Besides diffusive spin current, there is another spin current that is driven by an effective field. In contrast to the diffusive one, this field-driven contribution should not decay in uniform (single domain) ferromagnets, since the ratio of the spin current and the charge current is determined by the spin polarization ratio of the material, which is a statistical mechanical quantity. The field-driven (local) spin current and the diffusive spin current behave differently, as was recently demonstrated theoretically in the case of the inverse spin Hall effect [7]. In the field of the current-driven magnetization dynamics, the spin relaxation torque has been studied from the microscopic viewpoint [8–10]. In this context, Eq. (1) gives the expression for the torque acting on the spin density s as In the adiabatic limit, i.e., slowly varying magnetization, and under uniform current, the first term reduces to ∇ · j α s = ( P/ 2 e )( j · ∇ ) s $^{α}$, where P is the spin polarization of the current [9, 10], namely to the adiabatic spin-transfer torque. When the spin-relaxation sets in, the conduction electron no longer follows the magnetization profile, and new contribution to the torque arises from the T term. This torque was shown to be where β is a coefficient inversely proportional to the spin relaxation time τ$_{s}$ [8, 10]. This torque, called β term, turned out to be essential in determining the efficiency of the current- driven domain wall motion [11–13]. The magnitude of the parameter β has recently been intensively studied experimentally by measuring the domain wall speed under current [14, 15]. Theoretical formulation for estimating β in the first-principles calculations was carried out recently [16]. The spin relaxation torque has been studied also from the viewpoint of how to define the spin current. It was discussed that the spin relaxation torque contains a term written as a divergence of the torque dipole density, P [17]. Generalized argument was given by Shi et al. [18], where they discussed that the z component of the relaxation torque is written as a divergence, T z = −∇ · P , (4) T = − β P es $_{2}$( s × ( j · ∇ ) s ) , (3) τ α = −∇ · j α s + T $^{α}$. (2) 3