Disappearance of hyperscaling at low temperatures in non-Fermi-liquid ${\mathrm{CeCu}}_{5.2}{\mathrm{Ag}}_{0.8}$

Following the recently published results (down to 0.3 K) on magnetic-field induced non-Fermi-liquid behavior in polycrystalline ${\mathrm{CeCu}}_{6-x}{\mathrm{Ag}}_x$ $\mathrm{}(0.09<x<\mathrm{}1.2\mathrm{})\mathrm{}$ we present here specific heat C measurements down to $T=70\mathrm{}\mathrm{mK}$ on a ${\mathrm{CeCu}}_{5.2}{\mathrm{Ag}}_{0.8}$ single crystal. In the single crystal we find that in a critical magnetic field $B_c$ only along the magnetic easy (c) axis, where the long-range antiferromagnetic order ${(T}_N=0.7\mathrm{}\mathrm{K}$ in $B=0\mathrm{}\mathrm{T})$ is just suppressed to $T=0,$ a quantum critical point is reached with non-Fermi-liquid properties down to our lowest temperature of measurement. The lowest temperature $C/T$ data, $B\parallel c,$ for $B>\mathrm{}{B}_c$ are proportional to $1-{\mathrm{aT}}^{0.5},$ a temperature dependence proposed in the Gaussian ( weakly interacting spin fluctuations) self-consistent renormalized spin-fluctuation theory. In contrast, the data at higher temperatures—including scaling with ${B/T}^{\beta }$ of both C and magnetization as a function of B—require a non-Gaussian strongly interacting spin-fluctuation model. In order to test this apparent crossover in behavior we have examined the scaling of $C\left(B\right)\mathrm{}$ for $T<\mathrm{}0.2\mathrm{}\mathrm{K}$ and find that the high-temperature scaling with ${B/T}^{\beta }$ (“hyperscaling”) does not function at the lowest temperatures.