Ultrafast demagnetization after laser irradiation in transition metals: Ab initio calculations of the spin-flip electron-phonon scattering with reduced exchange splitting

Despite intensive research, the underlying mechanisms for ultrafast demagnetization after laser irradiation in transition metals are still not understood. We discuss the possible processes which have been suggested in order to explain the ultrafast demagnetization within several hundreds of femtoseconds and argue that the spin angular momentum has to go to the lattice in the end. Based on this argument, we consider spin-flip electron-phonon scatterings. The demagnetization time ${\tau }_M$ and the demagnetization rate $dM/dt$ due to spin-flip electron-phonon scattering is calculated for fcc Ni and bcc Fe. Thereby, the electronic states and phononic states are calculated ab initio. We find that the demagnetization rates for fcc Ni and bcc Fe are too small to explain experimental demagnetization rates, which is in agreement with earlier publications. In addition, the demagnetization rates for band structures with reduced exchange splitting are calculated, however, also these demagnetization rates are too small. Finally, the phase space for scattering processes which is related to the maximum possible demagnetization is estimated for band structures with ground-state exchange splitting and with reduced exchange splitting. The maximum possible demagnetization is too small for bcc Fe and fcc Co but not necessarily for fcc Ni. We suggest to include magnons and to consider independent combinations of spin-flip electron-phonon and spin-flip electron-magnon scattering processes as a possible explanation for the ultrafast demagnetization.

Figure 1

Calculated demagnetization rate $dM/dt\left(t_s\right)$ (black line, squares) at time $t_s$ as a function of the electron temperature $T_e\left(t_s\right)$ for the ground-state exchange splitting according to the ground-state magnetic moment: (a) 0.64 ${\mu }_{\mathrm{B}}$ for fcc Ni. (b) 2.2 ${\mu }_{\mathrm{B}}$ for bcc Fe. The demagnetization rate is split into the Elliott part $d{M}^{\mathrm{E}}/dt\left(t_s\right)$ (red line, circles) and the Yafet part $d{M}^{\mathrm{Y}}/dt\left(t_s\right)$ (green line, triangles).

Figure 2

Calculated demagnetization rate $dM/dt\left(t_{*}\right)$ at time $t_{*}$ as a function of the electron temperature $T_e\left(t_{*}\right)$ for different reduced exchange splittings according to reduced magnetic moments: (a) 0.5 ${\mu }_{\mathrm{B}}$ (black line, squares), 0.4 ${\mu }_{\mathrm{B}}$ (red line, circles) and 0.3 ${\mu }_{\mathrm{B}}$ (green line, triangles) for fcc Ni. (b) 1.6 ${\mu }_{\mathrm{B}}$ (black line, squares) and 1.1 ${\mu }_{\mathrm{B}}$ (red line, circles) for bcc Fe. $t_{*}$ is the time at which the magnetic moment per atom is reduced to the value used for the calculation.

Figure 3

Calculated maximum possible demagnetization $\Delta M$ as function of the electron temperature $T_e\left(t_{*}\right)$ up to 2000 K for the ground-state exchange splitting according to the ground-state magnetic moment and up to 1000 K for reduced exchange splittings according to reduced magnetic moments. (a) fcc Ni: 0.64 ${\mu }_{\mathrm{B}}$ (black line, squares), 0.5 ${\mu }_{\mathrm{B}}$ (red line, circles) and 0.3 ${\mu }_{\mathrm{B}}$ (green line, triangles). (b) bcc Fe: 2.2 ${\mu }_{\mathrm{B}}$ (black line, squares), 1.6 ${\mu }_{\mathrm{B}}$ (red line, circles) and 1.1 ${\mu }_{\mathrm{B}}$ (green line, triangles). (c) fcc Co: 1.6 ${\mu }_{\mathrm{B}}$ (black line, squares), 1.2 ${\mu }_{\mathrm{B}}$ (red line, circles) and 0.8 ${\mu }_{\mathrm{B}}$ (green line, triangles).