Nonlinearity in spin dynamics of frustrated Kagom\'e lattice system under harmonic perturbation

In this study, we investigate the spin dynamics of a frustrated Kagom\'e lattice system, focusing on the nonlinearity of spin oscillations induced by a harmonic magnetic field under varying strengths of Dzyaloshinskii-Moriya interaction (DMI), exchange field, and anisotropy energy. We have utilized Poincar\'e Surface Sections (PSS) and Power Spectra (PS) for different DMI and anisotropy energy to study the spin dynamics. Our findings reveal that when the DMI strength, external field, anisotropy, and applied magnetic field are weak, the oscillations are quasi-periodic, mostly dominated by the exchange field. With the increase in the DMI strength, the oscillation of the system becomes highly aperiodic. Strong anisotropy tends to induce periodic oscillations, but increasing DMI eventually leads to chaotic behaviour. Additionally, the external magnetic field destabilizes the periodicity of oscillations in systems with weak easy-axis anisotropy, but the systems with strong anisotropy, the oscillations remain unaffected by the external field's strength. Our analysis of magnon dispersion and magnetic resonance (MR) spectra reveals multiple resonance peaks at higher DMI strengths, indicating a complex interplay between spin wave excitation and system parameters. These results underscore the importance of understanding the inherent DMI and anisotropy in the Kagom\'e lattice during fabrication for various applications. Moreover, our comprehensive analysis of spin dynamics in a Kagom\'e lattice system demonstrates a clear transition from quasi-periodic to chaotic oscillations with the increase in DMI strength.