Search for magnetic long-range order in a spin-liquid candidate K2Ti2(PO4)3

Quantum spin liquids (QSLs), lacking long-range magnetic order (LRO) due to quantum fluctuations, are pursued in frustrated systems. Recent studies highlight 3D trillium lattices, e.g., K₂Ni₂(SO₄)₃, showing dynamic ground states despite weak order. We present K₂Ti₂(PO₄)₃, a langbeinite with Ti³⁺ (S=1/2) on a single trillium lattice—structurally akin to MnSi but localized. Contrary to theory, magnetization shows no LRO down to 0.3 K, with antiferromagnetic correlations (θ ≈ -30 K). AC susceptibility reveals a 0.2 K maximum, while zero-field μSR confirms a dynamic ground state at 30 mK, persisting under 2 T. These findings challenge single-trillium frustration models. We propose neutron diffraction on K₂Ti₂(PO₄)₃ powders (100 mK, WISH) to detect magnetic Bragg peaks or diffuse scattering. Prior work on K₂Ni₂(SO₄)₃ showed WISH’s sensitivity to subtle order (e.g., tripled magnetic cells) despite μSR dynamics. Measurements at 100 mK (~4h) and temperature scans (20 mK steps) will resolve structural/magnetic symmetry. Detecting order would challenge QSL criteria; absence strengthens 3D QSL evidence. This study bridges theory-experiment gaps in quantum magnetism. We request 2 days on WISH (cooldown included) to decode this S=1/2 trillium system’s ground state.