Three-Dimensional Bulk Fermiology of ${\mathrm{CeRu}}_2{\mathrm{Ge}}_2$ in the Paramagnetic Phase by Soft X-Ray $h\nu$-Dependent (700–860 eV) ARPES

By virtue of the soft x-ray angle-resolved photoelectron spectroscopy, the three-dimensional bulk fermiology has been successfully performed for a strongly correlated Ce compound, ferromagnet ${\mathrm{CeRu}}_2{\mathrm{Ge}}_2$ in the paramagnetic phase. A clear difference of the Fermi surface topology from either band calculation or de Haas–van Alphen results in the ferromagnetic phase is observed and interpreted by considering the difference of the $4f$ contribution to the Fermi surfaces in the paramagnetic phase.

Figure 1

Brillouin zone of the body-centered tetragonal crystal ${\mathrm{CeRu}}_2{\mathrm{Ge}}_2$ with $|\Gamma -\Lambda -Z|=2\pi /c$, in plane $|\Gamma -Z|=2\pi /a$.

Figure 2

ARPES spectra near $E_F$ of ${\mathrm{CeRu}}_2{\mathrm{Ge}}_2$ with an energy resolution of $\sim 200\mathrm{meV}$. The dashed lines are guides to the eye. Each colored spectrum in EDCs corresponds to the Fermi wave number ($k_F$). (a) EDCs along the $X\mathrm{\text{−}}Z\mathrm{\text{−}}X$ cut at $k_z\sim 2\pi /c$ ($h\nu =755\mathrm{eV}$). (a′),(a′′) Expanded EDCs and MDCs of (a) near the $Z$ point, respectively. (b) EDCs near the $\Gamma$ point along the $Z\mathrm{\text{−}}\Gamma \mathrm{\text{−}}Z$ cut at $k_z\sim 0$ ($h\nu =820\mathrm{eV}$). The shaded areas of (a) and (b) are located at bands 4 and 5 as discussed in text.

Figure 3

FS slice of ${\mathrm{CeRu}}_2{\mathrm{Ge}}_2$ obtained by integrating the photoelectron intensity from $+0.1$ to $-0.1\mathrm{eV}$. The solid lines represent the corresponding Brillouin zone and the dash-dotted lines represent high symmetry lines. White dots (with error bars) represent the estimated $k_F$ from EDCs and MDCs. The dashed lines represent the FSs following the experimentally evaluated $k_F$’s. (a) FS slice at $k_z\sim 2\pi /c$ ($h\nu =755\mathrm{eV}$), (b) at $k_z\sim 0$ ($h\nu =820\mathrm{eV}$). (c) FS slice in $k_z$ (ordinate)—$k_{xy}$ (abscissa) plane. Photon energies were varied from 735 to 840 eV with a 5 eV step. $h\nu =820$ and 755 eV correspond to the $\Gamma$ point and the $Z$ points, respectively, along the $\Gamma \mathrm{\text{−}}Z$ direction.

Figure 4

The FS shape of each band imaged from Fig. 3. Left panel: Holelike FSs centered at the $Z$ point derived from bands 2, 3, and 4. Right panel: Electron-like FS centered at the $\Gamma$ point from band 5.

Figure 5

(a) The band calculation with APW method for ${\mathrm{LaRu}}_2{\mathrm{Ge}}_2$ [25]. The FSs are formed by 5 bands. (b) MDCs displays of ARPES spectra near the $X$ point along the $X\mathrm{\text{−}}Z$ direction at $k_z\sim 2\pi /c$ ($h\nu =755\mathrm{eV}$). (c),(d) MDCs displays near the $\Gamma$ point and the $X$ point along the $X\mathrm{\text{−}}\Gamma$ direction at $k_z\sim 0$ ($h\nu =820\mathrm{eV}$), respectively.