Spontaneous symmetry breaking is a fundamental concept in modern physics, and fluctuations of order parameters give rise to characteristic collective excitations. In the field of superconductivity, recent advances in terahertz spectroscopy have further stimulated interest in nonequilibrium dynamics associated with collective modes.

Superconductivity and magnetism have been central topics in condensed matter physics. In general, these two phenomena are incompatible. However, in many unconventional superconductors, they are closely intertwined. In particular, their microscopic coexistence has been experimentally observed in certain cuprates, iron pnictides, and heavy-fermion compounds. In such a coexistence state, multiple order parameters are simultaneously present, and their fluctuations are inherently coupled.

In this study, we analyze an extended two-dimensional Hubbard model which describes microscopic coexistence of spin-singlet superconductivity and antiferromagnetism. Using a mean-field approximation, we determine the parameter region where the coexistence phase is stable. Then, the dynamical susceptibility is evaluated within the random phase approximation (RPA), and the dispersion relations of collective modes are obtained from its pole structure. We reveal that hybrid collective modes emerge due to mixing between antiferromagnetic spin-wave modes and the amplitude (Higgs) and phase modes of superconductivity.