Spin-dependent interface transmission

The magnetization dynamics of small monodomain ferromagnets are well described by the Landau-Lifshitz-Gilbert (LLG) equation down to the micron scale. On the submicron scale, however, the magnetization dynamics is no longer a highly coherent process because interfaces are relatively more important in small samples and new effects may play a role. One such effect, depending on the environment into which the ferromagnet is embedded, occurs when a time-dependent ferromagnetic order parameter pumps spin currents that carry angular momentum (and energy) into adjacent conducting materials. This angular-momentum loss is equivalent to a damping torque on the magnetization. It forms an additional, non-local source of ferromagnetic resonance (FMR) line broadening.

We used scattering matrices calculated from first-principles [1] to study spin transfer and magnetization damping in layered systems comprising normal metal and ferromagnetic films. An example of the spin-dependence of interface transmission is shown for an fcc Cu|Co(111) interface in Fig.1 (majority-spins) and Fig.2 (minority-spins). In [2] it was shown that the spin-current-induced magnetization torque is an interface effect and that quantum-interference effects are greatly overestimated by free-electron models and do not survive when realistic transition-metal band structures are used, especially when interface disorder is included. We also found that the additional term in the ferromagnetic equation of motion is of the Gilbert-damping form, with only a very small correction to the gyromagnetic ratio.

[1] K. Xia, M. Zwieryzycki, M. Talanana, P.J. Kelly, and G.E.W. Bauer, First-principles scattering matrices for spin transport, Phys. Rev. B 73, 064420 (2006).

[2] M. Zwieryzycki, Y. Tserkovnyak, P.J. Kelly, A. Brataas, and G.E.W. Bauer, First-principles study of magnetization relaxation enhancement and spin transfer in thin magnetic films, Phys. Rev. B71 064420 (2005).

CuCo_111_maj_mz

Figure 1. Top row, left-hand panel: Fermi surface (FS) of fcc Cu; middle panel: majority-spin FS of Co; right-hand panel: Cu FS viewed along the (111) direction with a projection of the bulk fcc Brillouin zone (BZ) onto a plane perpendicular to this direction and of the two dimensional BZ. Bottom row, left-hand and middle panels: projections onto a plane perpendicular to the (111) direction of the Cu and majority-spin Co Fermi surfaces; right-hand panel: transmission probability for majority-spin states as a function of transverse crystal momentum, T(k), for an fcc Cu|Co(111) interface.

CuCo_111_min_mz

Figure 1. Top row, left-hand panel: Fermi surface (FS) of fcc Cu; middle panels: third, fourth and fifth FS sheets of minority-spin fcc Co; right-hand panel: projection of the bulk fcc Brillouin zone (BZ) onto a plane perpendicular to the (111) direction and of the two dimensional BZ. Middle row: corresponding projections of individual FS sheets and (rhs) of Co total. The number of propagating states with positive velocity is colour-coded following the colour bar on the right. Bottom row: probability Tμν(k) for a minority-spin state on the single FS sheet of Cu (ν = 1) to be transmitted through a Cu|Co(111) interface into FS sheet μ of fcc Co as a function of the transverse crystal momentum k. Rightmost panel: transmission probability for majority-spin states as a function of transverse crystal momentum, T(k), for an fcc Cu|Co(111) interface.