The density of non-quasiparticle states in the ferrimagnetic full-Heuslers Mn$_2$VAl alloy is calculated from first principles upon appropriate inclusion of correlations. In contrast to most half-metallic compounds, this material displays an energy gap in the majority-spin spectrum. For this situation, non-quasiparticle states are located below the Fermi level, and should be detectable by spin-polarized photoemission. This opens a new way to study many-body effects in spintronic-related materials.
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