Correlation in the transition metal based Heusler compounds Co$_2$MnSi and Co$_2$FeSi

TL;DR

This paper investigates the role of electronic correlations in Co-based Heusler compounds, showing that including on-site Coulomb interactions explains experimental magnetic moments and half-metallicity, which standard calculations fail to reproduce.

Contribution

It demonstrates that on-site electron correlation effects are crucial for accurately modeling magnetic properties of Co$_2$MnSi and Co$_2$FeSi Heusler compounds, resolving discrepancies between theory and experiment.

Findings

LDA calculations underestimate magnetic moments without lattice expansion.

LDA+U with U_eff between 2-5 eV reproduces experimental moments.

Strong correlations can destroy half-metallicity in these compounds.

Abstract

Half-metallic ferromagnets like the full Heusler compounds with formula X$_2$YZ are supposed to show an integer value of the spin magnetic moment. Calculations reveal in certain cases of X = Co based compounds non-integer values, in contrast to experiments. In order to explain deviations of the magnetic moment calculated for such compounds, the dependency of the electronic structure on the lattice parameter was studied theoretically. In local density approximation (LDA), the minimum total energy of Co$_2$FeSi is found for the experimental lattice parameter, but the calculated magnetic moment is about 12% too low. Half-metallic ferromagnetism and a magnetic moment equal to the experimental value of $6\mu_B$ are found, however, only after increasing the lattice parameter by more than 6%. To overcome this discrepancy, the LDA$+U$ scheme was used to respect on-site electron correlation in the calculations. Those calculations revealed for Co$_2$FeSi that an effective Coulomb-exchange interaction $U_{eff}=U-J$ in the range of about 2eV to 5eV leads to half-metallic ferromagnetism and the measured, integer magnetic moment at the measured lattice parameter. Finally, it is shown in the case of Co$_2$MnSi that correlation may also serve to destroy the half-metallic behavior if it becomes too strong (for Co$_2$MnSi above 2eV and for Co$_2$FeSi above 5eV). These findings indicate that on-site correlation may play an important role in the description of Heusler compounds with localized moments.