Fig. 1

Cavity magnon–polaritons. a Sketched structure of the cavity magnon–polariton system, where a YIG sphere glued on a wooden rod is inserted into a 3D rectangular cavity through a hole of 5 mm in diameter in one side of the cavity. The displacement of the YIG sphere can be adjusted along the x direction using a position adjustment stage and the static magnetic field is applied along the y direction. The cavity has two ports for both measurement and feeding microwave fields into the cavity. b Diagram of the cavity magnon–polariton system with two feedings. The total output spectrum \(\left| {S_{{\mathrm{tot}}}^ - } \right|^2\) is the sum of output spectrum \(\left| {S_1^ - } \right|^2\) from port 1 and \(\left| {S_2^ - } \right|^2\) from port 2. When the system is designed to possess PT symmetry as described by Eq. (2), there is an exceptional point. In the unbroken-symmetry regime, the total output spectrum has two coherent perfect absorption (CPA) frequencies, but no CPA occurs in the broken-symmetry regime. c Normalized microwave magnetic-field distributions of the cavity modes TE₁₀₁ and TE₁₀₂. d Variations of the microwave magnetic fields of the TE₁₀₁ and TE₁₀₂ modes along the moving path of the YIG sphere marked in c. The gray area corresponds to our experimental region, where the magnetic-field intensity of the TE₁₀₂ mode shows an approximately linear relation with the displacement of the YIG sphere and the varying slope is estimated to be 1.3 MHz/mm. e The maximal coupling of the TE₁₀₂ mode to magnon is reached at the displacement \(\left| x \right|\sim 11\) mm of the YIG sphere, with the fitted coupling strength given as 9.2 MHz