Magnetic states in frustrated bilayer models: The ordered phase of mixed-layer pnictide oxides

We present results from a numerical investigation of bilayer classical spin systems with local interactions and frustration caused by lattice geometry. We find that when two identical square planes are displaced by half a lattice constant in one direction, a transition to a uniformly twisted spin state occurs at J/J_⊥>~0.25. An orthogonal state between layers is obtained in the limit T=0 and J_⊥=0. If instead the two layers are offset along a diagonal, we obtain the phase diagram of the classical J₁-J₂ model. A weakly canted phase is observed at the classical transition point of J/J_⊥=0.5, but frustration does not drive the system towards a state of orthogonal interlayer order. We propose a simple bilayer model with two inequivalent square lattices to study the frustrating interactions of the mixed layer pnictide oxides (Sr₂Mn₃Pn₂O₂, Pn=As,Sb). We find a ground state composed of two independent Néel ordered layers when the interlayer exchange is an order of magnitude weaker than the intralayer exchange, as suggested by experiment. Evidence for local orthogonal order between the layers is found, but it occurs in regions of parameter space which are not experimentally realized.