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Abstract: 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.
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)