Electron-electron correlations affect the band gap of half-metallic ferromagnets by introducing nonquasiparticle states just above the Fermi level. In contrast with the spin-orbit coupling, a large asymmetric nonquasiparticle spectral weight is present in the minority-spin channel, leading to a peculiar finite-temperature spin depolarization effects. Using recently developed first-principle dynamical mean-field theory, we investigate these effects for the half-metallic ferrimagnetic Heusler compound FeMnSb. We discuss depolarization effects in terms of strength of local Coulomb interaction U and temperature in FeMnSb. We propose Ni(1-x)Fe(x)MnSb alloys as a perspective materials to be used in spin-valve structures and for experimental search of nonquasiparticle states in half-metallic materials.