Field-induced valence fluctuations in YbB 12

We performed high-magnetic-field ultrasonic experiments on ${\mathrm{YbB}}_{12}$ up to 59 T to investigate the valence fluctuations in Yb ions. In zero field, the longitudinal elastic constant ${C}_{11}$, the transverse elastic constants ${C}_{44}$ and $\left({C}_{11}\ensuremath{-}{C}_{12}\right)/2$, and the bulk modulus ${C}_{\mathrm{B}}$ show a hardening with a change of curvature at around 35 K indicating a small contribution of valence fluctuations to the elastic constants. When high magnetic fields are applied at low temperatures, ${C}_{\mathrm{B}}$ exhibits a softening above a field-induced insulator-metal transition signaling field-induced valence fluctuations. Furthermore, at elevated temperatures, the field-induced softening of ${C}_{\mathrm{B}}$ takes place at even lower fields and ${C}_{\mathrm{B}}$ decreases continuously with field. Our analysis using the multipole susceptibility based on a two-band model reveals that the softening of ${C}_{\mathrm{B}}$ originates from the enhancement of multipole-strain interaction in addition to the decrease of the insulator energy gap. This analysis indicates that field-induced valence fluctuations of Yb cause the instability of the bulk modulus ${C}_{\mathrm{B}}$.