Spin-liquid regime in a single-trillium S=1/2 langbeinite K2Ti2(PO4)3

Quantum spin liquids (QSLs), marked by the absence of long-range magnetic order (LRO) due to quantum fluctuations, are explored in geometrically frustrated systems. Recent studies highlight materials like K₂Ni₂(SO₄)₃, with interconnected trillium lattices, which show dynamic ground states despite weak Bragg peaks. However, S=1/2 systems on single trillium lattices remain underexplored. We present K₂Ti₂(PO₄)₃, a langbeinite with Ti³⁺ (S=1/2) on a single trillium lattice—analogous to MnSi but with localized moments. Magnetization data show no LRO down to 0.3 K, consistent with antiferromagnetic interactions (Curie-Weiss θ ≈ -30 K). AC susceptibility reveals a broad maximum near 0.2 K, while zero-field muon spin relaxation (μSR) down to 30 mK confirms a dynamic ground state without static order, persisting under 2 T fields. This contrasts double trillium systems like K₂Ni₂(SO₄)₃, where dynamics freeze near 1–2 K despite weaker frustration (θ = -18 K). To probe the link between exchange interactions (∼|θ|) and dynamics, we propose zero-field μSR across 2–300 K. Temperature-dependent relaxation rates will test if the energy scale governs dynamics, addressing why K₂Ti₂(PO₄)₃ remains dynamic below |θ|. Measurements from 2–20 K (overlapping prior data), 20–100 K (log steps), and up to 300 K will map thermal evolution. This work identifies K₂Ti₂(PO₄)₃ as a rare S=1/2 trillium candidate for QSL behavior, advancing understanding of frustration in 3D quantum magnets.