Orbital angular momentum and interpretation of core-absorption magnetic circular dichroism on the band picture in Co-based Heusler alloys ${\mathrm{Co}}_{2}Y\mathrm{Sn}$ $(Y=\mathrm{Ti},$ $\mathrm{Zr},$ and $\mathrm{Nb})$

The magnetic circular dichroism (MCD) of core-level absorption [x-ray absorption spectroscopy (XAS)] spectra in the soft x-ray region has been measured for the ferromagnetic Heusler alloys ${\mathrm{Co}}_2\mathrm{TiSn},$ ${\mathrm{Co}}_2\mathrm{ZrSn},$ and ${\mathrm{Co}}_2\mathrm{NbSn}.$ The many-peak structures which are clearly observed in the Co $2\overrightarrow{p}3d$ XAS-MCD spectra cannot be well explained by atomic multiplet calculations but are better explained by the Co $3d$ unoccupied states predicted by linear muffin-tin orbital atomic sphere approximation band structure calculations. The MCD spectra show an obvious contribution of the orbital angular momentum component to the magnetic moment in these alloys. The ratio between the orbital angular momentum and spin derived from the MCD spectra varies by more than a factor of 2 within these alloys. The mechanism of this variation is discussed in comparison with the band structure calculations.