Inelastic scattering in ferromagnetic and antiferromagnetic spin valves

We use a ferromagnetic voltage probe model to study the influence of inelastic scattering on giant magnetoresistance and current-induced torques in ferromagnetic and antiferromagnetic metal spin valves. The model is based on the Green’s function formulation of transport theory and represents spin-dependent and spin-independent inelastic scatterers by interior voltage probes that are constrained to carry respectively no charge current and no spin or charge current. We find that giant magnetoresistance and spin transfer torques in ferromagnetic metal spin valve structures survive arbitrarily strong spin-independent inelastic scattering, while the recently predicted analogous phenomena in antiferromagnetic metal spin valves are partially suppressed. We use toy-model numerical calculations to estimate spacer layer thickness requirements for room temperature operation of antiferromagnetic metal spin valves.

Figure 1

(a) Parallel configuration and equivalent circuit consisting of two resistors $R$ and $r<R$, and (b) antiparallel configuration and equivalent circuit, of a spin valve consisting of two single-domain ferromagnets separated by a paramagnetic spacer. (c) Antiparallel configuration and equivalent circuit of an antiferromagnetic spin valve and (d) its parallel configuration and equivalent circuit. (For convenience, only two ferromagnetic layers within each antiferromagnet are shown.) Note that in the ferromagnetic case the resistance of parallel and antiparallel circuits is different, contrary to the equivalent circuits in the antiferromagnetic case.

Figure 2

Model system consisting of sites with an arbitrary on-site exchange and scalar potential. In addition to the coupling to its nearest neighbors, each site is coupled to a ferromagnetic reservoir.

Figure 3

Ferromagnetic GMR ratio as a function of the spacer thickness for various inelastic scattering lengths.

Figure 4

Spin-transfer torque for the case $L_{\mathrm{sf}}=L_{\varphi }$ normalized to $I∕\mid e\mid$, where $I$ is the charge current, as a function of $\theta$. The inset shows the conductance in units of $\mid e\mid ∕\left(2\pi \hslash \right)$. For this calculation the spacer thickness is taken equal to five sites.

Figure 5

Antiferromagnetic GMR ratio as a function of the spacer thickness for various inelastic scattering lengths.

Figure 6

Spin density component out of the plane spanned by the moments of the antiferromagnets opposite the paramagnetic spacer layer for various inelastic scattering lengths. In this calculation $L_{\varphi }=L_{\mathrm{sf}}$ and the angle between the two moments opposite the spacer is $\pi ∕2$.

Figure 7

Current-induced torques normalized to $I∕\mid e\mid$, where $I$ is the charge current, as a function of $\theta$. The inset shows the conductance in units of $\mid e\mid ∕\left(2\pi \hslash \right)$. In this calculation $L_{\varphi }=L_{\mathrm{sf}}$ and the number of spacer sites is 4.