Magnetism of PdNi alloys near the critical concentration for ferromagnetism

We report results of a muon spin rotation and relaxation ($\mu$SR) study of dilute Pd${}_{1-x}$Ni${}_x$ alloys, with emphasis on Ni concentrations $x=$ 0.0243 and 0.025. These are close to the critical value $x_{\mathrm{c}\mathrm{r}}$ for the onset of ferromagnetic long-range order (LRO), which is a candidate for a quantum critical point. The 2.43 and 2.5 at.% Ni alloys exhibit similar $\mu$SR properties. Both samples are fully magnetic, with average muon local fields $⟨B^{\mathrm{l}\mathrm{o}\mathrm{c}}⟩=$ 2.0 and 3.8 mT and Curie temperatures $T_C=$ 1.0 and 2.03 K for 2.43 and 2.5 at.% Ni, respectively, at $T=0$. The temperature dependence of $⟨B^{\mathrm{l}\mathrm{o}\mathrm{c}}⟩$ suggests ordering of Ni spin clusters rather than isolated spins. Just above $T_C$ a two-phase region is found with separate volume fractions of quasistatic short-range order (SRO) and paramagnetism. The SRO fraction decreases to zero with increasing temperature a few kelvin above $T_C$. This mixture of SRO and paramagnetism is consistent with the notion of an inhomogeneous alloy with Ni clustering. The measured values of $T_C$ extrapolate to $x_{\mathrm{c}\mathrm{r}}$ = 0.0236 $\pm$ 0.0027. The dynamic muon spin relaxation in the vicinity of $T_C$ differs for the two samples: a relaxation-rate maximum at $T_C$ is observed for $x$ = 0.0243, reminiscent of critical slowing down, whereas for $x=$ 0.025 no dynamic relaxation is observed within the $\mu$SR time window. The data suggest a mean-field-like transition in this alloy.