Electronic processes occurring during ultrafast demagnetization of cobalt triggered by x-ray photons tuned to the Co $L_3$ resonance

Magnetization dynamics triggered by ultrashort laser pulses has been attracting significant attention, with a strong focus on the dynamics excited by visible/near-infrared pulses. Only recently has a strong magnetic response in solid materials induced by intense x-ray pulses from free-electron lasers been observed. The exact mechanisms that trigger the x-ray-induced demagnetization are not yet fully understood. They are the subject of ongoing experimental and theoretical investigations. Here, we present a theoretical analysis of electronic processes occurring during demagnetization of a Co multilayer system irradiated by x-ray pulses tuned to the $L_3$ absorption edge of cobalt. We show that, like in the case of x-ray-induced demagnetization at the $M$ edge of Co, electronic processes play a predominant role in the demagnetization until the pulse fluence does not exceed the structural damage threshold. The impact of electronic processes can explain reasonably well the available experimental data, without a need to introduce the mechanism of stimulated elastic forward scattering.

Figure 1

Calculated density of states (per atom) for equilibrium fcc cobalt, with a schematic indication of the $2p$ band of cobalt and of the probed region in its $3d$ band (the conduction band). The width of the $2p$ band is $2\mathrm{\Delta }$. The density of states is shown for the spin-up domain (red line) and for the spin-down domain (green line).

Figure 2

Normalized magnetic scattering efficiency $S_{\mathrm{norm}}\left(F\right)$ as a function of the average absorbed dose, also converted into the effective pulse fluence (incoming on the uppermost Ta layer). Predictions including the demagnetization (blue solid line) and predictions assuming no demagnetization, i.e., $M\left(t\right)=M\left(0\right)$ (orange dashed line), are shown for comparison. Experimental data (red circles) are taken from Ref. [13]. The value of $\mathrm{\Delta }=2$ eV was used [23, 24].

Figure 3

Temporal evolution of (a) electronic temperature and the (b) number of excited electrons (per atom) in the spin-up and spin-down domains. The red line denotes the spin-up (majority-spin) electron fraction, and the green line denotes the spin-down (minority-spin) electron fraction. (c) Magnetization, with a schematically plotted x-ray pulse shape. The average absorbed dose used for this simulation was 0.93 eV/atom. The value of $\mathrm{\Delta }=2.0$ eV was used for (c) [23, 24].

Figure 4

(a) Number of high-energy electrons and (b) number of low-energy electrons (both per atom) as a function of time. The red line denotes the spin-up (majority-spin) electron fraction, and the green line denotes the spin-down (minority-spin) electron fraction. The results were obtained for the average absorbed dose of 0.93 eV/atom.