We report a detailed and comparative study of the single crystal CeCoInGa$_3$ in both experiment and theory. Resistivity measurements reveal the typical behavior of Kondo lattice with the onset temperature of coherence, $T^*approx 50,$K. The magnetic specific heat can be well fitted using a spin-fluctuation model at low temperatures, yielding a large Sommerfeld coefficient, $gammaapprox172,$mJ/mol K$^2$ at 6 K, suggesting that this is a heavy-fermion compound with a pronounced coherence effect. The magnetic susceptibility exhibits a broad field-independent peak at $T_{chi}$ and shows an obvious anisotropy within the $bc$ plane, reflecting the anisotropy of the coherence effect at high temperatures. These are compared with strongly correlated calculations combining first-principles band structure calculations and dynamical mean-field theory. Our results confirm the onset of coherence at about 50 K and reveal a similar anisotropy in the hybridization gap, pointing to a close connection between the hybridization strength of the low-temperature Fermi-liquid state and the high-temperature coherence effect.
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