Absence of Magnetic Order and Persistent Spin Dynamics in Tb$_2$Ge$_2$O$_7$

The terbium pyrochlores exhibit many unique magnetic properties, which has generated significant interest in this family of frustrated materials. A candidate spin liquid, Tb$_2$Ti$_2$O$_7$ fails to magnetically order, despite strong antiferromagnetic correlations. The application of external pressure has been found to produce partial antiferromagnetic order in Tb$_2$Ti$_2$O$_7$. Recently, we synthesized a new member of this family, Tb$_2$Ge$_2$O$_7$. Due to the large ionic radii decrease from titanium to germanium, Tb$_2$Ge$_2$O$_7$ can be considered a chemical pressure analog of Tb$_2$Ti$_2$O$_7$. However, neutron scattering measurements revealed an absence of magnetic order in Tb$_2$Ge$_2$O$_7$ down to 20 mK and dominant ferromagnetic correlations. Now, we have investigated the low temperature magnetism of Tb$_2$Ge$_2$O$_7$ with muon spin rotation. Our zero field $\mu$SR measurements confirm an absence of static order in Tb$_2$Ge$_2$O$_7$. We find a sharp increase in magnetic correlations below 10 K and persistent spin dynamics down to 25 mK. Our longitudinal field $\mu$SR measurements on Tb$_2$Ge$_2$O$_7$ at 25 mK are consistent with a system of fluctuating moments, with a fluctuation rate of 11 MHz. This fluctuation rate is nearly temperature independent below 2.5 K.