Quantum Griffiths phase near an antiferromagnetic quantum critical point: Muon spin relaxation study of Ce(Cu1−xCox)2Ge2

Abstract

The antiferromagnetic order in the heavy-fermion compound ${\mathrm{CeCu}}_{2}{\mathrm{Ge}}_{2}$ can be suppressed by Co-doping, and at critical composition ${x}_{c}=0.6$ (${T}_{N}\phantom{\rule{0.16em}{0ex}}\ensuremath{\rightarrow}0$ K) a quantum critical point has been observed. We have performed zero-field (ZF) and longitudinal-field muon spin relaxation ($\ensuremath{\mu}\mathrm{SR}$) measurements on polycrystalline samples of $\mathrm{Ce}{({\mathrm{Cu}}_{1\ensuremath{-}x}{\mathrm{Co}}_{x})}_{2}{\mathrm{Ge}}_{2}$ ($x=0,0.2,0.6,1$) over a temperature range of 100 mK to 10 K and in applied fields from 0 up to 3000 G. Above any ordering temperature, the muon relaxation spectra can be described by a Gaussian-Kubo-Toyabe times exponential line shape. Below the magnetic ordering temperature (i.e., for $x<0.6$), an additional Gaussian relaxation is observed. The zero-field muon relaxation rate suggests the presence of antiferromagnetic ordering below 4 and 0.8 K for $x=0$ and 0.2 samples, respectively. For $x=0.6$, the magnetic order is completely suppressed, and the quantum critical point is accompanied by non-Fermi-liquid behavior, manifested in the power-law divergence of exponential depolarization, i.e., $\ensuremath{\lambda}\phantom{\rule{0.16em}{0ex}}\ensuremath{\propto}\phantom{\rule{0.16em}{0ex}}{T}^{0.55}$. The relaxation rate of $x=0.6$ obeys the time-field scaling relation ${G}_{z}(t,H)={G}_{z}(t/{H}^{\ensuremath{\gamma}})$, which is considered to be a characteristic feature of quantum critical magnetic fluctuations. Furthermore, for $x=0.6$, the exponent of isotherm magnetization, $M\ensuremath{\sim}{H}^{\ensuremath{\eta}}$, and magnetization-field-temperature scaling is consistent with the ZF-$\ensuremath{\mu}\mathrm{SR}$ data. These results provide strong evidence for the formation of a quantum Griffiths phase near the antiferromagnetic quantum phase transition.