Inhomogeneous dynamic state in the double trillium lattice antiferromagnet KBaFe$_2$(PO$_4$)$_3$

Abstract: The three-dimensional (3D) magnet KBaFe$2$(PO$_4$)$_3$ hosts a double-trillium lattice of Fe$^{3+}$ (spin, $S=5/2$) ions offering a prototypical platform to study the frustration induced effects in 3D. Through magnetization, specific heat, $^{31}$P nuclear magnetic resonance (NMR), and muon spin relaxation ($μ$SR) experiments, supported by first principles calculations, we uncover an unconventional ground state. Despite strong antiferromagnetic interactions with a large Curie-Weiss temperature $θ{\rm CW} = -70(2)$ K, no magnetic long-range order is observed down to 30 mK. Below $T^{\ast}\simeq 3.5$ K, the NMR linewidth becomes nearly field-independent and the spin-spin relaxation rate $1/T_2$ saturates, accompanied by an inhomogeneous distribution of transverse nuclear magnetization $M_{xy}$. The latter indicates the emergence of short-range dynamical correlations, which was further corroborated by a robust and field-insensitive broad maximum in specific heat. In $μ$SR, we detect neither a static internal field nor spin freezing; instead the relaxation remains dynamic and is best described by two coexisting dynamic relaxation channels: a dominant fast (sporadic) channel and a slower Markovian component. Their differing weights and fluctuation rates suggest microscopic inhomogeneity in spin dynamics. Altogether, KBaFe$_2$(PO$_4$)$_3$ exemplifies a rare high-spin stochiometric 3D antiferromagnet that evades ordering and instead fosters a mosaic of spin dynamics driven by strong geometric frustration intrinsic to the trillium lattice.