Field response of metallic grains with magnetic and pairing correlations

We study the field response of an isolated mesoscopic grain in the presence of pairing and magnetic interactions, both for the ferromagnetic and the antiferromagnetic spin exchange. We show that the system is characterized by different regimes of quantum-pairing correlations that are strongly modified in the presence of a spin-polarized background. The intricate behaviors of the field response result from the subtle interplay between the pairing coupling and the magnetic exchange. By examining the ground-state diagram in the entire space of interaction parameters we are able to identify several unconventional features of the field response. In the ferromagnetic case the pairing correlation is renormalized down as soon as the polarization starts to occur, thus the magnetization jumps at the interface between the paired ground state and the spin-polarized state. In the antiferromagnetic case, there exists a regime where strong pairing coexists with the polarization, so the magnetization exhibits a two-stage behavior. An abrupt change in the initial broken-pair number, when polarization sets in, is revealed when the pairing strength increases. We clarify the mechanisms underlying these unusual features of the field response and obtain various analytic results for the detailed ground-state transitions.