Signature of spin liquid state in a frustrated 3D antiferromagnet

Frustrated pyrochlore lattices in transition-metal oxides provide an ideal platform for realizing exotic quantum states, including spin liquids with unconventional low-energy excitations arising from the macroscopic ground-state degeneracy of corner-sharing tetrahedral networks. Here, we report the synthesis and comprehensive characterization of ZnCrGaO$4$, a frustrated three-dimensional pyrochlore-like magnet in which intrinsic cation ordering gives rise to unavoidable atomic-site disorder. A Curie--Weiss analysis of the high-temperature magnetic susceptibility yields a large negative Curie--Weiss temperature, $\theta{\mathrm{CW}} \approx -205$ K, indicating dominant antiferromagnetic exchange interactions ($J/k_{\mathrm{B}} \sim 55$ K) between Cr$^{3+}$ ($S = 3/2$) moments. Despite the presence of strong antiferromagnetic interactions, no signature of long-range magnetic ordering is observed down to 125 mK, as evidenced by specific-heat and ac-susceptibility measurements. Furthermore, the absence of bifurcation between zero-field-cooled and field-cooled dc magnetic susceptibilities measured at 0.01 T indicates the absence of spin freezing, which is further supported by the frequency-independent ac susceptibility down to 250 mK. The presence of broad maxima in the magnetic specific heat and ac susceptibility at low temperatures suggests the development of short-range spin correlations within a dynamic magnetic state. In addition, the low-temperature specific heat follows a power-law behavior below 1 K, indicating the presence of unconventional low-energy excitations and algebraic spin correlations. These results provide compelling evidence for a dynamic correlated ground state in ZnCrGaO$_4$, establishing it as a promising platform for exploring highly frustrated $S > 1/2$ three-dimensional quantum magnets and potential spin-liquid behavior.