Seeing the orbital ordering in Iron-based superconductors with magnetic anisotropy

The orbital fluctuation of the conduction electrons in the Iron-based superconductors is found to contribute significantly to the magnetic response of the system. With the use of a realistic five-band model and group theoretical analysis, we have determined the orbital magnetic susceptibility in such a multi-orbital system. At $n=6.1$, the in-plane orbital magnetic susceptibility is predicted to be about 10$\mu_{\mathrm{B}}^{2}/\mathrm{eV}$, which is more than 2/3 of the observed total susceptibility around 200 K in 122 systems(of about 14$\mu_{\mathrm{B}}^{2}/\mathrm{eV}$ or $4.5\times10^{-4}\mathrm{erg}/\mathrm{G}^{2}\mathrm{mol}_{\mathrm{AS}}$\cite{Klingeler}). We find the in-plane orbital magnetic response is sensitive to the breaking of the tetragonal symmetry in the orbital space. In particular, when the observed band splitting(between the $3d_{xz}$ and the $3d_{yz}$-dominated band) is used to estimate the strength of the symmetry breaking perturbation\cite{Shen}, a 4.5% modulation in the in-plane orbital magnetic susceptibility can be produced, making the latter a useful probe of the orbital ordering in such a multi-orbital system. As a by product, the theory also explains the large anisotropy between the in-plane and the out-of-plane magnetic response observed universally in susceptibility and NMR measurements.