In conventional micromagnetism magnetic domain configurations are calculated based on a continuum theory for the magnetization. This theory assumes that the absolute magnetization value is constant in space and time. Dynamics is usually described with the Landau-Lifshitz-Gilbert LLG equation, the stochastic variant of which includes finite temperatures. Using simulation techniques with atomisti...

The Landau-Lifshitz-Gilbert (LLG) equation is a fascinating nonlinear evolution equation both from mathematical and physical points of view. It is related to the dynamics of several important physical systems such as ferromagnets, vortex filaments, moving space curves, etc. and has intimate connections with many of the well-known integrable soliton equations, including nonlinear Schrödinger and...

A spin polarized current may transfer angular momentum to a ferromagnet, resulting in a spin-torque phenomenon. At the same time the shot noise, associated with the current, leads to a nonequilibrium stochastic force acting on the ferromagnet. We derive a stochastic version of the Landau-Lifshitz-Gilbert equation for a magnetization of a "free" ferromagnetic layer in contact with a "fixed" ferr...

The rigorous derivation of Fourier’s law of heat conduction for an interacting system of Hamiltonian particles is a classical and fundamental goal of statistical physics. I will consider the ball-piston system which is a dimension-reduced-version of a 2008 model of Gaspard and Gilbert. The direct aim is to treat its rare interaction limit leading to the mesoscopic master equation, i. e. to a Ma...

The precessing magnetization of a magnetic islands coupled to a quantum spin Hall edge pumps charge along the edge. Conversely, a bias voltage applied to the edge makes the magnetization precess. We point out that this device realizes an adiabatic quantum motor and discuss the efficiency of its operation based on a scattering matrix approach akin to Landauer-Büttiker theory. Scattering theory p...

Magnetization reversal of uniaxial Stoner particles under the Slonczewski spin-transfer torques of polarized electric currents is investigated. Based on the modified Landau-Lifshitz-Gilbert equation of magnetization dynamics, the theoretical limit of critical currents required to reverse a magnetization with an arbitrary polarized current is obtained. Under a constant polarization degree and co...

The precession of the magnetization of a ferromagnet is shown to transfer spins into adjacent normal metal layers. This "pumping" of spins slows down the precession corresponding to an enhanced Gilbert damping constant in the Landau-Lifshitz equation. The damping is expressed in terms of the scattering matrix of the ferromagnetic layer, which is accessible to model and first-principles calculat...

The intrinsic Gilbert [1] magnetic damping of ferromagnetic resonant systems is a problem of long-standing interest. Recently, Hickey and Moodera [2] asserted that the spin-orbit interaction which arises from the nonrelativistic limit of the Dirac equation may be responsible for the intrinsic ferromagnetic linewidth. The theoretical methods employed by Hickey and Moodera involve previously deve...

Based on the modified Landau-Lifshitz-Gilbert equation for an arbitrary Stoner particle under an external magnetic field and a spin-polarized electric current, differential equations for the optimal reversal trajectory, along which the magnetization reversal is the fastest one among all possible reversal routes, are obtained. We show that this is a Euler-Lagrange problem with constrains. The Eu...