Coexistence of superconductivity and magnetism in CaK(Fe${}_{1-x}$Ni${}_x$)${}_4$As${}_4$ as probed by ${}^{57}$Fe Mössbauer spectroscopy

Abstract

Temperature dependent ${}^{57}$Fe Mössbauer spectroscopy and specific heat measurements for CaK(Fe${}_{1-x}$Ni${}_x$)${}_4$As${}_4$ with $x$ = 0, 0.017, 0.033, and 0.049 are presented. No magnetic hyperfine field (e.g. no static magnetic order) down to 5.5 K was detected for $x$ = 0 and 0.017 in agreement with the absence of any additional feature below superconducting transition temperature, $T_c$, in the specific heat data. The evolution of magnetic hyperfine field with temperature was studied for $x$ = 0.033 and 0.049. The long-range magnetic order in these two compounds coexists with superconductivity. The magnetic hyperfine field, $B_{hf}$, (ordered magnetic moment) below $T_c$ in CaK(Fe${}_{0.967}$Ni${}_{0.033}$)${}_4$As${}_4$ is continuously suppressed with the developing superconducting order parameter. The $B_{hf}(T)$ data for CaK(Fe${}_{0.967}$Ni${}_{0.033}$)${}_4$As${}_4$, and CaK(Fe${}_{0.951}$Ni${}_{0.049}$)${}_4$As${}_4$ can be described reasonably well by Machida's model for coexistence of itinerant spin density wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. {\bf 50}, 2195 (1981)]. We demonstrate directly that superconductivity suppresses the spin density wave order parameter if the conditions are right, in agreement with the theoretical analysis.

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