Magnetism and its coexistence with superconductivity in CaK(Fe 0.949 Ni 0.051 ) 4 As 4 : Muon spin rotation/relaxation studies
Here, the magnetic response of Ca K ( Fe 0.949 Ni 0.051 ) 4 As 4 was investigated by means of the muon spin rotation/relaxation. The long-range commensurate magnetic order sets in below the Néel temperature T N = 50.0 ( 5 ) K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the a b plane and the antiferromagnetic stacking along the c direction. The value of the ordered magnetic moment at T ≈ 3 K was estimated to be m Fe = 0.38 ( 11 ) μ B ( μ B is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature T c ≃ 9 K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at T → 0 and the ratio of the transition temperatures T c / T N . Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density-wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. 50 , 2195 (1981) ; S. L. Bud'ko et al. , Phys. Rev. B 98 , 144520 (2018) ].