  Photon-magnon coupling, where electromagnetic waves interact with spin waves,
and negative refraction, which bends the direction of electromagnetic waves
unnaturally, constitute critical foundations and advancements in the realms of
optics, spintronics, and quantum information technology. Here, we explore a
magnetic-field-controlled, on-off switchable, nonreciprocal negative refraction
within a non-Hermitian photon-magnon hybrid system. By integrating an yttrium
iron garnet film with an inverted split-ring resonator, we discover pronounced
negative refraction driven by the system's non-Hermitian properties. This
phenomenon exhibits unique nonreciprocal behavior dependent on the signal's
propagation direction. Our analytical model sheds light on the crucial
interplay between coherent and dissipative coupling, significantly altering
permittivity and permeability's imaginary components, crucial for negative
refraction's emergence. This work pioneers new avenues for employing negative
refraction in photon-magnon hybrid systems, signaling substantial advancements
in quantum hybrid systems.
