Magneto-optical Kerr spectroscopy of noble metals

Abstract

Magneto-optical (MO) response of the noble metals Cu, Ag, and Au in the joint experimental and ab initio theoretical study is reported. The magneto-optical polar Kerr effect (MOKE) spectra of the noble-metal films were measured with the high sensitivity in the applied magnetic field of 1.5 T over the photon energy range 0.74--5.8 eV. Complete set of the optical conductivity tensor elements was determined precisely from the MOKE and the optical spectra measured at the same energy points. The importance of the off-diagonal intraband Drude-type transitions is demonstrated explicitly for each noble metal and found to be a substantial contribution to the observed spectra. It is shown that the first-principles calculations using the spin-polarized fully relativistic Dirac linear-muffin-tin-orbital method with the inclusion of correlation effects by GGA+$U$ approach reproduce well the experimental spectra and allow to explain the microscopic origin of the noble metals' magneto-optical response in terms of interband transitions. Although the energy band structures of Cu, Ag, and Au are very similar, there are some distinctive differences in bandwidths and the energy positions of the bands (especially in $X$ and $L$ symmetry points), mainly due to different spin-orbit splitting and differences in the spatial extent of $3d, 4d$, and $5d$ valence wave functions of noble metals. It was found that the small differences in the band positions lead to significant differences in the MO properties of three noble metals. Although the spin-orbit interaction in Au is about six times larger than in Cu, and approximately two times larger than in Ag, the absolute value of Kerr rotation in Au is of the same magnitude as in Cu and one order of magnitude smaller as compared to Ag. The sharp Kerr effect spectral peak in Ag is not due to the electronic interband transitions, but rather to the plasma-edge splitting. The band-by-band decomposition of the Cu, Ag, and Au MO spectra is presented and the interband transitions responsible for the prominent structures in the spectra are identified. It has been found that main magneto-optical activity of noble metals in external magnetic field originates from interband transitions at well-defined small-volume regions of Brillouin zone located near the ``neck'' and ``belly'' of the Fermi surface.