Anomalous Hall and Nernst effects driven by static and fluctuating spin chiralities on Kagome lattice

We theoretically investigate the anomalous Hall and Nernst effects (AHE and ANE) in a two dimensional Kagome lattice to uncover the distinct roles of static and fluctuating scalar spin chi ralities. Employing Monte Carlo simulations incorporating with a tight binding Hamiltonian via the s-d exchange interaction, we explicitly evaluate the anomalous transport coefficients. A key finding is the systematic disentanglement of the macroscopic responses into an intrinsic contribu tion, governed by momentum space Berry curvature induced by static chirality, and an extrinsic skew scattering contribution driven by real space dynamical spin fluctuations. We demonstrate a pronounced mechanistic crossover: deep in magnetically ordered phases like the skyrmion crystal, the intrinsic Berry curvature dictates the transport behavior. However, approaching the magnetic order-disorder critical regime, strong thermal fluctuations disrupt static noncoplanar spin configu rations, drastically suppressing intrinsic responses. Here, dynamical chiral fluctuations emerge as the dominant driving force. By delineating the phase regimes governed by static versus fluctuating chiralities, this work elucidates the distinct microscopic mechanisms dictating anomalous transport in frustrated magnetic systems.