Novel Valence Transition in Elemental Metal Europium around 80 GPa

Valence transition could induce structural, insulator-metal, nonmagnetic-magnetic and superconducting transitions in rare-earth metals and compounds, while the underlying physics remains unclear due to the complex interaction of localized $4f$ electrons as well as their coupling with itinerant electrons. The valence transition in the elemental metal europium (Eu) still has remained as a matter of debate. Using resonant x-ray emission scattering and x-ray diffraction, we pressurize the states of $4f$ electrons in Eu and study its valence and structure transitions up to 160 GPa. We provide compelling evidence for a valence transition around 80 GPa, which coincides with a structural transition from a monoclinic ($C2/c$) to an orthorhombic phase ($Pnma$). We show that the valence transition occurs when the pressure-dependent energy gap between $4f$ and $5d$ electrons approaches the Coulomb interaction. Our discovery is critical for understanding the electrodynamics of Eu, including magnetism and high-pressure superconductivity.

Figure 1

(a) The normalized $L_3$-edge PFY XAS spectrum of Eu at 11 GPa. (b) RXES spectra collected at 11 GPa as a function of transfer energy $E_t$ and incident energy $E_i$.

Figure 2

(a) RXES spectra measured with $E_i=6970\mathrm{eV}$, which are normalized to the maximum intensity of $4f^7$ peak. (b) Pressure dependence of Eu valence at room temperature as determined by RXES (dark blue solid circles) from this study, and XANES (blue hollow circles) from Ref. [23] and dotted line from Ref. [25], along with the magnetic ground states of Eu from Refs. [25, 27]. The different colors represent different structures of bcc, hcp, monoclinic, and orthorhombic as determined by XRD in this study, respectively, which we will discuss later. The dashed line is a guide for the eye, where the increase valence around 80 GPa is highlighted by the red zone.

Figure 3

(a) Selected synchrotron XRD pattern with the subtracted background of Eu at various pressures. (b) Rietveld refinement of the XRD patterns collected at 96.6 GPa for the $Pnma$ structure at room temperature. The red circles, the solid black line, and the green line represent the experimental data, fitted data, and background, respectively. The inset schematic figure shows the local coordination in Eu.

Figure 4

Schematic of the promotional model in which valence transition is associated with the onsite charge transfer between $4f$ and $5d$ states, where $U_{df}$ is the interorbital Coulomb repulsion between the carrier and localized hole on the same site, $D_d$ is the bandwidth of $5d$ band. Once the gap approaches $U_{df}$, the valence transition occurs.