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

{Dy}_{3} B_{2} C_{3} O_{12}

garnets with different species on the

B

and

C

sites, namely,

{Dy}_{3} {Sc}_{2} {Al}_{3} O_{12}

(DyScAl),

{Dy}_{3} {Te}_{2} {Li}_{3} O_{12}

(DyTeLi),

{Dy}_{3} {Sc}_{2} {Ga}_{3} O_{12}

(DyScGa), and

{Dy}_{3} {In}_{2} {Ga}_{3} 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

{Dy}^{3 +}

dodecahedral oxygen environment and crystal field, and thus on the

{Dy}^{3 +}

spin magnetic anisotropy. In the four compounds, the magnetic ground state is a multiaxis antiferromagnetic order similar to that of

{Dy}_{3} {Al}_{5} O_{12}

, characterized by an ordered moment close to the theoretical maximum,

\sim 6 µ_{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

{Dy}^{3 +}

moment in those garnets. For a better understanding of the impact of the distortion of the oxygen environment on the

{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

Dy 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.

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