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

TL;DR

This study investigates the magnetic properties of K$_2$Ni$_2$(SO$_4$)$_3$, a 3D material near a quantum spin liquid state, using experiments and theoretical models to understand its dynamical magnetic behavior.

Contribution

The paper combines neutron scattering, PFFRG, and Monte Carlo calculations to elucidate the origin of dynamical states in K$_2$Ni$_2$(SO$_4$)$_3$ and identifies an 'island of liquidity' in its exchange parameter space.

Findings

Experimental and theoretical results show high agreement in magnetic behavior.

Identification of an 'island of liquidity' around a specific magnetic network.

K$_2$Ni$_2$(SO$_4$)$_3$ can be driven into a quantum spin liquid state with a modest magnetic field.

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.