Mechanisms for Pressure-Induced Isostructural Phase Transitions in EuO

We study pressure-induced isostructural electronic phase transitions in the prototypical mixed valence and strongly correlated material EuO using the global-hybrid density functional theory. The simultaneous presence in the valence of highly localized $d$- and $f$-type bands and itinerant $s$- and $p$-type states, as well as the half-filled $f$-type orbital shell with seven unpaired electrons on each Eu atom, have made the description of the electronic features of this system a challenge. The electronic band structure, density of states, and atomic oxidation states of EuO are analyzed in the 0–50 GPa pressure range. An insulator-to-metal transition at about 12 GPa of pressure was identified. The second isostructural transition at approximately 30–35 GPa, previously believed to be driven by an oxidation from Eu(II) to Eu(III), is shown instead to be associated with a change in the occupation of the Eu $d$ orbitals, as can be determined from the analysis of the corresponding atomic orbital populations. The Eu $d$ band is confined by the surrounding oxygens and split by the crystal field, which results in orbitals of $e_g$ symmetry (i.e., $d_{x^2-y^2}$ and $d_{2z^2-x^2-y^2}$, pointing along the Eu-O direction) being abruptly depopulated at the transition as a means to alleviate electron-electron repulsion in the highly compressed structures.

Figure 1

(Left top panel) Calculated energy-volume relation. (Left middle panel) band gap of EuO as a function of volume. (Left bottom panel) Population of $d$-type bands of Eu atoms in EuO as a function of volume. (Right top panel) $d$ orbitals of $e_g$ symmetry point along the Eu-O bonds of the EuO octahedron and $d$ orbitals of $t_{2g}$ symmetry point between O atoms (along the Eu-Eu direction). (Right bottom panel) Pressure-volume equation of state of EuO as fitted to the calculations in the present study (black line) and measured in previous experiments (colored symbols) [3, 22, 58]. Transition volumes and pressures are marked with dashed vertical lines, with colors matching the symbols.

Figure 2

(a) and (b) Evolution with pressure (blue tones and red tones below and above the metal-to-metal transition, respectively) of PDOSS of $d$ orbitals of Eu of (a) $e_g$ and (b) $t_{2g}$ symmetry. (c) and (d) Orbital population of $d$-type orbitals of Eu as a function of pressure. The Eu atom is in an octahedral environment with the $e_g$ (and $t_{2g}$) sets pointing towards (between) O atoms.

Figure 3

Calculated total DOS (sum of spin-up and spin-down contributions) of the $t_{2g}$ and $e_g$ band at selected pressures. Vertical blue dashed lines (separated by 5 eV) are a guide to the eye.