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

Frustrated classical Heisenberg and XY models in 2 dimensions with nearest neighbor exchange: exact solution for the ground state phase diagram