Visualizing Half-Metallic Bulk Band Structure with Multiple Weyl Cones of the Heusler Ferromagnet

Using a well-focused soft x-ray synchrotron radiation beam, angle-resolved photoelectron spectroscopy was applied to a full-Heusler-type ${\mathrm{Co}}_2\mathrm{MnGe}$ alloy to elucidate its bulk band structure. A large parabolic band at the Brillouin zone center and several bands that cross the Fermi level near the Brillouin zone boundary were identified in line with the results from first-principles calculations. These Fermi-level crossings are ascribed to majority spin bands that are responsible for electron transport with extremely high spin polarization especially along the direction perpendicular to the interface of magnetoresistive devices. The spectroscopy confirms there is no contribution of the minority spin bands to the Fermi surface, signifying half-metallicity for the alloy. Furthermore, two topological Weyl cones with band crossing points were identified around the $X$ point, yielding the conclusion that ${\mathrm{Co}}_2\mathrm{MnGe}$ could exhibit topologically meaningful behavior such as large anomalous Hall and Nernst effects driven by the Berry flux in its half-metallic band structure.

Figure 1

(a) Crystal structure of ${\mathrm{Co}}_2\mathrm{MnGe}$. (b) Experimental setup. (c)–(j) ARPES images vs photon energy. (k),(l) Constant energy surface at (k) $E_B=0\mathrm{eV}$ ($E_F$) and (l) $E_B=0.28\mathrm{eV}$ in the $k_x\text{−}{k}_z$ plane from ARPES denoted with high-symmetry lines. Green (red) lines correspond to $k_z=0(2\pi /a)$ at $k_x=0$. (m) Calculated constant energy surfaces ($E_B=0.2\mathrm{eV}$). (n) BZ and $k_x\text{−}{k}_z$ surface (shaded by green). Red curves correspond to $k_z$ line of each ARPES images at fixed photon energies.

Figure 2

(a),(b) ARPES images measured with a photon energies ($h\nu \mathrm{s}$) of 435 and 535 eV [the same $k$ cuts as Figs. 1 and 1, respectively]. (c) Second derivative momentum distribution curve along $E_B=0\mathrm{eV}$ line ($E_F$) in (b). (d) Calculated band dispersions along the $\mathrm{\Gamma }\text{−}K\text{−}{X}_{2\mathrm{nd}}$ line. Red (blue) corresponds to majority (minority) spin components. (e) Calculated band dispersions around the $K$ and $X$ point. (f) Measured ARPES band dispersions along the $\mathrm{\Gamma }\text{−}X$ line [red dashed line in Fig. 3]. (g) ARPES image normalized by the integrated intensity of momentum distribution curve from (f). (h) Calculated band dispersions along the $\mathrm{\Gamma }\text{−}X$ line. (i) BZ and high-symmetry points. The red line corresponds to the $k_z$ line of (f).

Figure 3

(a)–(e) Constant energy surfaces in the $k_x\text{−}{k}_y$ plane mapped by ARPES with a photon energy of 535 eV. (f)–(j) Characteristic features of constant energy surfaces depicted from (a)–(e). (k)–(o) Calculated constant energy surfaces with an energy offset of $-100\mathrm{meV}$ (40 meV) toward higher $E_B$ in a majority (minority) spin channel. (p) BZ and $k_x\text{−}{k}_y$ surface (shaded by green).

Figure 4

(a)–(e) ARPES images with changing photon energy around $h\nu =535\mathrm{eV}$. (d) corresponds to the blue dotted box in Fig. 1. (f)–(j) Second derivative ARPES images from (a)–(e). (k)–(o) Calculated band dispersion with an energy offset of $-100\mathrm{meV}$ (40 meV) toward higher $E_B$ in a majority (minority) spin channel. The momentum path is simulated from kinetic energy of the photoelectron and considering $k_z$ broadening of $\delta k_z\sim \pm 0.2{\AA }^{-1}$. (p)–(t) Red curves correspond to each ARPES image and calculated results.