Precession damping in itinerant ferromagnets
Precession damping in metallic ferromagnets had been assumed to result from the spinorbit interaction. While several theories of spin-orbit damping had been postulated, no convincing numerical comparisons to data existed. We selected one promising theory and performed first-principles numerical calculations of damping for bulk iron, cobalt, and nickel. Comparison of minimal calculated and measured damping rates demonstrated a 70 % agreement for nickel, 60 % for iron, and 40 % for cobalt. We then relaxed the initial constraint of a universal electron-lattice scattering rate by allowing the scattering rate to be spin dependent. The spin dependent lifetime ratio was equated to the ratio of the spin resolved density of states at the Fermi level. This modification improved the agreement to 95 % for nickel, 70 % for iron, and 47 % for cobalt. With this level of agreement, we next constructed a simple effective field explanation for the damping process. As the magnetization rotates, the energy of the spin system gets pushed out of equilibrium and this excitation is quenched by electron-lattice scattering.The energy of the spin system changes by two mechanism: the energies of the states change and transitions to excited states occur. The first mechanism had previously been described within the effective field picture as producing a breathing of the Fermi surface. As the magnetization precesses, the spin-orbit energy of each state changes leading to expansions and contractions of the Fermi surface that are periodic with the precession. To expand this metaphor, we have dubbed the second effect of transitions to excited states as a bubbling of the Fermi sea. In this picture, individual electrons across the Fermi surface undergo larger excitations. Finally, we investigated the dependence of the damping rate on the density of states and the spin-orbit coupling parameter. We found that the damping due to the breathing effect was roughly proportional to the density of states while damping from the bubbling terms correlated strongly with the density of states squared. By tuning the spin-orbit parameter we found that the breathing terms were proportional to the spin-orbit parameter cubed while the bubbling terms went as the spin-orbit parameter squared.