Spin order and excitations in the collinear kagome antiferromagnet Y$_{0.5}$Fe$_3$Sn$_3$

Kagome lattices host rich magnetic, topological, and transport phenomena owing to their geometric frustration and strong spin correlations. Here we present a systematic neutron scattering study of the kagome metal Y$_{0.5}$Fe$_3$Sn$_3$, which orders into a collinear $c$-axis antiferromagnetic (AF) state below $T_N =$ 551 K. An additional anomalous Hall effect (AHE) contribution beyond the conventional magnetization-scaling response is observed well below $T_N$ under an in-plane magnetic field $\mathbf{B} \parallel ab$. Elastic neutron scattering demonstrates that the Fe moments preserve their collinear $c$-axis AF alignment down to 1.5 K at zero field. Inelastic neutron scattering reveals a distinctive Y-shape spin excitation dispersion exhibiting a two-gap structure below 10 meV, likely arising from two nondegenerate spin-wave branches. Polarized neutron measurements further show that the low-temperature spin excitations are strongly anisotropic: the in-plane component $M_{ab}$ dominates while the $c$-axis component $M_c$ is nearly absent. Upon warming, $M_c$ gradually grows markedly but remains much weaker than $M_{ab}$ even at 300 K. We propose that the unconventional AHE originates from a nonzero scalar spin chirality induced by field-driven spin canting either in the static or dynamic configurations due to gapless excitations. These findings establish the collinear AF kagome metal Y$_{0.5}$Fe$_3$Sn$_3$ as a platform for chirality-driven AHE without spontaneous spin reorientation.