Magnetoelectric effect in superconductors with d-wave magnetization

We report on a study of the interplay between the supercurrent and spin-polarization in a two-dimensional superconducting system in the presence of a d-wave symmetric antiferromagnetic exchange interaction (altermagnetism). It is demonstrated that the supercurrent exhibits a transverse contribution in the presence of both constant and momentum-dependent exchange interactions. We also discuss the analog of the Edelstein effect for such magnetic material, showing that the induced spin polarization is quadratic in the supercurrent and d-wave symmetric.