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-YbAlB4 in a wide temperature range from 0.02 to 320K 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 vertical bar B-c vertical bar < 0.2mT. 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-YbAlB4. In addition, the heavy Fermi-liquid component is suppressed in the magnetic field above similar to 5T as in alpha-YbAlB4. This was also confirmed by the magnetization measurements up to similar to 50 T for both alpha- and beta-YbAlB4. 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 beta-YbAlB4 to illustrate how the characteristic temperature and field scales evolves near the QC.