  Exchange-coupled structures consisting of ferromagnetic and ferrimagnetic
layers become technologically more and more important. We show experimentally
the occurrence of completely reversible, hysteresis-free minor loops of [Co(0.2
nm)/Ni(0.4 nm)/Pt(0.6 nm)]$_N$ multilayers exchange-coupled to a 20 nm thick
ferrimagnetic Tb$_{28}$Co$_{14}$Fe$_{58}$ layer, acting as hard magnetic
pinning layer. Furthermore, we present detailed theoretical investigations by
means of micromagnetic simulations and most important a purely analytical
derivation for the condition of the occurrence of full reversibility in
magnetization reversal. Hysteresis-free loops always occur if a domain wall is
formed during the reversal of the ferromagnetic layer and generates an
intrinsic hard-axis bias field that overcomes the magnetic anisotropy field of
the ferromagnetic layer. The derived condition further reveals that the
magnetic anisotropy and the bulk exchange of both layers, as well as the
exchange coupling strength and the thickness of the ferromagnetic layer play an
important role for its reversibility.
