Magnetic properties of a spin-orbit entangled $J_{\mathrm{eff}}=\frac{1}{2}$ three-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 $J_{\mathrm{eff}}=\frac{1}{2}$ $\left({\mathrm{Yb}}^{3+}\right)$ 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.

Figure 1

Rietveld refinement of powder XRD data taken at room temperature.

Figure 2

(a) Crystal structure of ${\mathrm{Yb}}_3{\mathrm{Sc}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$. (b) Two interpenetrating hyperkagome networks of ${\mathrm{Yb}}^{3+}$ ions.

Figure 3

(a) The temperature dependence of magnetic susceptibility in different applied magnetic fields reordered in the ZFC mode. (b) The temperature dependence of zero-field-cooled and field-cooled magnetization data taken at 0.001 T. (c) Curie-Weiss fit to inverse susceptibility data taken at 0.1 T. Blue solid circles denote experimental data, whereas solid and dashed lines denote Curie-Weiss fits. The inset shows the same fit in the higher temperature range 200 $\le T\le$ 350 K. (d) Magnetic isotherms at different temperatures. Magnetization taken in ramping up and down modes remain identical, which adds further credence to the absence of spin glass physics. From the slope of the linear fit (solid red line) to high-field data taken at 1.8 K a Van Vleck contribution to susceptibility was extracted. Blue lines are Brillouin fits for $J_{\mathrm{eff}}=\frac{1}{2}$ at different temperatures.

Figure 4

ESR spectra of a polycrystalline sample of ${\mathrm{Yb}}_3{\mathrm{Sc}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$ at indicated temperatures and $X$-band frequency. $dP/dH$ denotes the first field derivative of the absorbed microwave power. The line denotes fitting of the 20 K data with a Lorentzian shape with a corresponding $g$ value of 3.6.

Figure 5

(a) Temperature dependence of specific heat (0.13 K $\le T\le 200$ K) for ${\mathrm{Yb}}_3{\mathrm{Sc}}_2{\mathrm{Ga}}_3{\mathrm{O}}_{12}$ in zero field. The nuclear Schottky contributions to the specific heat for $3\times 0.1431$ mol of ${}^{171}\mathrm{Yb}$ and 3 $\times$ 0.1613 mol of ${}^{173}\mathrm{Yb}$ are denoted by blue and pink lines, respectively. (b) Low-temperature specific heat (0.13 K $\le T\le 20$ K) in several applied magnetic fields. Corresponding Schottky fits are denoted by black solid lines. Phonon contributions were taken into account while fitting by adding the $\alpha T^3$ term indicated by the red solid line. (c) Linear behavior of the Schottky gap $\mathrm{\Delta }/k_{\mathrm{B}}$ with applied magnetic field; the solid red line is a linear fit. From the slope of the fit we found $g=3.3\left(1\right)$, and the intercept turns out to be 0.2(1) K. (d) Magnetic entropy in applied magnetic fields. Corresponding paramagnetic entropy in applied fields is denoted by red solid lines. Experimental entropy is slightly smaller than the ideal paramagnet, which suggests the existence of a small exchange interaction and/or magnetic frustration. For higher fields, it saturates at 97% of the full entropy ($Rln2$) expected for magnetic materials with $J_{\mathrm{eff}}=\frac{1}{2}$ degrees of freedom, consistent with magnetization results.

Figure 6

(a) The temperature dependence of $\chi T$ emphasizing the $\chi$ behavior at low temperatures. (b) The temperature dependence of specific heat measured in different magnetic fields. (c) Magnetization as a function of external magnetic field at several temperatures. Lines correspond to the CEF model presented in the text.