J. Phys.: Condens. Matter 2 No 1 (8 January 1990) 159-185 

Magnetisation processes, hysteresis and finite-size effects in model
multilayer systems of cubic or uniaxial anisotropy with antiferromagnetic
coupling between adjacent ferromagnetic layers

B Dieny, J P Gavigan and J P Rebouillat
Lab. Louis Neel, CNRS, Grenoble, France

Abstract. Magnetisation processes have been investigated for model
multilayer systems where antiferromagnetic interactions couple adjacent
ferromagnetic layers. In this first study, only coherent
rotations of the magnetisation of each layer are taken into
account. Depending on the direction of the applied magnetic field, the
initial moment configuration and the magnetocrystalline anisotropy,
various first- or second-order magnetic transitions may be observed. The
cases of cubic and uniaxial anisotropy bilayer systems are treated in
detail. Spin-flop and spin-flip transitions are calculated
to occur for both symmetries when starting from antiferromagnetic
configurations that are parallel to the field axis. In the cubic case,
various other transitions have been found. In particular, first-order
transitions between symmetric and nonsymmetric states have been
calculated, involving asymmetric behaviour of the magnetisation vectors of
adjacent layers. Such transitions give rise to a
transverse magnetisation. All the critical transition fields have been
calculated as a function of the anisotropy and are reported in the various
phase diagrams. Hysteresis loops have also been
calculated. They generally consist of an upper and a lower part shifted
symmetrically about the origin as in the case of bulk
antiferromagnets. The influence of the number of layers has been
investigated in some particular cases. It is shown that in most instances
when the number of layers n becomes very large (i.e. when boundary effects
disappear), the multilayer behaves like a bilayer
but with different transition-field values. For small numbers of layers,
whether or not the magnetism is compensated (n even or odd) has a very
strong effect on the magnetisation processes.