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When a current density jₗ crosses a 180^ domain wall in a metallic ferromagnet, the spin s of each conduction electron exerts an s-d exchange torque on the localized wall spins. Hence, the wall moment of a Bloch wall is canted out of the wall plane by an angle, given by jₗ= (eC/) sin (2), where C is the maximum restoring torque at =45^. This equation is the exact analog of the dc Josephson effect, and 2 is the analog of the superconducting phase difference across a junction. For jₗ>eC/10^6 A/cm^2, the s-d exchange torque overcomes the restoring torque, and the wall moment precesses with a frequency =d (2) /dt. A dc voltage is expected to appear across the wall, satisfying the famous ac Josephson relation 2e=-. This wall precession can be described as a translation of Bloch lines, and the Bloch lines are the exact analog of superconducting vortices. The electric current exerts a transverse force on Bloch lines.
L. Berger (Sat,) studied this question.