Ground-states of the Shastry-Sutherland Lattice Materials Gd$_2$Be$_2$GeO$_7$ and Dy$_2$Be$_2$GeO$_7$

The recent realization that the rare-earth melilites RE$_2$Be$_2$GeO$_7$ host the Shastry-Sutherland lattice within planes of RE$^{3+}$ ions has sparked a number of studies. This family of materials lacks appreciable site mixing and conductivity, making them promising candidates for the Shastry-Sutherland model. Herein, we present the magnetic ground states of two of these rare-earth melilites: RE = Gd and Dy. We find, through measurements of magnetic susceptibility, magnetization, and specific heat capacity (RE = Dy only), that these two melilites are antiferromagnets (T$_N$ $\sim$~1~K). Gd$_2$Be$_2$GeO$_7$, in accordance with its electronic configuration, has isotropic single-ion anisotropy but shows a quadratic contribution to its magnetization. Dy$_2$Be$_2$GeO$_7$ has Ising-like single-ion ansiotropy and is likely an effective spin-$1/2$ system. Both materials exhibit metamagnetic transitions. We identify this transition in Dy$_2$Be$_2$GeO$_7$, occurring at 86(1)~mT for T=500~mK, to likely be a spin-flip transition.