Exchange interaction between ferromagnetic domain wall and electric current in very thin metallic films

Since the wall thickness is at least 102 electron wavelengths, a domain wall acts, through the s-d exchange interaction, like a very weak and smooth potential barrier of height ≂10−2 eV, which does not reflect conduction electrons appreciably. The potential energy arises from the 4s conduction electron spin making a small angle with the local s-d exchange field. Anisotropic s-d exchange may also contribute to the potential barrier. A solution of the electron transport equations in the wall is obtained. In order for an electron current crossing the wall to exert an appreciable drive force on it, nonzero interband electron scattering by impurities or phonons is needed. The electron density for a given band varies slightly with location inside the wall, and depends on the current. Mutual electrostatic shielding between bands is taken into account. The drive force per unit wall area is F≂2Ms μ−1i (ve −vw), where ve and vw are electron drift speed and wall speed. In other words, this drive force at ve ≠0 is governed by the same intrinsic wall mobility μi as the well-known intrinsic wall damping force at vw ≠0. While hydromagnetic ‘‘domain drag’’ forces associated with the Hall effect are dominant in samples of usual thickness, this ‘‘exchange domain drag’’ force is expected to dominate in films thinner than ≂0.1 μm.