The magnetic phase diagram of $\mathrm{Ce}{\left({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x\right)}_2{\mathrm{Si}}_2$ contains a spin-density-wave (SDW) magnetic ordering temperature approaching $T=0$ at both $x\approx 0.03$ and 0.35–0.4 (i.e., a dome-shaped phase boundary) and long range, local moment antiferromagnetism, $T_N=36\mathrm{K}$, in pure $\mathrm{Ce}{\mathrm{Rh}}_2{\mathrm{Si}}_2$ suppressed with Ru doping to $T=0$ at $x\approx 0.6–0.65$. This latter possible second quantum critical point (QCP), and the possible interplay between the fluctuations caused at each of the two QCP’s, are investigated here using specific heat, resistivity, and dc-magnetic susceptibility data over a broad range of composition, from $x=0.04\text{to}0.8$. One principal result is that the specific heat divided by temperature, $C∕T$, for $x=0.6$ (0.65) near $T_{\text{local}\text{moment}}\to 0$ is proportional to $\log T$ over 2 $1∕2$ decades of temperature down to the lowest temperature of measurement, 0.04 $\left(0.3\right)\mathrm{K}$, indicative of strong fluctuations near a QCP. For the region in the phase diagram $x=0.4–0.5$, i.e., near the reported $T_{\mathrm{SDW}}\to 0$ composition, $C∕T$ measured down to $0.08\mathrm{K}$ in the present work, as well as literature data, show a distinctly different behavior with temperature, a saturation in $C∕T$ which can be fit by $\gamma -a\sqrt{T}$. Such a temperature dependence is consistent with a nearby QCP with weakly interacting spin fluctuations as proposed, e.g., in the theory of Moriya. In the region between the two QCP’s, at $x=0.55$, specific heat data down to $0.1\mathrm{K}$ are not well fit by $C∕T=\gamma -a\sqrt{T}$ and are consistent with $C∕T\sim \log T$ only down to $0.6\mathrm{K}$, i.e., this composition displays intermediate behavior. The residual resistivity, ${\rho }_0$, vs $x$ shows two strong peaks, at $x=0.4$ and 0.65, consistent with the existence of two quantum critical points. The exponent $\alpha$ in $\rho ={\rho }_0+A{T}^{\alpha }$ indicates non-Fermi liquid behavior, with $\alpha$ varying monotonically—in contrast to ${\rho }_0$—from $1.5\text{to}\sim 0.9$ between $x=0.3$ and 0.65. The Fermi liquid exponent, $\alpha =2$, is recovered at $x=0.8$. These results taken together indicate two distinct quantum critical points in the phase diagram of $\mathrm{Ce}{\left({\mathrm{Ru}}_{1-x}{\mathrm{Rh}}_x\right)}_2{\mathrm{Si}}_2$, with different fluctuation strengths at $x$ $(T_{\mathrm{SDW}}\to 0)=0.4$ and $x(T_{\text{local}\text{moment}}\to 0)\approx 0.6–0.65$.

• Received 28 April 2006

DOI:https://doi.org/10.1103/PhysRevB.74.165112