Influence of magnetic fields on spin-mixing in transition metals

In a relativistic description of a real solid the crystal wave functions are never pure but spin-mixed functions. As a direct result of the spin-mixing, scattering mechanisms, which are in principal diagonal in spin-space, as for example the deformation potential part of the electron-phonon scattering potential, may lead to spin flips. Spin-mixing thereby affects damping and lifetimes in the fast and ultrafast regime of magnetization dynamics. The average spin-mixing appears as an important parameter in many models, the most prominent being the Elliott-Yafet model of spin relaxation. The application of an external magnetic field, a laser-field, or a Faraday-field induced by a laser may be considered as a source of magnetic field in a sample. Therefore we will discuss the influence of a homogeneous applied magnetic field on the average spin-mixing calculated in the framework of spin-density-functional theory. It is shown that even high fields do not significantly change the spin-mixing in $3d$ transition metals. Therefore the related dynamics are unaffected, which is in accordance with the experimental data on ultrafast demagnetization's dependence on light polarization.

Figure 1

Dependence of $b^2(j,\mathbf{k})$ on the electronic energy ${\epsilon }_{j,\mathbf{k}}$ (whereby the Fermi energy ${\epsilon }_{\text{F}}$ is set to 0), for zero $\mathbf{B}$ (green dashed) and for $B=23.5$ T (red line), for (a) fcc Ni and (b) bcc Fe.