Half-Metallic Ferromagnetism in the Heusler Compound Co$_2$FeSi revealed by Resistivity, Magnetoresistance, and Anomalous Hall Effect measurements

We present electrical transport data for single-crystalline Co$_2$FeSi which provide clear-cut evidence that this Heusler compound is truly a half-metallic ferromagnet, i.e. it possesses perfect spin-polarization. More specifically, the temperature dependence of $\rho$ is governed by electron scattering off magnons which are thermally excited over a sizeable gap $\Delta\approx 100 K$ ($\sim 9 meV$) separating the electronic majority states at the Fermi level from the unoccupied minority states. As a consequence, electron-magnon scattering is only relevant at $T\gtrsim\Delta$ but freezes out at lower temperatures, i.e., the spin-polarization of the electrons at the Fermi level remains practically perfect for $T\lesssim\Delta$. The gapped magnon population has a decisive influence on the magnetoresistance and the anomalous Hall effect (AHE): i) The magnetoresistance changes its sign at $T\sim 100 K$, ii) the anomalous Hall coefficient is strongly temperature dependent at $T\gtrsim 100 K$ and compatible with Berry phase related and/or side-jump electronic deflection, whereas it is practically temperature-independent at lower temperatures.