Non- Fermi liquid behavior and quantum criticality in UCu$_{4+x}$Al$_{8-x }$ compound

We report on experimental studies of electrical and magneto-transport on some of the compounds of UCu$_{4+x}$Al$_{8-x}$ family as a function of temperature, hydrostatic pressure, and/or magnetic field. It has been reported that UCu$_{4+x}$Al$_{8-x}$ can be tuned through a quantum critical point (QCP) using chemical pressure. UCu$_{4}$Al$_{8}$, the x=0 compound, shows antiferromagnetic transition at T$_{N} \sim $ 32 K. It has also been reported that T$_{N}$ goes to zero at x = 1.15 and because of the presence of this QCP, further increase in the chemical pressure yields heavy fermion behavior with the highest value of $\gamma $ = 800mJ/K$^{2}$-mol for x =1.75. Our studies show that for the magnetically-ordered compounds, hydrostatic pressure is found to increase the N\'{e}el temperature, whereas for the heavy fermion compounds T$_{\rho , max}$ is increased with pressure. We also report on the heat capacity measurements in temperature down to 300 mK. The heat capacity results are discussed in terms of physics of non-Fermi liquid scaling and its relation to QCP.