Anomaly of longitudinal spin susceptibility at a superconducting instability inside a magnetic phase

We study the longitudinal spin susceptibility inside a magnetically ordered phase, which exhibits superconducting instability leading to coexistence of two phases. Inside magnetic gap acquires linear term in field applied along direction moment. find that such generates jump when occurs via continuous phase transition. This anomaly at is thermodynamic signature microscopic superconductivity and magnetism, can be general feature associated with breaking rotational symmetry phase.