Spin-flip diffusion in transition metals as a function of temperature

Because of spin-orbit coupling, a spin current injected into a non-magnetic material is not conserved. Valet and Fert characterized the spatial decay of a spin current in terms of a material dependent spin-flip diffusion (sfd) length that has become an extremely important parameter in the field of spin transport. In spite of their importance, almost everything that is known about them is from low-temperature transport measurements. In this work we perform a systematic study of the temperature dependence of sfd lengths for the 4d and 5d transition metal elements using a TB-LMTO based scattering code to calculate the conductance as well as local charge and spin currents. From the decay of a spin current injected into the material, we extract the sfd length. We mimic temperature by displacing atoms randomly in a Gaussian distribution to create a snapshot of frozen thermal lattice disorder. The distribution is characterized by a root mean square displacement and varying this yields different resistivities and sfd lengths. We use the relationship between the resulting resistivities and sfd lengths to determine how generally the Elliott-Yafet relationship is obeyed and whether there are any trends across the d series.