where E$_{‖}$ ≡ n · E and ∇ ‖ ≡ n · ∇ . In addition to the change of the magnitude, Eq. (45), there is a torque, which is per- pendicular to n . Such torque arises when the magnetization is not homogeneous, and plays important roles in current-induced magnetization dynamics. We have carried out the calcu- lation of the current-induced torque done in Ref. [10] on the same footing as the derivation of Eq. (5). As a result, we found that the β term becomes asymmetric as (see Appendix D for details of the calculation) where j$_{‖}$ ≡ n · j is the current along the local magnetization and δβ/β = − 1 / 5 in the present model. The spin transfer torque due to the spin-orbit interaction is thus different from that due to the spin-flip scattering. The expression of the total torque allowing for the spatially varying current density and the magnetization is therefore obtained as This expression clearly demonstrates that the spin relaxation torque requires some inhomo- geneity either of the applied current or the spin structure, in addition to the spin-orbit (or spin flip) interaction. Totally homogeneous system does not relax. The last term in Eq. (47) gives useful information for measuring the spin accumulation induced by the spin current. We have carried out a microscopic calculation of the spin relaxation torque and the spin current induced in disordered ferromagnetic metals by the applied electric field. The spin-orbit interaction arising from the random impurities is included as a source of spin relaxation, and inhomogeneity of the applied electric field is taken into account. We found that the spin relaxation torque in the uniform magnetization case is written as a divergence of the electric field plus an anisotropic term. The spin current was shown to be made up of field-driven (local) and diffusive (nonlocal) contributions, the latter written as a gradient of a spin chemical potential. We have derived a general linear response expression for the 14 VII. CONCLUSION ˙ s = − P 2 e ( ∇ · j ) n − P e [ β n × ( j · ∇ ) n + δβ n × ( j$_{‖}$ ∇ $_{‖}$) n ) ] + n ( γ$_{τ}$ ( ∇ · E ) + δγ$_{τ}$ ( ∂$_{‖}$E$_{‖}$ ) + ∑ ± ( ± )( ℓ$_{s}$$_{,}$$_{±}$ ) − $^{2}$µ$_{±}$ ) . (47) T ( β ) ,α so = − P es $_{2}$[ β s × ( j · ∇ ) s + δβ s × ( j$_{‖}$ ∇ $_{‖}$) s ] $^{α}$, (46)