Charge Fluctuations and the Valence Transition in Yb under Pressure

We present a dynamical mean-field theory study of the valence transition ($f^{14}\to f^{13}$) in elemental, metallic Yb under pressure. Our calculations reproduce the observed valence transition as reflected in the volume dependence of the $4f$ occupation. The transition is advanced by heating, and suggests quasiparticle or Kondo-like structure in the spectra of the trivalent end state, consistent with the early lanthanides. Results for the local charge fluctuations and susceptibility, however, show novel signatures uniquely associated with the valence transition itself, indicating that Yb is a fluctuating valence material in contrast with the intermediate valence behavior seen in the early trivalent lanthanides Ce, Pr, and Nd.

Figure 1

The $f$ shell occupation vs pressure at various temperatures compared to the experimental data (closed symbols, see text) and LDA (dash-dot-dot line). Open symbols are QMC data; the 630 K and 1160 K curves were obtained with CTQMC calculations, and the 1580 K curve with HFQMC at $L=80$. The consistency of HFQMC with the CTQMC data was checked by $L\to \infty$ extrapolation of the $L=80$, 112 and 160 data at 630 K. HI indicates Hubbard-I results. Inset shows the interaction $U$ vs specific volume.

Figure 2

Plot of Yb spectral function $A(\omega )$ calculated in (a) HI at $T=630\mathrm{K}$ and (b) CTQMC at $T=1160\mathrm{K}$ for selected volumes (in ${\AA }^3/\mathrm{\text{atom}}$). Dashed curves in (b) are for $j=\frac{5}{2}$; solid curves, $j=\frac{7}{2}$. Spin-orbit split peaks corresponding to the $f^{14}\to f^{13}$ excitation are near the chemical potential, while those corresponding to the $f^{13}\to f^{12}$ excitation are around $-U(V)$. An expanded view near the Fermi-level for $V=20.3{\AA }^3/\mathrm{\text{atom}}$ is shown in (c). The $j=\frac{7}{2}$ curve shows two shoulders around the large central peak.

Figure 3

(a) Equal time charge fluctuations in Yb (CTQMC), Ce, Pr, and Nd (HFQMC with $L\to \infty$ extrapolation) at 630 K. If not shown error bars are smaller than the symbol size. (b) Charge fluctuations for Yb (diamonds, the same as in left panel) compared to their imaginary-time average, $T{\chi }^{(1)}$, for Yb (closed circles) and Ce (open circles).

Figure 4

Imaginary part of the local $ff$ charge susceptibility at 630 K and specific volumes of $13.6{\AA }^3$ (black dashed line) and $29.0{\AA }^3$ (red solid line) per atom. The inset shows the corresponding imaginary-time correlation functions obtained with CTQMC.