Half-metallic ferromagnetism and intrinsic anomalous Hall effect in the topological Heusler compound Co2MnGe

Half-metallic ferromagnets (HMFs) are ferromagnetic metallic compounds with 100% spin polarization at the Fermi level $({E}_{F})$, and thus they are of particular interest in the field of spintronics, but the identification of HMFs with experiments is a challenging task. In principle, temperature-dependent electrical transport measurements should sensitively probe the half-metallic ferromagnetism since the spin-flip electron-magnon scattering mechanism is expected to be absent. In this work, we perform a systematic temperature-dependent electrical transport measurement on the ferromagnetic full Heusler compound ${\mathrm{Co}}_{2}\mathrm{MnGe}$. Our experimental results reveal that ${\mathrm{Co}}_{2}\mathrm{MnGe}$ exhibits an exponential suppression of spin-flip electron-magnon scattering below a characteristic crossover temperature $(\mathrm{\ensuremath{\Delta}}\ensuremath{\sim}79 \mathrm{K})$, which suggests that this material possesses a perfect spin polarization at the low temperature. The energy gap $({k}_{B}\mathrm{\ensuremath{\Delta}})$ characterizing the suppression of spin-flip electron-magnon scattering is $\ensuremath{\sim}7\phantom{\rule{0.28em}{0ex}}\mathrm{meV}$. This key finding is further established by a sign change in magnetoresistance at $T\ensuremath{\gtrsim}\mathrm{\ensuremath{\Delta}}$. Moreover, we have also studied the anomalous Hall effect (AHE) of the present compound. We find a notable change in the ordinary Hall coefficient $({R}_{0})$ and in the carrier density $(n)$ at $T\ensuremath{\lesssim}\mathrm{\ensuremath{\Delta}}$, which is consistent with the complete absence of minority-spin states at the ${E}_{F}$. The anomalous Hall resistivity $({\ensuremath{\rho}}_{yx}^{A})$ is observed to scale near quadratically with the longitudinal resistivity $({\ensuremath{\rho}}_{xx})$, and further experimental analysis indicates that the AHE in ${\mathrm{Co}}_{2}\mathrm{MnGe}$ is dominated by the intrinsic Karplus-Luttinger Berry phase mechanism. These findings imply that the ${\mathrm{Co}}_{2}\mathrm{MnGe}$ is a rare ferromagnetic full Heusler compound in which half-metallicity coexists with the topology-driven AHE.