Weak localization in ferromagnets with spin-orbit interaction
V. K. Dugaev1,2 , P. Bruno1 , J. Barnaś3,4
1 Max-Planck-Institut f¨ur Mikrostrukturphysik, Weinberg 2, D-06120 Halle, Germany
2 Institute of Materials Science Problems, Vilde 5, 58001 Chernovtsy, Ukraine
3 Department of Physics, A. Mickiewicz University, ul. Umultowska 85, 61-614 Poznań, Poland
4 Institute of Molecular Physics, Polish Academy of Sciences, ul. M. Smoluchowskiego 17, 60-179 Poznań, Poland
Physical Review B, 64, 144423 (2001)
Weak localization corrections to conductivity of ferromagnetic systems are studied theoretically in the case when spin-orbit interaction plays a significant role. Two cases are analyzed in detail: (i) the case when the spin-orbit interaction is due to scattering from impurities, and (ii) the case when the spin-orbit interaction results from reduced dimensionality of the system and is of the Bychkov-Rashba type. Results of the analysis show that the localization corrections to conductivity of ferromagnetic metals lead to a negative magnetoresistance -- also in the presence of the spin-orbit scattering. Positive magnetoresistance due to weak antilocalization, typical of nonmagnetic systems, does not occur in ferromagnetic systems. In the case of two-dimensional ferromagnets, the quantum corrections depend on the magnetization orientation with respect to the plane of the system.