Half-Metallic Ferromagnetism with Unexpectedly Small Spin Splitting in the Heusler Compound ${\mathrm{Co}}_2\mathrm{FeSi}$

Half-metallic ferromagnetism stands for the technologically sought-after metallicity with 100% spin polarization. Electrical transport should, in principle, sensitively probe half-metallic ferromagnetism, since electron-magnon scattering processes are expected to be absent, with clear-cut consequences for the resistivity and the magnetoresistance. Here we present electrical transport data for single-crystalline ${\mathrm{Co}}_2\mathrm{FeSi}$, a candidate half-metallic ferromagnet Heusler compound. The data reveal a textbooklike exponential suppression of the electron-magnon scattering rate with decreasing temperature which provides strong evidence that this material indeed possesses perfect spin polarization at low temperature. However, the energy scale for thermally activated spin-flip scattering is relatively low (activation gap $\Delta \approx 100\mathrm{K}$) which has decisive influence on the magnetoresistance and the anomalous Hall effect, which exhibit strong qualitative changes when crossing $T\approx 100\mathrm{K}$.

Figure 1

(a) $\mathrm{L}{2}_1$ crystal structure of ${\mathrm{Co}}_2\mathrm{FeSi}$. (b) Sketch of the density of states of a HMF for minority and majority electrons with an energy gap at Fermi level $E_{\mathrm{F}}$ for minority electrons. (c) Magnetic moment of a ${\mathrm{Co}}_2\mathrm{FeSi}$ single crystal.

Figure 2

Temperature dependence of the resistivity in zero and 15 T magnetic field. Upper left inset: difference [$\Delta \rho =\rho (15\mathrm{T})-\rho (0\mathrm{T})$, ${\rho }_0=\rho (0\mathrm{T})$] of these measurements. Lower right insets: close-up to low and high temperatures.

Figure 3

Resistivity as a function of the temperature. Measured values are displayed as black dots. Blue dashed lines show fits with magnonic ($\sim T^2$) and magnonic-phononic temperature dependence. The red continuous line shows a fit where an additional Boltzmann factor was added to the magnonic scattering; its fitting parameters are displayed (see the text for formulas).

Figure 4

Magnetic field dependence of resistivity at different temperatures. Inset: slope of $\rho (B)$ in the applied field range of ${\mu }_{0}H=(3–15)\mathrm{T}$.

Figure 5

Hall resistivity as a function of the applied magnetic field for different temperatures. Inset: ordinary Hall coefficient $R$ and anomalous Hall coefficient $R_{\mathrm{A}}$ as a function of the temperature.

Figure 6

Anomalous Hall coefficient $R_{\mathrm{A}}$ as a function of the zero-field resistivity $\rho$ (black circles). Line: quadratic fit for temperatures above 100 K.