Field evolution of quantum critical and heavy Fermi-liquid components in   the magnetization of the mixed valence compound beta-YbAlB4
  We present the high-precision magnetization data of the valence fluctuating heavy fermion superconductor $\beta$-YbAlB$_4$ in a wide temperature range from 0.02 K to 320 K spanning four orders of magnitude. We made detailed analyses of the $T/B$ scaling of the magnetization, and firmly confirmed the unconventional zero-field quantum criticality (QC) without tuning. We examined other possible scaling relationship such as $T/(B-B_c)^{\delta}$ scaling, and confirmed that $\delta = 1$ provides the best quality of the fit with an upper bound on the critical magnetic field $\vert B_c \vert <0.2$~mT. We further discuss the heavy Fermi-liquid component of the magnetization after subtracting the QC component estimated based on the $T/B$ scaling. The temperature dependence of the heavy Fermi-liquid component is found very similar to the magnetization of the polymorph $\alpha$-YbAlB$_4$. In addition, the heavy Fermi-liquid component is suppressed in the magnetic field above $\sim$ 5 T as in $\alpha$-YbAlB$_4$. This was also confirmed by the magnetization measurements up to $\sim 50$ T for both $\alpha$- and $\beta$-YbAlB$_4$. Interestingly, the detailed analyses revealed that the only a part of $f$ electrons participates in the zero-field QC and the heavy fermion behavior. We also present a temperature - magnetic field phase diagram of \ybal to illustrate how the characteristic temperature and field scales evolves near the QC. 
Yosuke Matsumoto, K. Kuga, Y. Karaki, Y. Shimura, T. Sakakibara, M.   Tokunaga, K. Kindo, S. Nakatsuji
cond-mat.str-el