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In several members of the ferro-pnictides, spin density wave (SDW) ordercoexists with superconductivity over a range of dopings. In this letter westudy the anomalous magnetic Zeeman response of this coexistence state and showthat it can be used to confirm the extended s-wave gap structure as well asstructure of superconducting (SC) gap in coexisting phase. On increasing thefield, a strongly anisotropic reduction of SC gap is found. The anisotropy isdirectly connected to the gap structure of superconducting phase. The signatureof this effect in quasiparticle interference measured by STM, as well as heattransport in magnetic field is discussed. For the compounds with the nodal SCgap we show that the nodes are removed upon formation of SDW. Interestingly thesize of the generated gap in the originally nodal areas is anisotropic in theposition of the nodes over the Fermi surface in direct connection with the formof SC pairing.

physical review. b, condensed matter and materials physics

Anomalous Zeeman response in coexisting phase of superconductivity and  spin-density wave as a probe of extended $s$-wave pairing structure in  ferro-pnictide