Electron-phonon scattering dynamics in ferromagnetic metals and their influence on ultrafast demagnetization processes

We theoretically investigate spin-dependent carrier dynamics due to the electron-phonon interaction after ultrafast optical excitation in ferromagnetic metals. We calculate the electron-phonon matrix elements including the spin-orbit interaction in the electronic wave functions and the interaction potential. Using the matrix elements in Boltzmann scattering integrals, the momentum-resolved carrier distributions are obtained by solving their equation of motion numerically. We find that the optical excitation with realistic laser intensities alone leads to a negligible magnetization change, and that the demagnetization due to electron-phonon interaction is mostly due to hole scattering. Importantly, the calculated demagnetization quenching due to this Elliot-Yafet-type depolarization mechanism is not large enough to explain the experimentally observed result. We argue that the ultrafast demagnetization of ferromagnets does not occur exclusively via an Elliott-Yafet type process, i.e., scattering in the presence of the spin-orbit interaction, but is influenced to a large degree by a dynamical change of the band structure, i.e., the exchange splitting.

Figure 1

Magnetization dynamics due to optical excitation alone. The magnetization is normalized to its equilibrium value.

Figure 2

Spin-resolved density of states for nickel and iron (a) as well as energy- and spin-resolved occupation change after the optical excitation for nickel (b) and iron (c).

Figure 3

Magnetization change achievable by optical excitation alone for a range of pump-photon energies.

Figure 4

Normalized magnetization dynamics (a) and energy difference to equilibrium of the electronic system (b) after the optical excitation including electron-phonon scattering. Results obtained including the spin-orbit coupling contribution in the electron-phonon matrix element are labeled “with SOC-ME.”

Figure 5

Energy- and spin-resolved occupation changes $\Delta N_{\sigma }$ at different times for nickel, as shown in Fig. 4, including the spin-orbit coupling in the electron-phonon matrix element. The representation is in analogy to the one for the optical excitation [Figs. 2b and 2c].

Figure 6

Theoretical limit for the minimal magnetization achievable by a pure redistribution in a fixed band structure for a range of deposited energies $\Delta E$.

Figure 7

Energy- and spin-resolved occupation distributions for nickel. (a) shows the distributions that is necessary to attain the minimal magnetization for $\Delta E=100\mathrm{meV}/\mathrm{cell}$ while (b) shows a typical distribution that would be created by the optical excitation (this is a slightly different representation of the data shown in Fig. 2b. Here we show the occupation distribution, which allows an easier comparison with the equilibrium distribution).