Frustration-induced quantum criticality in Ni-doped CePdAl as revealed by the $\mu$SR technique

In CePdAl, the 4$f$ moments of cerium arrange to form a geometrically frustrated kagome lattice. Due to frustration, in addition to Kondo- and Ruderman-Kittel-Kasuya-Yosida interactions, this metallic system shows a long-range magnetic order (LRO) with a $T_{\rm N}$ of only 2.7\,K. Upon Ni doping at the Pd sites, $T_{\rm N}$ is further suppressed, to reach zero at a critical concentration $x_c \approx 0.15$. Here, by using muon-spin relaxation and rotation ($\mu$SR), we investigate CePd${1-x}$Ni$_x$Al at a local level for five different Ni-concentrations, both above and below $x_c$. Like the parent CePdAl compound, for $x = 0.05$, we observe an incommensurate LRO, which turns into a quasi-static magnetic order for $x = 0.1$ and 0.14. More interestingly, away from $x_c$, for $x = 0.16$ and 0.18, we still observe a non-Fermi liquid regime, evidenced by a power-law divergence of the longitudinal relaxation at low temperatures. In this case, longitudinal field measurements exhibit a time-field scaling, indicative of a cooperative spin dynamics that persists for $x > x_c$. Furthermore, like the externally applied pressure, the chemical pressure induced by Ni doping suppresses the region below $T^*$, characterized by a spin-liquid like dynamical behavior. Our results suggest that the magnetic properties of CePdAl are similarly affected by the hydrostatic- and the chemical pressure. We also confirm that the unusual non-Fermi liquid regime (compared with conventional quantum critical systems) is due to the presence of frustration that persists up to the highest Ni concentrations.