Magnetism and its coexistence with superconductivity in CaK(Fe${}_{0.949}$Ni${}_{0.051}$)${}_4$As${}_4$: muon spin rotation/relaxation studies

Abstract

The magnetic response of CaK(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 $T_{\mathrm{N}}=50.0(5)$~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 $ab-$plane and the antiferromagnetic stacking along the $c-$direction. The value of the ordered magnetic moment at $T\approx 3$ K was estimated to be $m_{\mathrm{Fe}}=0.38(11)$ ${\mu }_{\mathrm{B}}$ (${\mu }_{\mathrm{B}}$ 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 $T_{\mathrm{c}}\simeq 9$ 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 $T\to 0$ and the ratio of the transition temperatures $T_{\mathrm{c}}/T_{\mathrm{N}}$. Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density wave magnetism and superconductivity [Machida, J. Phys. Soc. Jpn. 50, 2195 (1981) and Bud'ko et al., Phys. Rev. B 98, 144520 (2018)].

15 pages, 14 figures

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