Effects of the single-ion anisotropy on the striped antiferromagnetism of a frustrated Heisenberg model on a stacked square lattice

A frustrated Heisenberg model on a stacked square lattice in a striped antiferromagnetic spin order is studied by the Green's function approach. Besides the intra- and inter-layer exchange couplings, the single-ion anisotropy (Js) is also considered. The expressions of the spin spectrum gap (ΔΔ), the transition temperature (TN) and the zero-temperature average spin (〈Sz〉0〈Sz〉0) are derived analytically. Their dependences on the single-ion anisotropy are investigated. We find they are all increasing functions of Js. We make a further estimation of the magnitude of Js according to the experimental temperature TN=138K of the pure compound LaFeAsO.