Non-Hermitian spin dynamics in a coupled ferrimagnetic system

The interplay of non-Hermitian (NH) spin dynamics in coupled ferromagnetic (FM) systems has unveiled intriguing phenomena, notably the manifestation of FM-antiferromagnetic (AFM) phase transitions at exceptional points (EPs). Extending beyond traditional FM media, ferrimagnetic (FiM) media combine the advantages of AFM and FM systems, displaying distinct attributes especially at the angular momentum composition (AMC) point, ${x}_{\mathrm{AMC}}$. This study explores the profound influence of FiM composition on the NH spin dynamics of a coupled FiM system. At ${x}_{\mathrm{AMC}}$, the spin dynamics depicted by the N\'eel vector demonstrates a parity-time $(\mathcal{PT})$ symmetry, exhibiting power-law frequency splitting concerning external perturbations at the EP with a fixed power of 1/2. However, deviation from ${x}_{\mathrm{AMC}}$ leads to partial converging of eigenfrequency branches at the EP owing to the uncompensated angular momentum, displaying power-law frequency splitting with varied powers, akin to an effective coupled RLC circuit with capacitance influenced by frequency variations. This investigation opens a unique avenue in the area of $\mathcal{PT}$ symmetry in magnetic NH systems, unraveling the nuanced behaviors of coupled FiM configurations.