Abstract
Motivated by a need to understand spin-momentum transport in CPP (current perpendicular to the plane) structures, a quantum field theoretical treatment of spin-spin interactions in ferromagnets is presented. The interaction of the conduction electrons and the magnetic medium is treated nonperturbatively from first principles in real space. The localized magnetic moments also interact with each other through a Heisenberg exchange potential. To take into account correlation effects, a second quantized formulation is used. The semiclassical limit is taken by using a coherent-state path-integral technique which also allows us to go beyond a linear-response approach. We derive a set of coupled equations of motion for the nonuniform magnetization, the spin current, and the two-point correlation functions of the magnetization. The rate of change of the magnetization is shown to obey a generalized Landau-Lifshitz equation that takes into account interaction with the conduction electrons. Within the relaxation time approximation it is shown that the polarization of the conduction electrons obeys a generalized diffusion equation. The diffusion tensor, which has off-diagonal terms due to the exchange interaction, is now explicitly dependent on the magnetization of the medium. We also show that the magnetization fluctuations satisfy a diffusion-type equation. The derived equations are used in two illustrative examples.
- Received 7 February 2005
DOI:https://doi.org/10.1103/PhysRevB.72.064408
©2005 American Physical Society