Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic mirrors

We examine the conditions of validity for the Lifshitz-Matsubara sum formula for the Casimir pressure between magnetic metallic plane mirrors. As in the previously studied case of nonmagnetic materials [Guérout et al., Phys. Rev. E 90, 042125 (2014), 10.1103/PhysRevE.90.042125], we recover the usual expression for the lossy model of optical response, but not for the lossless plasma model. We also show that the modes associated with the Foucault currents play a crucial role in the limit of vanishing losses, in contrast to expectations.