Manipulation of the photonic spin Hall effect in a cavity magnomechanical system

In this paper, we examine the theoretical implications of photonic spin Hall effect (PSHE) amplification in a cavity magnomechanics system. In the framework of the PSHE, we show that spin-orbit interactions cause separation of space across the transverse plane between photons with opposing spins. Our findings reveal that the formation of photonic spin can be tuned across both positive and negative values, depending on the Brewster angle, while varying the magnon-phonon coupling. Notably, we find that in the absence of magnon-phonon coupling, we have magnomechanically induced transparency window at resonance and the PSHE has a higher peak value. Further in the presence of magnon-phonon coupling, the absorption peak occurs at resonance, which leads to a decrease of the PSHE. However, we observe a significant enhancement of the PSHE at two distinct detuning points where light transmission is maximized. Additionally, probe field detuning emerges as a crucial factor in controlling the PSHE. These results suggest that dynamically tuning the coupling between cavity magnons and magnon-phonon modes can greatly enhance the PSHE, presenting new opportunities for advanced nanoscale light manipulation.