muSR in Ba$_{2}$CoO$_{4}$

A positive muon spin rotation and relaxation ($\mu^+$SR) experiment on the single crystal Ba$_2$CoO$_4$ indicates the existence of an antiferromagnetic (AF) transition occurring at $T_{N}\sim$25~K. Weak transverse field measurements (wTF-$\mu^+$SR) show that the paramagnetic volume fraction of the sample decreases rapidly at the magnetic transition indicating a bulk effect. Zero field measurements (ZF-$\mu^+$SR) show the presence of a magnetically ordered state below $T_{N}$. The results are compared to recent magnetic susceptibility and neutron measurements. Although there are two possible AF spin structures proposed by recent neutron experiments, the $\mu$SR results clearly exclude AF order along the $c$-axis while supporting AF order in the $ab$ plane.