Europium $c$-axis ferromagnetism in Eu(Co$_{1-x}$Ni$_{x}$)$_{2-y}$As$_{2}$: A single-crystal neutron diffraction study

We report neutron diffraction results for the body-centered-tetragonal series Eu(Co$_{1-x}$Ni$_x$)$_{2-y}$As$_2$, $x=0.10$, $0.20$, $0.42$, and $0.82$, $y\leq0.10$, that detail changes to the magnetic ordering with nominal hole doping. We report the antiferromagnetic (AFM) propagation vectors, magnetic transition temperatures, and the ordered magnetic moments. We find a nonmonotonic change of the AFM propagation vector with $x$, with a minimum occurring at the tetragonal to collapsed-tetragonal phase crossover. For $x=0.10$ and $0.82$ we find $c$-axis helix ordering of the Eu magnetic moments (spins) similar to $x=0$ and $1$, with the spins oriented within the $ab$-plane. For $x=0.20$ and $0.42$ we find higher-temperature $c$-axis FM order and lower-temperature $c$-axis cone order. Using the extinction conditions for the space group, we discovered that the Eu spins are ordered in the higher-temperature $c$-axis FM phase for intermediate values of $x$, contrary to a previous report suggesting only Co/Ni spin ordering. Although we cannot directly confirm that the Co/Ni spins are also ordered, we suggest that $c$-axis itinerant-FM ordering of the Co/Ni spins could provide a molecular field that drives FM ordering of the Eu spins, which in turn provides the anisotropy for the lower-temperature $c$-axis cone order.