Ferromagnetic domains in an atomic monolayer.

We investigate the range of values of the uniaxial surface anisotropy k sub s that lead to the formation of domains in an atomic monolayer of ferromagnetically coupled spins. If f, the ratio of k sub s to the dipolar energy, is larger than a minimum value f sub (min) determined by the ratio of exchange to dipolar energy, then a domain pattern is energetically favorable compared to any uniformly magnetized configuration. The component of magnetization normal to the layer, M sub z (chi), increases continuously from zero as f increases from its threshold f sub (min) and reaches the saturation magnetization value in the flat region of the domains. A function depending on two variational parameters is assumed for M sub z (chi). We find that at threshold M sub z (chi) is simply a cosine function of chi so that there is no finite portion of the layer where the magnetization is constant.