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Temperature dependent $^{57}$Fe M\"ossbauer spectroscopy and specific heatmeasurements 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 magneticorder) down to 5.5 K was detected for $x$ = 0 and 0.017 in agreement with theabsence of any additional feature below superconducting transition temperature,$T_c$, in the specific heat data. The evolution of magnetic hyperfine fieldwith temperature was studied for $x$ = 0.033 and 0.049. The long-range magneticorder in these two compounds coexists with superconductivity. The magnetichyperfine field, $B_{hf}$, (ordered magnetic moment) below $T_c$ inCaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$ is continuously suppressed with thedeveloping superconducting order parameter. The $B_{hf}(T)$ data forCaK(Fe$_{0.967}$Ni$_{0.033}$)$_4$As$_4$, andCaK(Fe$_{0.951}$Ni$_{0.049}$)$_4$As$_4$ can be described reasonably well byMachida's model for coexistence of itinerant spin density wave magnetism andsuperconductivity [K. Machida, J. Phys. Soc. Jpn. {\bf 50}, 2195 (1981)]. Wedemonstrate directly that superconductivity suppresses the spin density waveorder parameter if the conditions are right, in agreement with the theoreticalanalysis.

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