  A comprehensive theoretical investigation on the field-driven reorientation
transitions in uniaxial multilayers with antiferromagnetic coupling is
presented. It is based on a complete survey of the one-dimensional solutions
for the basic phenomenological (micromagnetic) model that describes the
magnetic properties of finite stacks made from ferromagnetic layers coupled
antiferromagnetically through spacer layers. The general structure of the phase
diagrams is analysed. At a high ratio of uniaxial anisotropy to
antiferromagnetic interlayer exchange, only a succession of collinear magnetic
states is possible. With increasing field first-order (metamagnetic)
transitions occur from the antiferromagnetic ground-state to a set of
degenerate ferrimagnetic states and to the saturated ferromagnetic state. At
low anisotropies, a first-order transition from the antiferromagnetic
ground-state to an inhomogeneous spin-flop state occurs. Between these two
regions, transitional magnetic phases occupy the range of intermediate
anisotropies. Detailed and quantitative phase diagrams are given for the basic
model of antiferromagnetic multilayer systems with N = 2 to 16 layers. The
connection of the phase diagrams with the spin-reorientation transitions in
bulk antiferromagnets is discussed. The limits of low anisotropy and large
numbers of layers are analysed by two different representations of the magnetic
energy, namely, in terms of finite chains of staggered vectors and in a general
continuum form. It is shown that the phenomena widely described as ``surface
spin-flop'' are driven only by the cut exchange interactions and the
non-compensated magnetic moment at the surface layers of a stacked
antiferromagnetic system.
