Competing interactions in dysprosium garnets and generalized magnetic phase diagram of S=1/2 spins on a hyperkagome network

Abstract

The anisotropy and magnetic ground state of hyperkagome dysprosium gallium garnet Dy_{3}Ga_{5}O_{12} are investigated, along with that of its closest structural analog and archetypal Ising multiaxis antiferromagnet, dysprosium aluminum garnet Dy_{3}Al_{5}O_{12}, using a combination of neutron scattering techniques, including polarized neutron powder diffraction. Results show a dramatic change from an Ising-like anisotropy in Dy_{3}Al_{5}O_{12}, to a quasiplanar one in Dy_{3}Ga_{5}O_{12}. According to a point charge modeling, this is due to small variations of the oxygen positions surrounding Dy^{3+} ions. The magnetic ground state of Dy_{3}Ga_{5}O_{12} is investigated for the first time and is found to be similar to that of Dy_{3}Al_{5}O_{12}, yet with a much lower T_{N}. Mean-field calculations show that the dipolar interaction favors distinct magnetic ground states, depending on the anisotropy tensor: a multiaxis antiferromagnetic state is favored in the case of strong Ising-like anisotropy, like in Dy_{3}Al_{5}O_{12}, whereas a complex ferrimagnetic state is stabilized in the case of planar anisotropy. The Dy_{3}Ga_{5}O_{12} crystal field parameters locate the latter close to the boundary between those two ground states, which, alongside competition between dipolar and a small but finite magnetic exchange, may explain its low T_{N}. To widen the scope of these experimental results, we performed mean-field calculations to generate the magnetic phase diagram of an effective anisotropic pseudospin S=1/2, characterized by general g_{xx}, g_{yy}, and g_{zz} Landé factors. A very rich magnetic phase diagram, encompassing complex phases, likely disordered, is evidenced when magnetic anisotropy departs from the strong Ising case. With magnetic anisotropy being controllable through appropriate tuning of the rare-earth oxygen environment, these results emphasize the potential of rare-earth hyperkagome networks for the exploration of new magnetic phases.