Unveiling spin-dependent unoccupied electronic states of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ (Ga) film via Ge (Ga) $L_{2,3}$ absorption spectroscopy

X-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD) spectroscopy were applied at the Ge (Ga) $L_{2,3}$ edge to unravel the spin-resolved unoccupied electronic states of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ (Ga). Complicated spectral features were observed in both XAS and XMCD spectra. For their interpretation, we compared the experimental XAS and XMCD spectra with the calculated Ge (Ga) $4s$ and $4d$ orbital partial density of states. The comparison enabled a qualitative explanation of the XMCD spectra as the difference between the majority- and minority-spin unoccupied density of states summed over the $4s$ and $4d$ orbitals. Our finding provides a new approach to uncover the spin-split partial density of states above the Fermi level.

Figure 1

$L_{2,3}$ XAS (upper) and XMCD (lower) spectra of (a) the Ge site of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ and (b) the Ga site of ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$.

Figure 2

(a) Schematic XMCD considering the transition probability for ${\mu }_{+}$. [(b) and (c)] Calculated spin-dependent total DOS, and [(d) and (e)] the Ge and Ga PDOS for orbitals $4s$ and $4d$ in the extended energy range for ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ and ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$, respectively.

Figure 3

Calculated total and majority- and minority-spin Ge PDOS for $4d$ (a) and $4s$ (b) convoluted with the Voigt function (upper) and the difference between majority and minority spin DOS (lower) for comparison (see text for details) together with the experimental Ge $L_{2,3}$ edge absorption spectra ${\mu }_{-}$ (pink), ${\mu }_{+}$, and XMCD spectrum (open circles).

Figure 4

Computed XAS [(a) and (d)] and XMCD [(b), (c), (e), and (f)] spectra using Eqs. (5) at $L_3$ (green), $L_2$ (red), and sum (blue) together with experimental Ge and Ga $L_{2,3}$ edge absorption spectra (pink circle) for ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ge}$ and ${\mathrm{Co}}_2\mathrm{Mn}\mathrm{Ga}$, respectively.