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Muon spin rotation and relaxation studies have been performed on a "111"family of iron-based superconductors NaFe_1-xNi_xAs. Static magnetic order wascharacterized by obtaining the temperature and doping dependences of the localordered magnetic moment size and the volume fraction of the magneticallyordered regions. For x = 0 and 0.4 %, a transition to a nearly-homogeneous longrange magnetically ordered state is observed, while for higher x than 0.4 %magnetic order becomes more disordered and is completely suppressed for x = 1.5%. The magnetic volume fraction continuously decreases with increasing x. Thecombination of magnetic and superconducting volumes implies that aspatially-overlapping coexistence of magnetism and superconductivity spans alarge region of the T-x phase diagram for NaFe_1-xNi_xAs . A strong reductionof both the ordered moment size and the volume fraction is observed below thesuperconducting T_C for x = 0.6, 1.0, and 1.3 %, in contrast to other ironpnictides in which one of these two parameters exhibits a reduction below TC,but not both. The suppression of magnetic order is further enhanced withincreased Ni doping, leading to a reentrant non-magnetic state below T_C for x= 1.3 %. The reentrant behavior indicates an interplay betweenantiferromagnetism and superconductivity involving competition for the sameelectrons. These observations are consistent with the sign-changing s-wavesuperconducting state, which is expected to appear on the verge of microscopiccoexistence and phase separation with magnetism. We also present a universallinear relationship between the local ordered moment size and theantiferromagnetic ordering temperature TN across a variety of iron-basedsuperconductors. We argue that this linear relationship is consistent with anitinerant-electron approach, in which Fermi surface nesting drivesantiferromagnetic ordering.

Disentangling superconducting and magnetic orders in NaFe_1-xNi_xAs using muon spin rotation