Spin-flip transition rate due to electron-magnon scattering in ferromagnetic thin films

In a free-electron model of very thin ferromagnetic films, an electron occu pies a "Fermi disk," which is reduced from one of the two bulk Fermi sphere s, corresponding to spin-up and spin-down electrons. The spin-flip transiti on rate due to electron-magnon scattering in such ferromagnetic thin films is due to electron scattering between two of these "Fermi disks." We study how electron confinement affects this rate. Normally the spin-flip scatteri ng rate decreases as the film thickness increases. But when the film thickn ess increases to a point such that electrons of opposite spin start occupyi ng a higher subband, the scattering increases abruptly. This abrupt increas e is more prominent at higher temperatures. As the film thickness increases toward infinity, the spin-flip scattering rate in the film decreases to th e value for the hulk magnetic material.