Low-temperature susceptibilities of the $S=\frac{1}{2}$, simple cubic $\mathrm{XY}$ antiferromagnet [Co${\left({\mathrm{C}}_5{\mathrm{H}}_5\mathrm{N}\mathrm{O}\right)}_6$]${\left(\mathrm{N}{\mathrm{O}}_3\right)}_2$

The zero-field magnetic susceptibilities parallel and perpendicular to the trigonal axis of [Co${\left({\mathrm{C}}_5{\mathrm{H}}_5\mathrm{N}\mathrm{O}\right)}_6$]${\left(\mathrm{N}{\mathrm{O}}_3\right)}_2$ have been measured in the antiferromagnetically ordered state. The easy ($\mathrm{XY}$) plane of magnetization is found to be perpendicular to this axis. The magnetic ordering temperature is $T_c=0.432\mathrm{}\pm 0.005$ K. The data in the paramagnetic region can be well fitted by predictions for the simple cubic, $S=\frac{1}{2}$, $\mathrm{XY}$ (planar) antiferromagnet, using an exchange constant $\frac{J}{k_B}=-0.22\mathrm{}$ K. The susceptibilities in the ordered region can be explained in terms of a three-domain model, arising from a transition from trigonal to tetragonal symmetry as $T$ is lowered below $T_c$. This transition is a magnetic analog of the [111]-stress-induced trigonal to tetragonal transition in SrTi${\mathrm{O}}_3$.