From Approximate Floquet Engineering to Full Floquet Theory: Coherent Control of Chiral Spin Systems in Spintronics

Coherent control of interacting spin systems under time-periodic driving is a central challenge in spin-based quantum technologies. Here we demonstrate the applicability of a full Floquet-space formalism, adapted from Nuclear Magnetic Resonance (NMR) methodologies, to model the dynamics of driven coupled electron spins in the presence of a static magnetic field B0 and a transverse oscillating field B1. The framework explicitly includes isotropic exchange coupling J and the chiral Dzyaloshinskii-Moriya antisymmetric exchange interaction (DMI), and its numerical convergence is systematically validated with respect to Fourier-space truncation. In the non-interacting limit, the expected driven-spin dynamics is recovered, with the oscillation periodicity governed by B1. Exchange coupling alone does not modify the collective spin expectation values under the chosen initial condition, consistent with symmetry considerations. In contrast, increasing DMI generates a finite expectation value of Sy, suppresses the expectation value of Sz, and produces tilted, elliptical Bloch-sphere trajectories, reflecting the emergence of chiral spin-spin correlations. These effects are pronounced for open boundary conditions, while remaining nearly negligible in the periodic boundary case. When exchange coupling and DMI coexist, the dynamics becomes strongly perturbed and multi-frequency in nature. Together, these results demonstrate that full Floquet-space modeling provides a robust and predictive framework for analyzing and engineering coherent dynamics in driven interacting spin systems beyond simple coherent-rotation regimes.