  It is widely known that the magneto-optical Faraday effect is linear in
magnetization, and therefore the Faraday angles for the states with opposite
magnetizations are of opposite sign but equal in modulus. Here we demonstrate
that under certain spatial symmetry-breaking conditions, an asymmetric Faraday
effect (AFE) arises, meaning that the Faraday angles for opposite magnetic
states differ not only in sign but in absolute value as well. Experimental
investigations of AFE are performed in a one-dimensional all-garnet
magnetophotonic crystal, where AFE appears in the vicinity of the cavity
resonance for an oblique incidence of light with an inclined light polarization
plane. The magnitude of the observed asymmetry between Faraday rotations for
the two opposite magnetizations is very large and reaches 30$\%$ of the
absolute value of the Faraday effect. We confirm the generality of the
suggested effect by the numerical analysis of several different configurations
in which AFE arises. The discovered AFE is of prime importance for nanoscale
magnonics and optomagnetism.
