Correlation in the transition-metal-based Heusler compoundsCo2MnSiandCo2FeSi

Abstract

Half-metallic ferromagnets, such as the Heusler compounds with formula ${X}_{2}YZ$, are expected to show an integer value for the spin magnetic moment. In contrast to experiments, calculations give noninteger values in certain cases where the compounds are based on $X=\mathrm{Co}$. In order to explain deviations of the magnetic moment calculated for such compounds, the dependence of the electronic structure on the lattice parameter was studied theoretically. In the local density approximation (LDA), the minimum total energy of ${\mathrm{Co}}_{2}\mathrm{FeSi}$ is found for the experimental lattice parameter, but the calculated magnetic moment is approximately 12% too low. In addition, half-metallic ferromagnetism and a magnetic moment equal to the experimental value of $6{\ensuremath{\mu}}_{B}$ are found only after increasing the lattice parameter by more than 6%. To overcome these discrepancies, the $\mathrm{LDA}+U$ scheme was used to respect on-site electron correlation in the calculations. For ${\mathrm{Co}}_{2}\mathrm{FeSi}$, these calculations showed that an effective Coulomb exchange interaction ${U}_{eff}=U\ensuremath{-}J$ in the range of approximately $2--5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ leads to half-metallic ferromagnetism and to the measured integer magnetic moment at the measured lattice parameter. Finally, it is shown for ${\mathrm{Co}}_{2}\mathrm{MnSi}$ that correlation may also serve to destroy the half-metallic behavior if the correlation becomes too strong (above $2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${\mathrm{Co}}_{2}\mathrm{MnSi}$ and above $5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for ${\mathrm{Co}}_{2}\mathrm{FeSi}$). These findings indicate that on-site correlation may play an important role in the description of Heusler compounds with localized moments.