Diverging entanglement of critical magnons in easy-axis antiferromagnets

We study the instability of antiferromagnets with easy-axis anisotropy under a magnetic field, uncovering single or even multiple phase transitions at the boundary between non-collinear and collinear spin orderings. The entanglement and number of magnons, influenced by antiferromagnetic exchange and non-collinear order, diverge at critical points, illustrating a critical phenomenon. Furthermore, our study reveals that this criticality extends to a superradiant phase transition within cavity magnonics systems, where magnon-photon coupling affects the criticality. At the transition point, cavity photon numbers diverge with infinite squeezing in the ground state. This investigation not only elucidates the criticality of multi-component squeezed magnons but also proposes cavity photon measurements as a viable method for detecting magnetic phase transitions.