Short-range Spin Freezing State in the Double Trillium Lattice Spin-Liquid Candidate KSrFe$_2$(PO$_4$)$_3$ Revealed via $^{31}$P NMR

Abstract: A comprehensive $^{31}$P nuclear magnetic resonance (NMR) study, combined with thermodynamic measurements and first-principle band-structure calculations, has been conducted to explore the ground state of the $S = 5/2$ double trillium lattice antiferromagnet KSrFe$_2$(PO$_4$)$_3$. Our experimental results indicate that the magnetic ground state is neither a conventional three-dimensional (3D) long-range order (LRO) nor a pure gapless spin-liquid state, as conjectured previously [Boya et al., APL Mater. 10, 101103 (2022)]. Specifically, the observation of a nearly field-independent NMR linewidth below $T^{*}$ = (3.5 $\pm$ 0.4) K, and a significant enhancement of spin-spin relaxation rate $1/T_2$ below $2T^{*}$ (where $T^{*}$ is the characteristic temperature identified from the magnetic susceptibility), indicate a complex magnetic ground state where spin freezing coexists with persistent dynamics. Furthermore, we argue that the lack of magnetic LRO and the persistence of strong magnetic fluctuations in KSrFe$_2$(PO$_4$)$_3$ are unlikely to originate from intersite K/Sr disorder, rather arise due to intrinsic magnetic frustration. Our findings position KSrFe$_2$(PO$_4$)$_3$ into a broader family of geometrically frustrated magnets characterized by coexisting spin freezing and pronounced antiferromagnetic fluctuations, marking it as a promising platform for investigating exotic phenomena in 3D frustrated magnets.