Unified Description of Bulk and Interface-Enhanced Spin Pumping

Abstract

The dynamics of non-equilibrium spin accumulation generated in metals or semiconductors by rf magnetic field pumping is treated within a diffusive picture. The dc spin accumulation produced in a uniform system by a rotating applied magnetic field or by a precessing magnetization of a weak ferromagnet is in general given by a (small) fraction of ω, where ω is the rotation or precession frequency. With the addition of a neighboring, field-free region and allowing for the diffusion of spins, the spin accumulation is dramatically enhanced at the interface, saturating at the universal value ω in the limit of long spin relaxation time. This effect can be maximized when the system dimensions are of the order of 2πD/ω, where D is the diffusion constant. We compare our results to the interface spin pumping theory of A. Brataas et al. [Phys. Rev. B 66, 060404(R) (2002)].

Spin pumping into two-dimensional electron systems

“…Much larger exchange splittings have been predicted for graphene on EuO [32] and observed for graphene| EuS [33]. Spin pumping into two-dimensional (2D) systems by an electrically insulating magnetic gate may efficiently emulate the spin pumping and maser action predicted to occur by inhomogeneous Zeeman fields [34,35].…”

Magnetization oscillations induced by spin current in a paramagnetic disc

“…We search for solutions of a steady-state precessing in-plane spin accumulation μ = (μ || cos(ωt),μ || sin(ωt),μ z ). We find our solutions in the rotating reference frame 13 where the frame rotates with frequency ω along the z axis. In this case, the solutions we try to find are static, μ = (μ || ,0,μ z ), such that In the absence of an applied magnetic field, the in-plane components of Eq.…”

“…It is determined by spin relaxation μ(t)τ −1 , precession ω B × μ(t), and an external spin injection source I s (t) in units of power. We have ignored the spin pumping term previously used 13 as well as diffusion. Spin pumping can be shown to be of minor importance since any rotating magnetic fields are only consequences of the effect we describe here and are not directly relevant for the effect itself.…”

“…3,4 The eddy fields that stabilize the precessional motion and the spin accumulations in the disk were calculated using a paramagnetic spin theory. 13,14 The threshold for the injected spin accumulation that is needed to realize this effect is determined for a general paramagnet. An analysis of this effect in three modern spin-preserving materials, aluminum, graphite and n-GaAs, shows that stable precession is hard to achieve.…”

“…Assuming a steady-state precession of μ || with frequency ω, the change in magnetic field the disk is exposed to is ∂(μ 0 M)/∂t = C e ωμ || , where we defined a material constant C e = 1 4 gμ b μ 0 N F . 13,14 Here g is the electron g factor, μ b is the bohr magneton, μ 0 is the vacuum permeability, and N F is the density of states at the fermi level.…”