Europium $c$-axis ferromagnetism in $\mathrm{Eu}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_{2-y}{\mathrm{As}}_2$: A single-crystal neutron diffraction study

We report neutron diffraction results for the body-centered-tetragonal series $\mathrm{Eu}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_{2-y}{\mathrm{As}}_2, x=0.10$, 0.20, 0.42, and 0.82, $y\le 0.10$, 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 $\mathbf{ab}$-plane. For $x=0.20$ and 0.42 we find higher-temperature $c$-axis ferromagnetic (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.

Figure 1

(a) Temperature vs composition magnetic phase diagram for $\mathrm{Eu}{\left({\mathrm{Co}}_{1-x}{\mathrm{Ni}}_x\right)}_2{\mathrm{As}}_2$ from our neutron diffraction data and previously reported magnetic susceptibility data [26]. The ${\mathrm{ThCr}}_2{\mathrm{Si}}_2$-type body-centered-tetragonal chemical-unit cell with space group $I4/mmm$ and room-temperature lattice parameters of $a=3.9478\left(7\right)$ Å and $c=11.232\left(2\right)$ Å for $x=0$ [24] is also shown. (b) The component of the antiferromagnetic propagation vector $\mathit{\tau }=(0,0,{\tau }_z)$ vs composition. The $x=0$ point is from Ref. [23] and the $x=1$ point is from Ref. [27]. Dashed lines are approximate phase boundaries, and solid lines are guides for the eye. The shading illustrates the crossover between the tetragonal (Tet) and collapsed-tetragonal (cT) structures occurring between $x=0.10$ and 0.20 [26]. r.l.u. stands for reciprocal-lattice unit.

Figure 2

$(0,0,l)$ neutron diffraction patterns for a temperature $T$ above and below the Néel temperature for $x=0.10$ (a), 0.20 (b), 0.42 (c), and 0.82 (d). Lines show fits to Gaussian line shapes and an empirical background. Note that the $y$-axis scale is different for each panel and that the background for $x=0.20$ [panel (b)] is different from the other panels. This is because the $x=0.20$ sample was measured on the TRIAX instrument, whereas the other samples were measured on DEMAND.

Figure 3

Temperature dependence of the $(0,0,4-{\tau }_z)$ magnetic-Bragg peak for $x=0.10$ (a), the $(0,0,4-{\tau }_z)$ magnetic-Bragg peak for $x=0.20$ (b), the $(0,0,2+{\tau }_z)$ magnetic and (1,1,0) structural and magnetic-Bragg peaks for $x=0.42$ (c), and the $(0,0,2+{\tau }_z)$ magnetic-Bragg peak for $x=0.82$ (d). Solid lines are guides to the eye. The lower-temperature vertical-dashed lines indicate the Néel temperature $T_{\text{N}}$, and the higher-temperature vertical-dashed line for $x=0.42$ indicates the Curie temperature $T_{\text{C}}$.

Figure 4

Data from rocking scans across the (1,1,0) Bragg peak at various temperatures for (a) $x=0.10$, (b) $x=0.20$, (c) $x=0.42$, and (d) $x=0.82$. Lines are fits to Gaussian line shapes. The shapes of the peaks for $x=0.82$ are strongly influenced by absorption. Gaussian fits for these peaks are not shown as the line shapes are apparently similar within uncertainty for the different temperatures.

Figure 5

Temperature dependence of the (1,0,1) structural and magnetic-Bragg peaks for $x=0.42$.

Figure 6

The square of the calculated structure factor vs the square of the observed structure factor from the single-crystal refinements for the (a) nuclear (structural) and (b) magnetic-Bragg peaks of the $x=0.10$, 0.20, 0.42. and 0.82 compounds. The temperatures for the nuclear (magnetic) data are the same as those for the higher- (lower-) temperature data shown in Fig. 2.

Figure 7

(a) The $c$-axis helix order of the Eu magnetic moments for $x=0.10$ and 0.82. (b) The $c$-axis cone order of the Eu magnetic moments for $x=0.20$ and 0.42.