Ab initio investigation of laser-induced ultrafast demagnetization of $L{1}_0$ FePt: Intensity dependence and importance of electron coherence

We theoretically investigate the optically induced demagnetization of ferromagnetic FePt using the time-dependent density functional theory (TDDFT). We compare the demagnetization mechanism in the perturbative and nonperturbative limits of light-matter interaction and show how the underlying mechanism of the ultrafast demagnetization depends on the driving laser intensity. Our calculations show that the femtosecond demagnetization in TDDFT is a longitudinal magnetization reduction and results from a nonlinear optomagnetic effect, akin to the inverse Faraday effect. The demagnetization scales quadratically with the electric field $E$ in the perturbative limit, i.e., $\mathrm{\Delta }{M}_z\propto E^2$. Moreover, the magnetization dynamics happens dominantly at even multiples $n{\omega }_0$, ($n=0,2,\cdots$) of the pump-laser frequency ${\omega }_0$, whereas odd multiples of ${\omega }_0$ do not contribute. We further investigate the demagnetization in conjunction to the optically induced change of electron occupations and electron correlations. Dynamical correlations within the Kohn-Sham local-density framework are shown to have an appreciable yet distinct effect on the amount of demagnetization depending on the laser intensity. Comparing the ab initio computed demagnetizations with those calculated from spin occupations, we show that electronic coherence plays a dominant role in the demagnetization process, whereas interpretations based on the time-dependent occupation numbers poorly describe the ultrafast demagnetization.

Figure 1

Laser-induced change in the magnetization (scaled) of ${\mathrm{L1}}_0$ FePt for incident laser intensities (fluences) of (a) ${10}^{10}$ ${\mathrm{W/cm}}^2$ (56.25 $\mu {\mathrm{J/cm}}^2$) and (b) $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$ (11.25 ${\mathrm{mJ/cm}}^2$) calculated within TDDFT (violet) and IP (orange) approaches. The vector potential of the laser field (gray) has a central wavelength of 800 nm.

Figure 2

(a) Laser-induced change in magnetization as a function of the peak intensity of the laser field. Magnetization dynamics in the frequency domain ($\mathcal{G}$, see text for definition) for incident laser intensities of (b) ${10}^{10}$ ${\mathrm{W/cm}}^2$ and (c) $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$.

Figure 3

(a) A typical frequency distribution of an ultrashort laser field with central frequency ${\omega }_0$. (b) Electronic Raman excitation and (c) two-photon absorption, where $|n,s\rangle$, $|l,s^{\prime }\rangle$, and $|m,s^{″}\rangle$ are electronic spinor states at a particular $\mathit{k}$ point.

Figure 4

Laser-induced modification of electron occupations (orange line) after the laser pulse for a laser of peak intensity (a) ${10}^{10}$ ${\mathrm{W/cm}}^2$ and (c) $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$. Majority and minority electrons are represented, respectively, by the positive and negative $y$ axis. The ground-state density of states is shown by the green shaded area. Panels (b) and (d) show the laser-induced change in the electron occupations corresponding to panels (a) and (c), respectively.

Figure 5

Ultrafast laser-induced demagnetization computed with TDDFT ($\mathrm{\Delta }{\mathit{M}}_{\mathrm{tot}}$) along with the magnetization change due to change in the electronic occupations ($\mathrm{\Delta }{\mathit{M}}_{\mathrm{occ}}$) for a laser of peak intensity (a) ${10}^{10}$ ${\mathrm{W/cm}}^2$ and (b) $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$. For comparison, results computed with the IP approximation are also given.

Figure 6

Element-resolved change in magnetization of ${\mathrm{L1}}_0$ FePt for a laser with a peak intensity of ${10}^{10}$ ${\mathrm{W/cm}}^2$ (left panels) and $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$ (right panels). The demagnetization of Fe and Pt is normalized in panels (a) and (b). The absolute value of the demagnetization is given in panels (c) and (d). The change in the magnetization in the interstitial region is presented in panels (e) and (f).

Figure 7

The change in the number of majority (top panels) and minority electrons (bottom panels) around atoms when lasers of peak intensity ${10}^{10}$ ${\mathrm{W/cm}}^2$ (left panels) and $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$ (right panels) interact with FePt. The spin-orbit coupling is turned off in these calculations.

Figure 8

The calculated change in total energy of the electronic system during the ultrafast demagnetization for a laser pulse of peak intensity of ${10}^{10}$ ${\mathrm{W/cm}}^2$ (blue) and of $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$ (orange).

Figure 9

The spectral distribution of excited Kohn-Sham wave function in FePt using the TDDFT and IP approaches for a laser with peak intensity of (a) ${10}^{10}$ ${\mathrm{W/cm}}^2$ and (c) $2\times {10}^{12}$ ${\mathrm{W/cm}}^2$. The difference $\mathrm{\Delta }\eta$ ($={\eta }_{\mathrm{TDDFT}}-{\eta }_{\mathrm{IP}}$) of the spectral distributions of the two approaches is shown by the blue shaded lines in (b) and (d).

Figure 10

Calculated change in the spin and orbital magnetizations during the ultrafast demagnetization of FePt. The laser parameters used are the same as in Fig. 1.

Figure 11

Ultrafast (normalized) demagnetization of Fe in ${\mathrm{L1}}_0$ FePt (pink curve) and of bcc Fe (black curve). The laser parameters used are the same as in Fig. 1.