Spin-Torque Driven Macrospin Dynamics subject to Thermal Noise

This thesis considers the general Landau-Lifshitz-Gilbert theory underlying the magnetization dynamics of a macrospin subject to spin-torque effects and thermal fluctuations, as a function of the spin-polarization angle. The macrospin has biaxial magnetic anisotropy, typical of thin film magnetic elements, with an easy axis in the film plane and a hard axis out of the plane. When magnetic diffusion due to spin-torque and thermal noise effects occurs on a timescale that is much larger than the conservative precessional timescale due to magnetic anisotropies, it is possible to explore steady-state dynamics perturbatively by averaging the magnetization dynamics over constant energy orbits. This simplifies the magnetization dynamics to a 1D stochastic differential equation governing the evolution of the macropsin's energy. Current induced steady-state motions are then found to appear whenever the magnetization settles onto a stable constant energy trajectory where a balance of spin-torque and damping effects is achieved: with the remaining gyromagnetic motion due to anisotropy fields driving precessions. After averaging, all the relevant dynamical scenarios are found to depend on the ratio between hard and easy axis anisotropies. We derive the range of currents for which in-plane and out-of-plane limit cycles exist and discuss the regimes in which the constant energy orbit averaging technique is applicable. We find that there is a critical angle of the spin-polarization necessary for the occurrence of such states and predict a hysteretic response to applied current. This model can be tested in experiments on orthogonal spin-transfer devices, which consist of both an in-plane and out-of-plane magnetized spin-polarizers, effectively leading to an angle between the easy and spin-polarization axes. The technique developed allows for a detailed study of thermally driven macrospin escape phenomena within a stochastic Langevin framework. By employing Friedlin- Wentzell theory, we discuss how the most probable escape trajectories followed by the macrospin's magnetization depend on the parameters appearing in the model. We argue that the small size of the damping constant guarantees that the nature of such trajectories will not be altered significantly across a relatively large range of parameter values. This in turn sheds light on the topological structure of the underlying effective Lagrangian manifold spanned by the thermally driven dynamical processes.