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Quantum spin liquids (QSLs) have become a key area of research in magnetismdue to their remarkable properties, such as long-range entanglement, fractionalexcitations, pinch-point singularities, and topologically protected phenomena.In recent years, the search for QSLs has expanded into the three-dimensionalworld, where promising features have been found in materials that formpyrochlore and hyper-kagome lattices, despite the suppression of quantumfluctuations due to high dimensionality. One such material is the $S = 1$K$_2$Ni$_2$(SO$_4$)$_3$ compound, which belongs to the langbeinite familyconsisting of two interconnected trillium lattices. Although magneticallyordered, K$_2$Ni$_2$(SO$_4$)$_3$ has been found to exhibit a highly dynamicaland correlated state which can be driven into a pure quantum spin liquid undermagnetic fields of only $B \simeq 4$~T. In this article, we combine inelasticneutron scattering measurements with pseudo-fermion functional renormalizationgroup (PFFRG) and classical Monte Carlo (cMC) calculations to study themagnetic properties of K$_2$Ni$_2$(SO$_4$)$_3$, revealing a high level ofagreement between the experiment and theory. We further reveal the origin ofthe dynamical state in K$_2$Ni$_2$(SO$_4$)$_3$ by studying a larger set ofexchange parameters, uncovering an `island of liquidity' around a focal pointgiven by a magnetic network composed of tetrahedra on a trillium lattice.

Dynamics of K$_2$Ni$_2$(SO$_4$)$_3$ governed by proximity to a 3D spin liquid model