Theory of nonlinear surface magneto-optics for ferromagnetic nickel: Effects of band structure and matrix elements

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Abstract
The nonlinear magneto-optical Kerr effect has been proposed as an ultrafast spectroscopic probe for the magnetic and electronic properties of ferromagnetic surfaces. We extend our previous calculation of the linear (first-order) and nonlinear (second-order) magneto-optical susceptibilities by the inclusion of the complete nickel band structure and the dipole transition matrix elements within the combined interpolation scheme. As ab initio band-structure calculations usually cannot describe optical and magneto-optical absorption (especially in nickel), the band-structure parameters are taken from a fit to spin-polarized photoemission data and de Haas–van Alphen measurements of the Fermi surface. The detailed shape of the Brillouin zone is included. Comparison to linear magneto-optical Kerr-effect measurements shows that the inclusion of the full anisotropic band structure and of the dipole matrix elements is necessary to remove parameter ambiguities and leads to strongly improved agreement between theory and experiment. This electronic theory confirms the previous assertion that the nonlinear magneto-optical Kerr effect should be observable and clearly shows that this effect contains detailed information about the electronic and magnetic surface properties (band structure, exchange interaction, spin-orbit coupling). Thus, the theory can help to interpret forthcoming nonlinear magneto-optical measurements. We discuss possible geometries for experimental and technological applications.