The half-metallicity of the Co$_{2}$FeSi full Heusler alloy in bulk, clean surface and interfaces with Si ; first-principles investigation

We report the \textit{ab-initio} calculational results on the half-metallicity of Co$_{2}$FeSi full Heusler alloys in bulk, (001) surfaces and interface with Si. Employing the +U corrections within the FLAPW[1] method, we investigate the effect of correlation interaction on half-metallicity and magnetic properties. For bulk, the +U approach reproduces experimental values of the minority spin band gap and total spin magnetic moment. The (001) surfaces and interfaces with Si are calculated to be metallic by both LDA and GGA due to the surface and interface states developed at E$_{F}$. Upon +U correction, the Co-terminated clean surface recovers half-metallicity with a reduced band gap (0.40 eV) from the bulk value while the rest of the systems are still metallic, which can be explained by the correlation and hybridization effects. [1] E. Wimmer, H. Krakauer, M. Weinert, and A. J. Freeman, PRB \textbf{24}, 864 (1981).