Magnetic Correlations in Yb$_{4}$LiGe$_{4}$: A $\mu $SR and $^{7}$Li NMR Study*

We present results from zero and longitudinal $\mu $SR and $^{7}$Li NMR together along with magnetization and dynamic susceptibility on the multivalent, intermetallic compound Yb$_{4}$LiGe$_{4}$. A magnetic transition at 1.4K in dynamic susceptibility is observed, corresponding to a rapid increase in the quasi-static relaxation component of the ZF MuSR spectra. The strong magnetic field dependence exhibited in these measurements demonstrates a non-trivial criticality, and suggests a close relation to the quantum critical phenomenon observed in other Yb and Ce based systems. Based on support from NMR spectra, we discuss the potential of competing low temperature phases, and the importance of the spin fluctuations in describing the observed phenomena.