Solid oxygen is known to have spontaneous antiferromagnetic order in i
ts lowest temperature phase. Muons implanted in alpha-O-2 in zero appl
ied magnetic field take up positions where the local held is non-zero
and precess at a frequency proportional to the sublattice magnetisatio
n. The reduction of the magnetisation as the temperature increases tow
ard T-N is similar to that expected for the case of an anisotropic AFM
coupling among spins of O-2 molecules. A fit to a simple non-interact
ing, harmonic spin wave model yields an anisotropy-induced gap in the
spin wave density of states E-g/k(B) = 80.5(6) K, implying a large ani
sotropy constant K approximate to 16J.