Equilibrium spin configurations and their stability limits have been calculated for models of magnetic superlattices with a finite number of thin ferromagnetic layers coupled antiferromagnetically through spacers. Depending on values of applied magnetic field and uniaxial anisotropy, the system assumes collinear (antiferromagnetic, ferromagnetic, various ferrimagnetic) phases, or spatially inhomogeneous (symmetric spin-flop phase and asymmetric, canted and twisted, phases) via series of field induced continuous and discontinuous transitions. Contrary to semi-infinite systems a surface phase transition, so-called surface spin flop, does not occur in the models with a finite number of layers. It is shown that discrete jumps observed in some Fe/Cr superlattices and interpreted as surface spin flop transition are first-order volume transitions between different canted phases. Depending on the system these collinear and canted phases can co-exist as metastable states in broad ranges of the magnetic fields, which may cause severe hysteresis. The results explain magnetization processes in recent experiments on antiferromagnetic Fe/Cr and Co/Ru superlattices.
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