Theory of the Interband Ferromagnetic Kerr Effect in Nickel

A detailed discussion is given of the way in which the experimentally observed structure in the ferromagnetic Kerr effect (FKE) for nickel can be attributed to optical transitions involving the $d$ and $s$ bands near the Fermi surface. Absolute calculations are presented for ${{\epsilon }_m}^{\mathrm{}\left(1\right)\mathrm{}}$, the absorptive part of the off-diagonal element of the dielectric-constant tensor measured by the FKE, for models based on those recently proposed by Ehrenreich, Philipp, and Olechna and by Phillips and Mattheiss for the band structure of ferromagnetic nickel. For both models, the peak in ${{\epsilon }_m}^{\mathrm{}\left(1\right)\mathrm{}}$ is associated with transitions involving ↓ (minority-electron) spin bands. The results for the two models are compared with experiment, and this comparison is used to discuss their relative merit. Besides serving as a check on the validity of models for the band structure of ferromagnetic nickel developed from other experimental information, the FKE itself can be used as a tool for developing such models. A brief discussion of Models $3A$ and $3B$ previously developed on this basis is given. We call attention to the "step" expected at the onset of the contribution of the ↑ (majority-electron) bands to the FKE structure. Experimental observation of such structure in addition to the peak already associated with ↓-band transitions would serve to determine the $d$-band exchange splitting.