We measured the transverse magnetoresistivity of the mixed valence compound $alpha$-YbAlB$_4$. Two configurations were used where current was applied along [110] direction for both and magnetic field was applied along [-110] and $c$-axis. We found th
e transverse magnetoresistivity is highly anisotropic. In the weak field below 1 T, it is consistent with stronger $c$-$f$ hybridization in the $ab$ plane which was suggested from the previous zero field resistivity measurements. At the higher field above 3 T, we observed a negative transverse magnetoresistivity for the field applied along the $c$-axis. The temperature dependences of the resistivity measured at several different fields suggest the suppression of the heavy fermion behavior at the characteristic field of $sim 5.5$ T.
Fermi liquid theory, the standard theory of metals, has been challenged by a number of observations of anomalous metallic behavior found in the vicinity of a quantum phase transition. The breakdown of the Fermi liquid is accomplished by fine-tuning t
he material to a quantum critical point using a control parameter such as the magnetic field, pressure, or chemical composition. Our high precision magnetization measurements of the ultrapure f-electron based superconductor {beta}-YbAlB4 demonstrate a scaling of its free energy indicative of zero-field quantum criticality without tuning in a metal. The breakdown of Fermi-liquid behavior takes place in a mixed-valence state, in sharp contrast with other known examples of quantum critical f-electron systems that are magnetic Kondo lattice systems with integral valence.
