Spin and orbital magnetism in ordered Fe 3 ± δ Si 1 ∓ δ binary Heusler structures: Theory versus experiment

The spin and orbital magnetism of $8\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ thick ${\mathrm{Fe}}_{2.8}{\mathrm{Si}}_{1.2}$, ${\mathrm{Fe}}_{3}\mathrm{Si}$, and ${\mathrm{Fe}}_{3.2}{\mathrm{Si}}_{0.8}$ films epitaxially grown on MgO(001) was determined experimentally by ferromagnetic resonance and superconducting quantum interference device magnetometry and theoretically by fully relativistic density functional theory calculations. The experimental average spin (orbital) moment of the stoichiometric ${\mathrm{Fe}}_{3}\mathrm{Si}$ $[{\ensuremath{\mu}}_{S(L)}^{\mathrm{av}}=1.38(0.051){\ensuremath{\mu}}_{B}]$ is in reasonable agreement with the theoretical one $[{\ensuremath{\mu}}_{S(L)}^{\mathrm{av}}=1.75(0.029){\ensuremath{\mu}}_{B}]$. Slight increases (reductions) of the Fe content are experimentally found to increase (decrease) the spin and orbital moments as predicted by theory. The results reveal an important step toward tailoring spin and orbital magnetism in the binary Heusler alloys.