Anisotropic heavy Fermi-liquid formation in the valence fluctuating $α$-YbAlB$_4$

$α$-YbAlB$_4$ is the locally isostructural polymorph of $β$-YbAlB$_4$, the first example of an Yb-based heavy fermion superconductor which exhibits pronounced non-Fermi-liquid behavior above $T_{\rm c}$. Interestingly, both $α$-YbAlB$_4$ and $β$-YbAlB$_4$ have strongly intermediate valence. Our single crystal study of the specific heat, magnetization and resistivity has confirmed the Fermi liquid ground state of $α$-YbAlB$_4$ ~in contrast with the quantum criticality observed in $β$-YbAlB$_4$. Both systems exhibit Kondo lattice behavior with the characteristic temperature scale $T^* \sim$ 8 K in addition to a valence fluctuation scale $\sim 200$ K. Below $T^*$, $α$-YbAlB$_4$ a heavy Fermi liquid state with an electronic specific heat coefficient $γ\sim$ 130 mJ/mol K$^2$ and a large Wilson ratio more than 7, which indicates ferromagnetic correlation between Yb moments. A large anisotropy in the resistivity suggests that the hybridization between 4$f$ and conduction electrons is much stronger in the $ab$-plane than along the c-axis. The strongly anisotropic hybridization as well as the large Wilson ratio is the key to understand the unusual Kondo lattice behavior and heavy fermion formation in mixed valent compounds.

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