Distinctive Picosecond Spin Polarization Dynamics in Bulk Half Metals

Femtosecond laser excitations in half-metal (HM) compounds are theoretically predicted to induce an exotic picosecond spin dynamics. In particular, conversely to what is observed in conventional metals and semiconductors, the thermalization process in HMs leads to a long living partially thermalized configuration characterized by three Fermi-Dirac distributions for the minority, majority conduction, and majority valence electrons, respectively. Remarkably, these distributions have the same temperature but different chemical potentials. This unusual thermodynamic state is causing a persistent nonequilibrium spin polarization only well above the Fermi energy. Femtosecond spin dynamics experiments performed on ${\mathrm{Fe}}_3{\mathrm{O}}_4$ by time- and spin-resolved photoelectron spectroscopy support our model. Furthermore, the spin polarization response proves to be very robust and it can be adopted to selectively test the bulk HM character in a wide range of compounds.

Figure 1

Electron distribution function $n$ during the thermalization following a femtosecond laser excitation in a metal (a) and a semiconductor (b). Both linear (left column) and logarithmic (right column) representations are plotted to highlight the location of $E_F$ and the electronic temperature (see text for details).

Figure 2

Electron thermalization after a laser pulse excitation in ${\mathrm{Fe}}_3{\mathrm{O}}_4$: (a) Time evolution (up to 200 fs) of the electron distribution $n$ in the $-\ln (n^{-1}-1)$ representation for the metallic minority spin channel (bottom panel). The top panel shows the corresponding DOS of bulk ${\mathrm{Fe}}_3{\mathrm{O}}_4$. (b) Same for the insulating majority spin channel showing the presence of two chemical potentials. Using the metallic surface DOS, the calculations converge toward the solid green line with a single chemical potential. (c)–(e) Time dependence of the SP calculated for the bulk (HM), the surface (metal), and for a $50:50$ mixture of bulk and surface contributions, respectively.

Figure 3

Photoemission from ${\mathrm{Fe}}_3{\mathrm{O}}_4$. (a) The Fe $3d(t_{2g})$ EDC at 4.65 eV photon energy (lower panel, log scale, grey dots) is fitted (solid blue line) by a function including the one-step PE calculation (top panel), a FD distribution, and a broadening function (blue dashed lines). (b) Both measured and calculated SP (top panel) are referenced to the bulk DOS (lower panel) indicating the position (vertical green line) of the bottom of the CB.

Figure 4

Spin dynamics in ${\mathrm{Fe}}_3{\mathrm{O}}_4$ above $E_F$. (a) Spin-integrated EDC (top panel) before (black line) and 200 fs after (orange line) pump excitation. The corresponding SP (bottom panel) increases at the bottom of the CB (green bar) as theoretically predicted for a HM. (b) The dynamics of the hot carriers (top panel) at this energy is well described by an exponential decay function characteristic of an electron-phonon cooling. The SP (bottom panel) relaxes on a similar time scale whereas the SP below $E_F$ (empty blue diamond), proportional to the macroscopic magnetization, remains unchanged.