Agenda

Résumé : Amongst geometrically frustrated architectures is the hyperkagome lattice, which consists in a twisted spatial arrangement of corner-sharing triangles and which can be found in rare-earth (R) garnets R₃B₂C₃O₁₂ [1].  Mean-field calculations on a hyperkagome lattice, for an effective anisotropic pseudospin S = ½, generate a very rich magnetic phase diagram, encompassing complex disordered phases, when magnetic anisotropy departs from the strong Ising case [2].  Tuning the rare-earth magnetic anisotropy in garnets is the key to exploring this phase diagram, and can be achieved through appropriate distortions of the rare-earth oxygen environment, the latter being controlled by the B and C ionic size.  Point charge calculations further underline the potential for interesting magnetocaloric properties for given distortions of the rare-earth cage.
Several compositions belonging to the R = Dy garnets system have been studied on the basis of extensive neutron diffraction and neutron spectroscopy experiments.  Results show that a more distorted oxygen environment favours an Ising anisotropy of the Dy³⁺ moment [3]. A k = 0 multi axis antiferromagnetic ground state is observed for all compositions, except for a high level of disorder (achieved through high entropy) on the B site, whose lack of ordering still remains to be understood. 
[1] S. Geller, Z. Kristallogr. Bd. 125, S1 (1967)
[2] I. Kibalin et al, Phys. Rev. Research 2, 033509, (2020)
[3] F. Damay et al., Phys. Rev. B 109, 014419 (2024)