We present experimental results for the heavy-electron compound CeCu$_{4}$Ga which show that it possesses short-range magnetic correlations down to a temperature of $T = 0.1$ K. Our neutron scattering data show no evidence of long-range magnetic order occurring despite a peak in the specific heat at $T^{*} =1.2$ K. Rather, magnetic diffuse scattering occurs which corresponds to short-range magnetic correlations occurring across two unit cells. The specific heat remains large as $Tsim0$ K resulting in a Sommerfeld coefficient of $gamma_{0} = 1.44(2)$ J/mol-K$^{2}$, and, below $T^{*}$, the resistivity follows $T^{2}$ behavior and the ac magnetic susceptibility becomes temperature independent. A magnetic peak centered at an energy transfer of $E_{rm{c}}=0.24(1)$ meV is seen in inelastic neutron scattering data which shifts to higher energies and broadens under a magnetic field. We discuss the coexistence of large specific heat, magnetic fluctuations, and short-range magnetic correlations at low temperatures and compare our results to those for materials possessing spin-liquid behavior.
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