Effectively One-Dimensional Frustrated Magnetism in Ca$_{1-x}$Sr$_{x}$Co$_{2-y}$As$_{2}$

In search of a quantum phase transition between the two-dimensional ($2$D) ferromagnetism of CaCo$_{2-y}$As$_{2}$ and stripe-type antiferromagnetism in SrCo$_{2}$As$_{2}$, we rather find evidence for $1$D magnetic frustration between magnetic square Co layers. We present neutron diffraction data for Ca$_{1-x}$Sr$_{x}$Co$_{2-y}$As$_{2}$ that reveal a sequence of $x$-dependent magnetic transitions which involve different stacking of $2$D ferromagnetically-aligned layers with different magnetic anisotropy. We explain the $x$-dependent changes to the magnetic order by utilizing classical analytical calculations of a $1$D Heisenberg model where single-ion magnetic anisotropy and frustration of antiferromagnetic nearest- and next-nearest-layer exchange are all composition dependent.