Influence of ${\mathrm{Dy}}^{3+}$ environment on magnetic anisotropy and magnetocaloric effect in ${\mathrm{Dy}}_3{B}_2{C}_3{\mathrm{O}}_{12}$ $(B=\mathrm{In},\mathrm{Sc},\mathrm{Te};C=\mathrm{Ga},\mathrm{Al},\mathrm{Li})$ garnets

In the framework of the general phase diagram published recently for a pseudospin $S=1/2$ on a hyperkagome network [Kibalin et al., Phys. Rev. Res. 2, 033509 (2020)], four ${\mathrm{Dy}}_3{B}_2{C}_3{\mathrm{O}}_{12}$ garnets with different species on the $B$ and $C$ sites, namely, ${\mathrm{Dy}}_3{\mathrm{Sc}}_2{\mathrm{Al}}_3{\mathrm{O}}_{12}$ (DyScAl), ${\mathrm{Dy}}_3{\mathrm{Te}}_2{\mathrm{Li}}_3{\mathrm{O}}_{12}$ (DyTeLi), ${\mathrm{Dy}}_3{\mathrm{Sc}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$ (DyScGa), and ${\mathrm{Dy}}_3{\mathrm{In}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$ (DyInGa), have been studied by neutron powder diffraction and inelastic neutron scattering, to investigate the impact of $B$ and $C$ substitutions on the ${\mathrm{Dy}}^{3+}$ dodecahedral oxygen environment and crystal field, and thus on the ${\mathrm{Dy}}^{3+}$ spin magnetic anisotropy. In the four compounds, the magnetic ground state is a multiaxis antiferromagnetic order similar to that of ${\mathrm{Dy}}_3{\mathrm{Al}}_5{\mathrm{O}}_{12}$, characterized by an ordered moment close to the theoretical maximum, $\sim 6{\mu }_{\mathrm{B}}$. The gap between the ground state and the first excited crystal electric field level varies from $\sim 3.2$ meV (DyInGa) up to 11.2 meV (DyScAl), confirming the rather strong Ising character of the ${\mathrm{Dy}}^{3+}$ moment in those garnets. For a better understanding of the impact of the distortion of the oxygen environment on the ${\mathrm{Dy}}^{3+}$ magnetic anisotropy, point-charge calculations were then performed, mapping a magnetic anisotropy diagram versus a wide range of distortions. Results show that Ising-like behaviors mostly predominate, associated with large $g_x, g_y$, or $g_z$ Landé values, whose stable area is determined by the shape of the $\mathrm{Dy}{\mathrm{O}}_8$ cage. Magnetic entropy calculations confirm that the magnetocaloric effect increases sharply near those boundaries and validate the use of dysprosium garnets for low temperature, low magnetic field adiabatic demagnetization refrigeration cryostats.