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The coexistence of antiferromagnetism with superconductivity is studiedtheoretically within the t-J model with the Zeeman term included. The strongelectron correlations are accounted for by means of the extended Gutzwillerprojection method within a statistically-consistent approach proposed recently.The phase diagram on the band filling - magnetic field plane is shown, andsubsequently the system properties are analyzed for the fixed band fillingn=0.97. In this regime, the results reflect principal qualitative featuresobserved recently in selected heavy fermion systems. Namely, (i) with theincreasing magnetic field the system evolves from coexistingantiferromagnetic-superconducting phase, through antiferromagnetic phase,towards polarized paramagnetic state, and (ii) the onset of superconductingorder suppresses partly the staggered moment. The superconducting gap has boththe spin-singlet and the staggered-triplet components, a direct consequence ofa coexistence of the superconducting state with antiferromagnetism.

Coexistence of antiferromagnetism and superconductivity within t-J model with strong correlations and nonzero spin polarization