  We study the spin S=1 antiferromagnetic Heisenberg model on the square
lattice with, in addition to the nearest-neighbor interaction, a three-site
interaction of the form (S_i S_j)*(S_j S_k) + h.c.. This interaction appears
naturally in a strong coupling exansion of the two-orbital, half-filled Hubbard
model. For spin 1/2, this model reduces to a Heisenberg model with bilinear
interactions up to third neighbors, with a second-neighbor interaction twice as
large the third-neighbor one, a very frustrated model with an infinite family
of helical classical ground states in a large parameter range. Using a variety
of analytical and numerical methods, we show that the spin-1 case is also very
frustrated, and that its phase diagram is even richer, with possibly the
succession of seven different phases as a function of the ratio of the
three-site interaction to the bilinear one. The phases are either purely
magnetic phases with collinear order, or of mixed magnetic and quadrupolar
character with helical order.
