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Motivated by recent neutron scattering experiments in Fe-basedsuperconductors, we study how the magnetic resonance in the superconductingstate is affected by the simultaneous presence of either static or fluctuatingmagnetic orders using the random phase approximation. We find that for theunderdoped materials with coexisting superconducting and antiferromagneticorders, spin rotational symmetry is explicitly broken at the ordering momentum$Q_1 = (\pi,0)$. Only the longitudinal susceptibility exhibits the resonancemode, whereas a spin-wave Goldstone mode develops in the transverse component.Meanwhile, at the frustrated momentum $Q_2 = (0,\pi)$, the susceptibilitybecomes isotropic in spin space and the magnetic resonance exists for bothcomponents. Furthermore, the resonance energies at $Q_1$ and $Q_2$ havedistinct scales, which provides a natural explanation for the recently observeddouble resonance peaks. In addition, we show that near optimal doping theexistence of strong magnetic fluctuations, which are modeled here via aGaussian mode, can still induce the spin anisotropy in the magneticsusceptibility.

Double magnetic resonance and spin anisotropy in Fe-based superconductors due to static and fluctuating antiferromagnetic orders