Pressure-induced valence change in ${\text{YbAl}}_3$: A combined high-pressure inelastic x-ray scattering and theoretical investigation

High-resolution x-ray-absorption (XAS) experiments in the partial fluorescence yield mode (PFY) and resonant inelastic x-ray emission (RXES) measurements were performed on the intermediate-valence compound ${\text{YbAl}}_3$ under pressure of up to 38 GPa. The results of the ${\text{YbAl}}_3$ PFY-XAS and RXES studies show that the valence of Yb increases smoothly from 2.75 at ambient pressure to 2.93 at 38 GPa. In situ angle-dispersive synchrotron high-pressure x-ray-diffraction experiments carried out using a diamond cell at room temperature show that the ambient pressure cubic phase is stable up to 40 GPa. The results obtained from self-interaction corrected local spin density-functional calculations to understand the pressure effect on the Yb valence and compressibility are in good agreement with the experimental results.

Figure 1

(Color online) (a) X-ray-absorption spectra of ${\text{YbAl}}_3$ in the PFY mode. The dotted arrow indicates the continuous decrease in the $2+$ component as a function of pressure. The XAS spectrum of the ${\text{YbAl}}_3$ sample at ambient temperature and pressure is shown with Yb and ${\text{Yb}}_2{\text{O}}_3$ standards. (b) Decomposition of the $2+$ and $3+$ components (continuous lines) of the XAS spectrum at 38 GPa. The dotted line represents the fit and the open symbols represent the observed spectrum.

Figure 2

(Color online) Resonant x-ray emission spectra of ${\text{YbAl}}_3$ at 38 GPa. The incident energy was scanned in steps of 2 eV from 8.930 keV. A schematic representation of the transition is shown on the left. The RXES experiments were performed at the $L_3$ edge of Yb by measuring the $L{\alpha }_1$ x-ray emission as a function of pressure. (a) RXES spectrum with $E_{\text{in}}=8.938\text{keV}$ at different pressures and (b) 2D image of the ambient spectrum.

Figure 3

(Color online) Valence as a function of pressure for PFY-XAS (squares) and RXES (circles) experiments. The solid line represents the theoretical simulation as discussed in Sec. 3C.

Figure 4

Representative x-ray-diffraction patterns at different pressures for ${\text{YbAl}}_3$. The dotted lines are guides for the eye and indicate the shift observed in selected diffraction lines on increasing pressure. The patterns were collected using an incident x-ray wavelength of $\lambda =0.3888\text{Å}$.

Figure 5

(Color online) Pressure-volume relation of ${\text{YbAl}}_3$. The solid line is the fit with a second-order Birch-Murnaghan equation of state. The dotted line is the theoretical simulation. The estimated error bars lie within the size of the symbols.

Figure 6

(Color online) Total energy as a function of volume (per formula unit) for ${\text{YbAl}}_3$ calculated with the SIC-LSD approach with either 13 (squares) or 14 (circles) localized $f$ electrons. The triangle marks the experimental equilibrium volume.

Figure 7

SIC-LSD density of states (DOS) for ${\text{YbAl}}_3$ (units are states per formula unit and per eV). The Fermi energy is at zero energy. The full line is the total DOS, while the dashed line gives the $\text{Yb}f$ projected DOS. The inset shows the region close to the Fermi level, where the partial occupation of the $f$ resonance is evident. With pressure this resonance moves upward in energy with respect to the Al bands with an ensuing gradual depletion; i.e., Yb approaches the trivalent configuration.