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We report that special care is needed when longitudinal magneticsusceptibility is computed in a magnetically ordered phase, especially inmetals. We demonstrate this by studying static susceptibility in both aferromagnetic and an antiferromagnetic state in the random phase approximationto the two-dimensional Hubbard model on a square lattice. In contrast to thecase in the disordered phase, a first derivative of the chemical potential (orthe density) with respect to a magnetic field does not vanish in a magneticallyordered phase when the field is applied parallel to the magnetic moment. Thiseffect is crucial and should be included when computing magnetic susceptibilityin the ordered phase, otherwise an unphysical result would be obtained. Inaddition, consequently the magnetic susceptibility becomes different whencomputed at a fixed density and a fixed chemical potential in the orderedphase. In particular, we cannot employ magnetic susceptibility at a fixedchemical potential to describe a system with a fixed density even if thechemical potential is tuned to reproduce the correct density.

Static spin susceptibility in magnetically ordered states