  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.
