The single-ion anisotropy in LaFeAsO

We use Green's function method to study the Heisenberg model of LaFeAsO with the striped antiferromagnetic collinear spin structure. In addition to the intra-layer spin couplings $J_{1a},J_{1b},J_2$ and the inter-layer coupling $J_c$, we further consider the contributions of the single-ion anisotropy $J_s$. The analytical expressions for the magnetic phase-transition temperature $T_N$ and the spin spectrum gap $\Delta$ are obtained. According to the experimental temperature $T_N=138$K and the previous estimations of the coupling interactions, we make a further discussion about the magnitude and the effects of the single-ion anisotropy $J_s$. We find that the magnitudes of $J_s$ and $J_c$ can compete. The dependences of the transition temperature $T_N$, the zero-temperature average spin and the spin spectrum gap on the single-ion anisotropy are investigated. We find they both increase as $J_s$ increases. The spin spectrum gap at low temperature $T\to0$ is calculated as a function of $J_s$, the result of which is a useful reference for the future experimental researches.