Incipient Ferromagnetism in Tb2Ge2O7: Application of Chemical Pressure to the Enigmatic Spin Liquid, Tb2Ti2O7

The origin of the spin liquid state in Tb$_2$Ti$_2$O$_7$ has challenged experimentalists and theorists alike for nearly 20 years. To improve our understanding of the exotic magnetism in Tb$_2$Ti$_2$O$_7$, we have synthesized a chemical pressure analog, Tb$_2$Ge$_2$O$_7$. Germanium substitution results in a lattice contraction and enhanced exchange interactions. We have characterized the magnetic ground state of Tb$_2$Ge$_2$O$_7$ with specific heat, ac and dc magnetic susceptibility, and polarized neutron scattering measurements. Akin to Tb$_2$Ti$_2$O$_7$, there is no long-range order in Tb$_2$Ge$_2$O$_7$ down to 20 mK. The Weiss temperature of $-$19.2(1) K, which is more negative than that of Tb$_2$Ti$_2$O$_7$, supports the picture of stronger antiferromagnetic exchange. Polarized neutron scattering of Tb$_2$Ge$_2$O$_7$ reveals that at 3.5 K liquid-like correlations dominate in this system. However, below 1 K, the liquid-like correlations give way to intense short-range ferromagnetic correlations with a length scale related to the Tb-Tb nearest neighbor distance. Despite stronger antiferromagnetic exchange, the ground state of Tb$_2$Ge$_2$O$_7$ has ferromagnetic character, in stark contrast to the pressure-induced antiferromagnetic order observed in Tb$_2$Ti$_2$O$_7$.