Mean field theory for cooperative magnetism in non-Kramers garnets

Kramers’ theorem entails a fundamental symmetry valid only for odd-electron systems, i.e. any eigenstate and its time-reversed counterpart belong to the same spectrum. Notwithstanding, the magnetic states of non-Kramers ions, which have even number of electrons, can be constrained because of time-reversal symmetry. Indeed, if the low-lying singlets of a crystal of such ions are well gapped from the eigenstates at higher energies, then the magnetic moments at low-temperatures can only be axially anisotropic and only magneto-striction can account for low energy fluctuations. Rare-earth garnets are a suitable playground for studying the competition of magnetic frustration, magneto-elasticity, induced magnetic ordering, and the role of nuclear moments. This talk presents our current theoretical understanding of the non-Kramers garnet Tb₃Ga₅O₁₂, benefitting from state of the art neutron scattering experiments for the crystal-field and magnetic structure – PRB,100,094442(2019). The discussion highlights the mean-field theory proposed in the 70s by Hammann & Manneville for the induced magnetic ordering found in both Tb₃Ga₅O₁₂ and Ho₃Ga₅O₁₂. We contrast our study to the work of Paddison et al. on the magnetic ordering and excitations of the non-Kramers Ho₃Ga₅O₁₂ – arXiv:1908.03530(2019).