Generalized Gilbert equation including inertial damping: Derivation from an extended breathing Fermi surface model

Isotropic non-local Gilbert damping driven by spin pumping in epitaxial Pd/Fe films on MgO(001) substrates

“…Gilbert damping, one of the key parameters in spin dynamics, characterizes the energy transfer from the spin subsystem to the lattice and governs the magnetization switching time and the critical current density in spin transfer torque devices [4][5][6]. An anisotropic Gilbert damping is expected in single crystal ultrathin films if the Fermi surface or the spin-orbit coupling can change with magnetization orientation [7][8][9][10]. Chen et al discovered the anisotropic damping in ultrathin Fe films on GaAs(001) substrates due to the presence of robust interfacial spin-orbit coupling.…”

Spin dynamics with inertia in metallic ferromagnets

“…In ref. [11], an extended breathing Fermi surface model was used, and the relation between the Gilbert damping coefficient and the spin inertia was given in terms of physical quantities (such as Fermi-Dirac occupation numbers) of conduction electrons. The time scale for the nutational motion to be damped by the Gilbert damping was estimated to be sub-picosecond order.…”

“…Although the expressions of the inertia of spin were given as integral forms [11,12], an explicit expression of the inertia of spin in terms of parameters of a model has not been obtained so far. Furthermore, the effect of the inertia of spin on the dynamics of spin has been discussed only for spatially homogeneous spin system under time-independent magnetic field.…”

Thermokinetic considerations about spin-dependent voltage generated by heat currents

“…A current of angular momentum can be taken into account in the kinetic energy and into heat currents. The reason is that the configuration space of the ferromagnet should be extended to that of the angular momentum degrees of freedom, as studied in references [38][39][40] .…”