Non-Hermitian cavity magnomechanics, which incorporates the magnon-photon and magnon-phonon interactions simultaneously, enables rich physical phenomena, including exceptional-point-enhanced sensing, and offers pathways toward topological transitions and nonreciprocal quantum transformation. These interactions exert a pivotal influence on the optical response of a weak probe field and pave the way for novel applications in quantum technologies. In this work we consider a yttrium-iron-garnet (YIG) sphere coupled to a microwave cavity. The magnon mode of the YIG sphere is directly excited through microwave field coupling, whereas the cavity mode is probed via a weak-field interrogation scheme. The direct interaction of a traveling field with the magnon mode induces gain in the system, thereby establishing non-Hermitian dynamics. The parity-time ($\mathcal{PT}$)-symmetric behavior of a hybrid non-Hermitian cavity magnomechanical system is designed and investigated. Eigenvalue spectrum analysis demonstrates that a third-order exceptional point (${\mathrm{EP}}_3$) emerges under tunable effective magnon-photon coupling when the traveling field is oriented at an angle of $\pi /2$ relative to the cavity's $x$ axis. The photonic spin Hall effect (PSHE) in a reflected probe field is subsequently examined in such a system. Under balanced gain and loss conditions and in the presence of effective magnon-phonon coupling, tunable effective magnon-photon coupling enables coherent control of the PSHE across the broken $\mathcal{PT}$-symmetric phase, at the ${\mathrm{EP}}_3$ and in the $\mathcal{PT}$-symmetric phase. Investigation reveals that the PSHE can be significantly enhanced or suppressed via effective magnon-photon coupling. The influence of intracavity length on the PSHE is further explored, providing an additional parameter for fine-tuning the transverse shift. These findings establish a direct correspondence between the PSHE and the underlying non-Hermitian eigenvalue spectrum. They further demonstrate that non-Hermitian cavity magnomechanical platforms provide a pathway to tunable photonic functionalities, with immediate prospects for quantum switching and precision sensing.

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• Magneto-optics
• PT-symmetry