Ab initio investigation of light-induced relativistic spin-flip effects in magneto-optics

Excitation of a metallic ferromagnet such as Ni with an intensive femtosecond laser pulse causes an ultrafast demagnetization within approximately 300 fs. It was proposed that the ultrafast demagnetization measured in femtosecond magneto-optical experiments could be due to relativistic light-induced processes. We perform an ab initio investigation of the influence of relativistic effects on the magneto-optical response of Ni. To this end, first, we develop a response theory formulation of the additional appearing ultrarelativistic terms in the Foldy-Wouthuysen transformed Dirac Hamiltonian due to the electromagnetic field, and second, we compute the influence of relativistic light-induced spin-flip transitions on the magneto-optics. Our ab initio calculations of relativistic spin-flip optical excitations predict that these can give only a very small contribution $(\le 0.1\%)$ to the laser-induced magnetization change in Ni.

Figure 1

Calculated optical conductivity spectra $\mathrm{Re}\left[{\sigma }_{xx}\left(\omega \right)\right]$ (top) and $\omega \mathrm{Im}\left[{\sigma }_{xy}\left(\omega \right)\right]$ (bottom) of fcc Ni, using the relativistic and nonrelativistic current density formulations. The blue lines are calculated considering the momentum operator in nonrelativistic approximation ($\mathit{p}=-i\hslash \mathbf{\nabla }$). The orange dotted-dashed lines are the calculations performed using Eq. (14) as momentum operator.

Figure 2

Calculated magneto-optical Kerr rotation and Kerr ellipticity of Ni. The black and blue lines are, respectively, the Kerr rotation ${\theta }_{\mathrm{K}}$ and ellipticity ${\varepsilon }_{\mathrm{K}}$ calculated without taking into account the additional relativistic terms of the momentum operator. The red and yellow dashed lines are the Kerr rotation and ellipticity, respectively, calculated retaining the relativistic terms of the momentum operator.

Figure 3

(Top) Differences between the off-diagonal conductivity ${\sigma }_{xy}\left(\omega \right)$ components computed with the relativistic and the nonrelativistic current operators. (Bottom) Calculated absolute value of the difference in ${\sigma }_{xy}$ (${\Phi }_{\mathrm{K}}$) normalized to the quantities $|{\sigma }_{xy,\mathrm{nr}}|$ ($|{\Phi }_{\mathrm{K},\mathrm{nr}}|$) computed with the nonrelativistic momentum operator.