Magnetic properties of a spin-orbit entangledJeff=12three-dimensional frustrated rare-earth hyperkagome material

The interplay between competing degrees of freedom can stabilize nontrivial magnetic states in correlated electron materials. Frustration-induced strong quantum fluctuations can evade long-range magnetic ordering, leading to exotic quantum states such as spin liquids in two-dimensional spin lattices such as triangular and kagome structures. However, experimental realization of dynamic and correlated quantum states is rare in three-dimensional (3D) frustrated magnets, wherein quantum fluctuations are less prominent. Here, we report the crystal structure, magnetic susceptibility, electron spin resonance, and specific heat studies accompanied by crystal electric field calculations on the 3D frustrated magnet ${\mathrm{Yb}}_{3}{\mathrm{Sc}}_{2}{\mathrm{Ga}}_{3}{\mathrm{O}}_{12}$. In this material, ${\mathrm{Yb}}^{3+}$ ions form a three-dimensional network of corner-sharing triangles known as a hyperkagome lattice without any detectable antisite disorder. Our thermodynamic results reveal a low-energy state with ${J}_{\mathrm{eff}}=\frac{1}{2}$ degrees of freedom in the Kramers doublet state. The zero-field-cooled and field-cooled magnetic susceptibilities taken at 0.001 T rule out the presence of spin freezing down to 1.8 K. The Curie-Weiss fit of magnetic susceptibility at low temperature yields a small and negative Curie-Weiss temperature, indicating the presence of a weak antiferromagnetic interaction between ${J}_{\mathrm{eff}}=\frac{1}{2}$ $({\mathrm{Yb}}^{3+})$ moments. The Yb-electron spin resonance displays a broad line of asymmetric shape consistent with the presence of considerable magnetic anisotropy in ${\mathrm{Yb}}_{3}{\mathrm{Sc}}_{2}{\mathrm{Ga}}_{3}{\mathrm{O}}_{12}$. The crystal electric field calculations suggest that the ground state is well separated from the excited states, which are in good agreement with experimental results. The absence of long-range magnetic ordering inferred from specific heat data indicates a dynamic liquidlike ground state at least down to 130 mK. Furthermore, zero-field specific heat shows a broad maximum around 200 mK, suggesting the presence of short-range spin correlations in this three-dimensional frustrated antiferromagnet.