  The entire magnetic phase diagram of the quasi two dimensional (2D) magnet on
a distorted triangular lattice KFe(MoO4)2 is outlined by means of
magnetization, specific heat, and neutron diffraction measurements. It is found
that the spin network breaks down into two almost independent magnetic
subsystems. One subsystem is a collinear antiferromagnet that shows a simple
spin-flop behavior in applied fields. The other is a helimagnet that instead
goes through a series of exotic commensurate-incommensurate phase
transformations. In the various phases one observes either true 3D order or
quasi-2D order. The experimental findings are compared to theoretical
predictions found in literature
