Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K 2 Fe 2 ( MoO 4 ) ( PO 4 ) 2

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Trillium lattices, where magnetic ions form a chiral network of corner-sharing triangles, offer a three-dimensional magnetic framework that can host fragile classical spin-liquid states. Herein, we report on the magnetization, specific heat, electron spin resonance (ESR), and muon spin relaxation ($μ$SR) of K₂Fe₂(MoO₄)(PO₄)₂ single crystals. Magnetization measurements reveal strong antiferromagnetic interactions coexisting with weak magnetic order at TN = 5.2~K, as evidenced by a $λ$-like anomaly observed in the magnetic susceptibility, a critical enhancement of the muon spin relaxation rate and the wipeout of the ESR signal as the temperature approaches TN. Above TN, two distinct developments of short-range spin correlations are identified at TH = 34~K and TL = 10~K, supported by magnetic specific heat anomalies and the temperature dependence of the ESR linewidth and g-factor. Upon cooling below TN, an anomaly appears at T* = 3.2~K in thermodynamic observables and the muon spin relaxation rate, indicative of spin reorientation driven by residual interactions. Despite the presence of magnetic order, $μ$SR experiments reveal dynamically fluctuating spins persisting even in the ordered state. Moreover, the suppression of TN under applied magnetic fields (μ₀H ≥ 2~T) suggests that K₂Fe₂(MoO₄)(PO₄)₂ constitutes a promising candidate for exploring field-induced spin-liquid behavior in three-dimensionally coupled trillium lattices.