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

Abstract

Quantum spin liquids (QSLs) have become a key area of research in magnetism due to their remarkable properties, such as long-range entanglement, fractional excitations, pinch-point singularities, and topologically protected phenomena. In recent years, the search for QSLs has expanded into the three-dimensional world, where promising features have been found in materials that form pyrochlore and hyper-kagome lattices, despite the suppression of quantum fluctuations due to high dimensionality. One such material is the $S=1$ K${}_2$Ni${}_2$(SO${}_4$)${}_3$ compound, which belongs to the langbeinite family consisting of two interconnected trillium lattices. Although magnetically ordered, K${}_2$Ni${}_2$(SO${}_4$)${}_3$ has been found to exhibit a highly dynamical and correlated state which can be driven into a pure quantum spin liquid under magnetic fields of only $B\simeq 4$~T. In this article, we combine inelastic neutron scattering measurements with pseudo-fermion functional renormalization group (PFFRG) and classical Monte Carlo (cMC) calculations to study the magnetic properties of K${}_2$Ni${}_2$(SO${}_4$)${}_3$, revealing a high level of agreement between the experiment and theory. We further reveal the origin of the dynamical state in K${}_2$Ni${}_2$(SO${}_4$)${}_3$ by studying a larger set of exchange parameters, uncovering an `island of liquidity' around a focal point given by a magnetic network composed of tetrahedra on a trillium lattice.

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• A Classical Chiral Spin-Liquid from Chiral Interactions on the Pyrochlore Lattice
• Field-induced spin liquid in the decorated square-kagome antiferromagnet nabokoite KCu${}_7$TeO${}_4$(SO${}_4$)${}_5$Cl
• Quantum effects on pyrochlore higher-rank U(1) spin liquids: Pinch-line singularities, spin nematics, and connections to oxide materials
• Short-range Spin Freezing State in the Double Trillium Lattice Spin-Liquid Candidate KSrFe${}_2$(PO${}_4$)${}_3$ Revealed via ${}^{31}$P NMR
• Coexistence of anomalous spin dynamics and weak magnetic order in a chiral trillium lattice K2FeSn(PO4)3
• Taming spin susceptibilities in frustrated quantum magnets: Mean-field form and approximate nature of the quantum-to-classical correspondence
• Frustration and chirality in three-dimensional trillium lattices: Insights and Perspectives
• High-temperature series expansion of the dynamic Matsubara spin correlator
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism
• Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2