Multistage development of short-range spin correlations and weak magnetic order in the two coupled trillium lattices of K2Fe2(MoO4)(PO4)2

Abstract

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 ($\mu$SR) of K$_{2}$Fe$_{2}$(MoO$_{4}$)(PO$_{4}$)$_{2}$ single crystals. Magnetization measurements reveal strong antiferromagnetic interactions coexisting with weak magnetic order at $T_{\rm N} = 5.2$~K, as evidenced by a $\lambda$-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 $T_{\rm N}$. Above $T_{\rm N}$, two distinct developments of short-range spin correlations are identified at $T_{\rm H} = 34$~K and $T_{\rm L} = 10$~K, supported by magnetic specific heat anomalies and the temperature dependence of the ESR linewidth and $g$-factor. Upon cooling below $T_{\rm N}$, 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, $\mu$SR experiments reveal dynamically fluctuating spins persisting even in the ordered state. Moreover, the suppression of $T_{\rm N}$ under applied magnetic fields ($\mu_{0}H \geq 2$~T) suggests that K$_{2}$Fe$_{2}$(MoO$_{4}$)(PO$_{4}$)$_{2}$ constitutes a promising candidate for exploring field-induced spin-liquid behavior in three-dimensionally coupled trillium lattices.