content_image/342373.jpg content_image/342369.jpg content_image/342367.jpg content_image/342368.jpg
where ℓ$_{s}$ in the spin diffusion length in the normal metal ( ℓ$_{s}$ is a long ( ∼ µ m) length scale and thus does not depend on the spin). We therefore obtain from Eq. (30) the chemical potential as 

<img src='content_image/342373.jpg'>

where q$_{s}$ ≡ ( ∑ σ σD$_{σ}$ν$_{σ}$ ) eV$_{FN}$ ) A$_{FN}$/d , is the spin accumulation rate at the interface (per unit time), and A$_{FN}$ is the area of the junction. This result of µ$_{s}$ is consistent with intuitive and phenomenological results of the spin injection in the perpendicular structure shown in Fig. 4(a). In contrast, when the voltage is applied parallel to the ideal interface as shown in Fig. 4(b), spin injection does not occur since ∇ · E = 0 at the interaface and thus µ (N) s = 0. 

## VI. TOTAL TORQUE AND ASYMMETRIC β TERM 

<img src='content_image/342369.jpg'>

The continuity equation (1), indicates that the spin polarization (magnetization) changes due to the spin relaxation. (Change of the magnetization magnitude is a feature of the itinerant magnetism.) By use of Eqs. (5)(33)(37), we see that Eq. (1) results in 

<img src='content_image/342367.jpg'>

where γ$_{τ}$ ≡ γ − δσ$_{s}$ and δγ$_{τ}$ ≡ δγ + δσ$_{s}$ . General case with uniform magnetization along any unit vector n is given by ( s ≡ s n ) 

<img src='content_image/342368.jpg'>

