Magnetization Dissipation in Bulk Ferromagnets and Ferromagnetic Quantum Dots

Abstract

We study the magnetization dynamics of a nano-scale ferromagnet. We show that the phenomenological Landau-Lifschitz-Gilbert predicts a damped precession of the magnetization. The ferromagnet is coupled to two large reservoirs via normal metal leads, and we focus on the effects related to electron transport into the leads. A derivation of an expression for the Gilbert damping in terms of the S matrix of the conduction electrons is reproduced. A tight binding model is used to model the conduction electrons. We consider a single domain ferromagnet made from permalloy with silver leads. We also consider an otherwise identical model where we neglect the spin-orbit coupling in the ferromagnet. We determine the S matrix of the system by using the python package kwant and calculate the corresponding Gilbert damping in python. We consider a range of systems with different sizes and discuss the relation between the Gilbert damping and the system length. A bulk contribution to the Gilbert damping and a contribution from the interface effect spin pumping are identified. The bulk contribution is a material property, which we attempt to compare to experimental data.Finally we reduce the coupling between the ferromagnet and the leads, and discuss the effect of doing so on the conductance and the spin pumping and the bulk contribution in the Gilbert damping. We show that in very small ferromagnets, the electron transport and the bulk Gilbert damping become dominated by narrow resonance lines in the energy spectrum. We show that the spin pumping contribution to the Gilbert damping falls off quickly as we reduce the interface coupling.