Enhancing One-Way Steering and Non-Classical Correlations in Magnomechanics via Coherent Feedback

In this work, we propose a theoretical scheme to explore the enhancement of quantum correlation hierarchies in a cavity magnonmechanical system via the coherent feedback tool. We use Gaussian geometric discord to quantify quantum correlations between the two magnon modes, including those beyond entanglement, in the steady state. Logarithmic negativity and Gaussian quantum steering are employed to characterize entanglement and steerability, respectively. Our results show that adjusting the beam splitter's reflective parameter can significantly enhance quantum correlations and increase their resilience to thermal noise. Moreover, we demonstrate that coherent feedback can achieve enhanced genuine tripartite entanglement among the photon, magnon $M_1$, and phonon. These findings present promising strategies for enhancing entanglement in magnon-based systems and advancing quantum information technologies. We conclude by validating the system and demonstrating its ability to detect entanglement.