${\mathrm{Ca}}_3{\mathrm{Co}}_{2-x}{\mathrm{Mn}}_x{\mathrm{O}}_6$ is a quasi-one-dimensional Ising chain magnet with a unique collinear up-up-down-down $(\uparrow \uparrow \downarrow \downarrow )$ magnetic ordering, that gives rise to ferroelectricity below the Néel temperature of 13 K. This unique long-range magnetic ordering, however, was argued to get stabilized only with Co excess (i.e., $x<1.0$) nonstoichiometric ${\mathrm{Ca}}_3{\mathrm{CoMnO}}_6$, and not so for the chemically stoichiometric compound $x=1.0$. Combining several experiments along with first-principles density-functional-based calculations, we elucidate that this unique $\uparrow \uparrow \downarrow \downarrow$ magnetic ordering can be stabilized even in the stoichiometric ${\mathrm{Ca}}_3{\mathrm{CoMnO}}_6$ (i.e., $x=1.0$) compound, albeit through the presence of optimum cationic positional disorder, where some Mn and Co ions occupy the trigonal-prismatic (Co sites for the ordered case) and octahedral (Mn-sites for the ordered one) sites respectively through relative tuning of the various magnetic exchange interactions. Specifically, the relative energy stability of the $\uparrow \uparrow \downarrow \downarrow$ magnetic order in ${\mathrm{Ca}}_3{\mathrm{CoMnO}}_6$ exhibits a nonmonotonic dependency on the extent of cationic disorder with a maximum of around 16% disorder. Thus our study helps to elucidate the mechanism that leads to stabilization of this unique functional $\uparrow \uparrow \downarrow \downarrow$ magnetic ordering in this promising class of multiferroic compounds.

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• Magnetic order
• Methods in magnetism
• Density functional calculations
• Spin chains
• X-ray absorption fine structure spectroscopy