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We extend the Lifshitz theory of the Casimir force to the case of twoparallel magnetic metal plates possessing a spatially nonlocal dielectricresponse. By solving Maxwell equations in the configuration of anelectromagnetic wave incident on the boundary plane of a magnetic metalsemispace, the exact surface impedances are expressed in terms of its magneticpermeability and longitudinal and transverse dielectric functions. This allowsapplication of the Lifshitz theory with reflection coefficients written via thesurface impedances for calculation of the Casimir pressure between magneticmetal (Ni) plates whose dielectric responses are described by the alternativenonlocal response functions introduced for the case of nonmagnetic media. It isshown that at separations from 100 to 800~nm the Casimir pressures computedusing the alternative nonlocal and local plasma response functions differ byless than 1\%. At separations of a few micrometers, the predictions of thesetwo approaches differ between themselves and between that one obtained usingthe Drude function by several tens of percent. We also compute the gradient ofthe Casimir force between Ni-coated surfaces of a sphere and a plate using thealternative nonlocal response functions and find a very good agreement with themeasurement data. Implications of the obtained results determined by theoff-shell quantum fluctuations to a resolution of long-standing problems in theCasimir physics are discussed.

Casimir effect for magnetic media: Spatially nonlocal response to the off-shell quantum fluctuation