We experimentally demonstrate that anti-parity-time (anti-$\mathcal{P}\mathcal{T}$) symmetry can induce a negative refractive index (NRI) in a coupled photon-magnon hybrid system. Using an analytical circuit model, we show that the non-Hermitian dynamics originating from anti-$\mathcal{P}\mathcal{T}$ symmetry give rise to antiphase propagation, reversing the phase velocity and resulting in an NRI. Furthermore, we identify cooperativity as the critical threshold parameter dictating the presence of an NRI in the anti-$\mathcal{P}\mathcal{T}$-symmetric regime. These findings provide an alternative framework for manipulating wave propagation and refractive properties in non-Hermitian hybrid quantum systems, opening avenues for advanced control of wave phenomena using magnetic materials.

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• Light-matter interaction
• Magnetic coupling
• Negative refraction
• PT-symmetric quantum mechanics
• Spintronics
• Non-Hermitian systems
• PT-symmetry