Strong Valence Fluctuation in the Quantum Critical Heavy Fermion Superconductor $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$: A Hard X-Ray Photoemission Study

Electronic structures of the quantum critical superconductor $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ and its polymorph $\alpha \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ are investigated by using bulk-sensitive hard x-ray photoemission spectroscopy. From the Yb $3d$ core level spectra, the values of the Yb valence are estimated to be $\sim 2.73$ and $\sim 2.75$ for $\alpha$- and $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$, respectively, thus providing clear evidence for valence fluctuations. The valence band spectra of these compounds also show ${\mathrm{Yb}}^{2+}$ peaks at the Fermi level. These observations establish an unambiguous case of a strong mixed valence at quantum criticality for the first time among heavy fermion systems, calling for a novel scheme for a quantum critical model beyond the conventional Doniach picture in $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$.

Figure 1

HX-PES spectra of Yb $3d$ and Al $1s$ core levels in $\alpha \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ (upper) and $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ (lower).

Figure 2

Comparison of experimental spectra for Yb $3d_{5/2}$ core level with calculation in (a) $\alpha \mathrm{\text{−}}{\mathrm{YbAlB}}_4$ and (b) $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$. Experimental data and fitting results are shown as upper and middle spectra, respectively. Dashed curves represent the integral background. Lower spectra represent calculated Yb $3d_{5/2}$ multiplet lines and the broadened (shaded curves) and plasmon satellites (solid curves).

Figure 3

HX-PES spectra of the $4f^{13}$ final state in the valence band of $\alpha$- and $\beta \mathrm{\text{−}}{\mathrm{YbAlB}}_4$.