new devices that exploit the electronic spin in order to augment the performance of current microelectronic technologies. The sucessful implementation of these devices is largely contingent on a quantitative understanding of nonequilibrium magnetism in conducting ferromagnets. This thesis is largely devoted to expanding the microscopic theory of magnetization relaxation and current-induced spin torques in transition metals ferromagnets as well as in (III,Mn)V dilute magnetic semiconductors. We start with two theoretical studies of the Gilbert damping in electric equilibrium, which treat disorder exactly and include atomic-scale spatial inhomogeneities of the exchange field. These studies enable us to critically review the accuracy of the conventional expressions used to evaluate the Gilbert damping in transition metals. We follow by generalizing the calculation of the Gilbert damping to current-carrying steady states. We find that the magnetization relaxation changes in presence of an electric current. We connect this change with the non-adiabatic spin transfer torque parameter, which is an elusive yet potentially important quantity of nonequilibrium magnetism. This connection culminates in a concise analytical expression that will lead to the first ab initio estimates of the non-adiabatic spin transfer torque in real materials. Subsequently we predict that in gyrotropic ferromagnets the magnetic anisotropy can be altered by a dc current. In these systems spin-orbit coupling, broken inversion symmetry and chirality conspire to yield current-induced spin torques even for uniform magnetic textures. We thus demonstrate that a transport current can switch the magnetization of strained (Ga,Mn)As. This thesis concludes with the transfer of some fundamental ideas from nonequilibrium magnetism into the realm of superconductors, which may be viewed as easy-plane ferromagnets in the particle-hole space. We emphasize on the analogies between nonequilibrium magnetism and superconductivity, which have thus far been studied as completely separate disciplines. Our approach foreshadows potentially new effects in superconductors. / text