We present results from a Monte Carlo investigation of a simple bilayer modelwith geometrically frustrated interactions similar to those found in the mixedlayer pnictide oxides $(Sr_{2}Mn_{3}Pn_{2}O_{2}, Pn=As,Sb).$ Our model iscomposed of two inequivalent square lattices with nearest neighbor intra- andinterlayer interactions. We find a ground state composed of two independentN\'{e}el ordered layers when the interlayer exchange is an order of magnitudeweaker than the intralayer exchange, as suggested by experiment. We observethis result independent of the number of layers in our model. We find evidencefor local orthogonal order between the layers, but it occurs in regions ofparameter space that are not experimentally realized. We conclude thatfrustration caused by nearest neighbor interactions in the mixed layer pnictideoxides is not sufficient to explain the long--range orthogonal order that isobserved experimentally, and that it is likely that other terms (e.g., localanisotropies) in the Hamiltonian are required to explain the magnetic behavior.
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