  The ground state phase diagram is determined exactly for the frustrated
classical Heisenberg model plus nearest-neighbor biquadratic exchange
interactions on a 2-dimensional lattice. A square- and a rhombic-symmetry
version are considered. There appear ferromagnetic, incommensurate-spiral,
"up-up-down-down" (uudd) and canted ferromagnetic states, a non-spiral coplanar
state that is an ordered vortex lattice, plus a non-coplanar ordered state (a
"conical vortex lattice"). In the rhombic case, which adds biquadratic terms to
the Heisenberg model used widely for insulating manganites, the uudd state
found is the E-type state observed; this along with accounting essentially for
the variety of ground states found in these materials, shows that this model
probably contains the long-sought mechanism behind the uudd state.
