Fermi-surface topology of rare-earth dihydrides

We report high-resolution angle-resolved photoemission experiments on epitaxial thin films of different rare-earth (RE) dihydrides $(\mathrm{RE}=\mathrm{Gd},\mathrm{La})$ and of $\mathrm{Y}{\mathrm{H}}_2$ and $\mathrm{Sc}{\mathrm{H}}_2$. It is found through ab initio calculations and confirmed by Fermi surface mapping that the electronic structure becomes very similar upon hydrogenation, rendering the studied dihydrides isoelectronic. We propose that the dihydride phase acts as a common precursor state for the formation of the insulating trihydride phase. For states with higher binding energies (which exhibit considerable H character) the agreement between calculation and measurement is less convincing. Independent of the difficulties to describe these hydrogen related states, we note in the comparison between experiment and calculation a very convincing description of the Fermi surface for the dihydrides. Therefore we trace the apparent inability of density, functional theory to describe the hygrogenation up to the trihydride phase to an insufficient description of hydrogen states in general and, in particular, involving octahedral sites.

Figure 1

Band structure along high-symmetry directions for (a) $\mathrm{Sc}{\mathrm{H}}_2$, (b) $\mathrm{Y}{\mathrm{H}}_2$, (c) $\mathrm{Gd}{\mathrm{H}}_2$, and (d) $\mathrm{La}{\mathrm{H}}_2$; one notices three bands labeled 1,2, and 3 with an indirect gap, respectively, overlap between band 1 and band 2 marked as feature 4 in (d). The calculation for $\mathrm{Gd}{\mathrm{H}}_2$ is spin polarized in order to avoid a placement of the $4f$ levels at the Fermi level, the majority bands are shown in gray.

Figure 2

(a) Surface Brillouin zone for $\mathrm{Y}{\mathrm{H}}_2$. (b) Side view of the BZ for a fcc structure in the $\Gamma \mathrm{KLUX}$ plane and its relation to the surface Brillouin zone for a [111]-oriented crystal. Free-electron final state model in an extended zone scheme for $\mathrm{Y}{\mathrm{H}}_2$. The free-electron final state spheres $(V_0=13\mathrm{eV},\varphi =3.1\mathrm{eV})$ are drawn for the Fermi energy and a binding energy of $-3\mathrm{eV}$. Shown in thick black is the Fermi surface contour, which was obtained via calculating the eigenstates on a cubic $k$ space grid, which is shown with open circles. The occupied region is shown hatched for one pocket. Features one, two and three denote regions of coincidence between the free-electron final state of $E_F$ and the Fermi surface contour. Feature four shows a possible Fermi surface nesting vector (see text). Contributions of a second domain are shown in gray. (c) Fermi surface and bulk BZ.

Figure 3

Fermi surface maps measured with He I radiation, high intensities are shown in white, outer ring corresponds to 90° emission, center corresponds to normal emission, all intensities are shown in parallel projection, the raw data are symmetrized and divided by a background of Gaussian shape; the high-symmetry points and the SBZ are indicated. The size difference of the SBZ originates from the different lattice constants. (a) $\mathrm{Sc}{\mathrm{H}}_2$, (b) $\mathrm{Y}{\mathrm{H}}_2$, (c) $\mathrm{Gd}{\mathrm{H}}_2$ and (d) $\mathrm{La}{\mathrm{H}}_2$.

Figure 4

Second derivative of experimental momentum distribution curves (a) $\mathrm{Sc}{\mathrm{H}}_2$, (b) $\mathrm{Y}{\mathrm{H}}_2$, (c) $\mathrm{Gd}{\mathrm{H}}_2$ (d) $\mathrm{La}{\mathrm{H}}_2$, color coded such that white corresponds to high intensity, the dashed lines serve as guide to the eye.

Figure 5

Experimental and theoretical $E\left(k\right)$ for $\mathrm{Y}{\mathrm{H}}_2$. (a) Second derivative of experimental $E\left(k\right)$ distribution curves (b) theoretical $E\left(k\right)$ distribution, eigenvalues were computed on a $k$ grid, which is adapted to the experimental $E\left(k\right)$ distribution curves, both inequivalent domains (see text) are considered.

Figure 6

(a) Experimental spectra $\mathrm{Sc}{\mathrm{H}}_2$, $\mathrm{Y}{\mathrm{H}}_2$, $\mathrm{Gd}{\mathrm{H}}_2$ and $\mathrm{La}{\mathrm{H}}_2$, all measured at an emission angle of 30°. (b) ARPES spectra along the $\left[\overline{\Gamma }\overline{M}\right]$ direction for $\mathrm{Gd}{\mathrm{H}}_2$ up to an emission angle of 60°.

Figure 7

(a) Susceptibility of $\mathrm{Y}{\mathrm{H}}_2$ in the [100] plane, derived from LDA band structure; grayscale with dark regions corresponding to high susceptibilities. (b) Susceptibility in the [100] direction, yielding only small variations (indicated by arrow) due to weak Fermi surface nesting (see text).