The driving mechanism of the d-wave orbital order in the iron-based superconductors

We study the driving mechanism and the form of the orbital order in the electronic nematic phase of the iron-based superconductors (IBSs) within the random phase approximation of a 5-band model. We find the magnetic correlation energy of the system can be significantly improved when an orbital order of the d-wave form is spontaneously generated. On the other hand, the magnetic correlation energy increases as one introduce either an on-site or an extended s-wave orbital order. More specifically, we find that the on-site orbital order is disfavored by the Hund's rule coupling and the extended s-wave orbital order is disfavored by the stripy magnetic correlation pattern in the IBSs. Our work indicates that the orbital order and the spin nematic order in the IBSs develop in a cooperative fashion in the electronic nematic phase of the IBSs and should be both understood as a component of a composite order.