Quantification of local Ising magnetism in rare-earth pyrogermanates Er2Ge2O7 and Yb2Ge2O7

Recently, a local-Ising-type magnetic order was inferred from neutron diffraction of the antiferromagnetic ${\mathrm{Er}}₂{\mathrm{Ge}}₂{\mathrm{O}}₇$ (pg-ErGO) with an applied magnetic field. Here, we use neutron spectroscopy to investigate the energetics of pg-ErGO and the isostructural ${\mathrm{Yb}}₂{\mathrm{Ge}}₂{\mathrm{O}}₇$ (pg-YbGO) to evaluate the adequacy of the local-Ising description. To begin, we generate a model of the magnetic structure of pg-YbGO using neutron diffraction and find a net ferromagnetic moment. While pg-ErGO and pg-YbGO have highly symmetric crystal structures ($P{4}₁{2}₁2$ tetragonal space group 92) with only one trivalent rare-earth magnetic site, the point symmetry of the rare-earth site is low with only a single symmetry element (point group ${\mathrm{C}}₁$). For both compounds, the energy scale of the first excited state is large compared to the magnetic ordering temperature, suggesting Ising character. The ground-state Kramer's doublet of both compounds is dominated by the maximal ${m}_{\mathrm{J}}$ component. However, the low point group symmetry of the rare-earth site leads to finite mixing of all other ${m}_{\mathrm{J}}$'s, which suggests potential deviations from Ising behavior. Moreover, quasielastic scattering is observed deep in the ordered state of pg-ErGO and pg-YbGO that may be due to non-Ising behavior. The dominant magnetic interaction in both compounds is found to be magnetostatic by considering the magnetic excitations in the ordered state. From consideration of these data, the pg-YbGO is more Ising-like than pg-ErGO. Also, quantum multicritical points are anticipated with applied magnetic field in both compounds.