Geometric frustration in the mixed layer pnictide oxides

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