Ground state selection in XY pyrochlore antiferromagnets R$_{2}$Ge$_{2}$O$_{7}$ (R = Er, Yb)

Elastic neutron scattering, ac susceptibility, and specific heat experiments on the pyrochlores Er$_{2}$Ge$_{2}$O$_{7}$ and Yb$_{2}$Ge$_{2}$O$_{7}$ show that both systems are antiferromagnetically ordered in the $\Gamma_5$ manifold. The ground state is a $\psi_{3}$ phase for the Er sample and a $\psi_{2}$ or $\psi_{3}$ phase for the Yb sample, which suggests "Order by Disorder"(ObD) physics. Furthermore, we unify the various magnetic ground states of all known R$_{2}$B$_{2}$O$_{7}$ (R = Er, Yb, B = Sn, Ti, Ge) compounds through the enlarged XY type exchange interaction $J_{\pm}$ under chemical pressure. The mechanism for this evolution is discussed in terms of the phase diagram proposed in the theoretical study [Wong et al., Phys. Rev. B 88, 144402, (2013)].