We determine the range of values of the uniaxial surface anisotropy $K_s$ that leads to the formation of domains in an atomic monolayer of ferromagnetically coupled spins. If the ratio f of $K_s$ to the dipolar energy is larger than a minimum value $f_{\min }$ determined by the ratio of exchange to dipolar energies, and if the easy direction is normal to the layer plane, then a domain pattern is energetically favorable compared to any uniformly magnetized configuration. The maximum component of magnetization normal to the layer, $M_{\perp }$, increases continuously from zero as f increases from its threshold $f_{\min }$ and tends to the saturation magnetization value for large f. Above threshold (f=$f_{\min }$), the width of the domains is very sensitive to the value of f, increasing very rapidly with f and reaching the macroscopic value of the order of 1 cm for a value f=1.4. Contrary to the usual assumption of thin domain walls determined by the ratio of exchange to anisotropy energy, in monolayers it is necessary to treat the domain structure as a whole and to include explicitly the dipolar energy. A variational treatment gives, at the threshold of $K_s$, a simple cosine dependence on distance for the magnetization normal to the layer. The calculation is extended to layers consisting of a few atomic planes.

• Received 3 December 1987

DOI:https://doi.org/10.1103/PhysRevB.38.9145