Silver(II) compounds exhibit powerful oxidizing properties and strong magnetic superexchange. AgSO4 is a rare fluorine-free salt of Ag(II) which found some application in organic chemistry. Here, we report a discovery of a new AgSO4 polymorph (\b{eta}). The distinct nature of the two polytypes of AgSO4 is established using powder x-ray diffraction, vibrational spectroscopy and theoretical calculations. The \b{eta} polymorph crystallizes in the monoclinic system (P21/n) and shows structural similarities with CuSO4. DFT calculations indicate very small differences in the energy of the two polymorphs AgSO4, but the relative stability of the \b{eta} polymorph should increase with temperature. The monoclinic distortion of the orthorhombic CuSO4 prototype originates from an unprecedented strong antiferromagnetic interaction between Ag sites along the unit cell diagonal.

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