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Negative refraction, which reverses many fundamental aspects of classical optics, can be obtained in systems with negative magnetic permeability and negative dielectric permittivity. This Letter documents an experimental realization of negative refraction at millimeter waves, finite magnetic fields and cryogenic temperatures utilizing a multilayer stack of ferromagnetic and superconducting thin films. In the present case the superconducting YBa_2Cu_3O_7 layers provide negative permittivity while negative permeability is achieved via ferromagnetic (La:Sr)MnO_3 layers for frequencies and magnetic fields close to the ferromagnetic resonance. In these superlattices the refractive index can be switched between positive and negative regions using external magnetic field as tuning parameter.