NONPERTURBATIVE THEORY OF MAGNETOCRYSTALLINE ANISOTROPY ENERGY FOR WIRES AND RINGS OF FE ADATOMS

The magnetocrystalline anisotropy energy E(anis) for free-standing cha ins (quantum wires) and rings of Fe adatoms N=(2,...,48) is determined using an electronic tight-binding theory. Treating spin-orbit couplin g nonperturbatively, we analyze the relationship between the electroni c structure of the Fe d electrons and E(anis)(n(d)), for both the chai n and ring conformations. We find that E(anis)(N) is larger for wires than for rings or infinite monolayers. Generally E(anis)(n(d)) decreas es in chains upon increasing N, while for rings E(anis)(n(d)) is essen tially independent of N. For increasing N, E(anis)(n(d)) in rings appr oaches the results for free-standing monolayers. Small rings exhibit c lear odd-even oscillations of E(anis)(N). Within our theoretical frame work we are able to explain the experimentally observed oscillations o f E(anis)(nd) during film growth with a period of one monolayer. Final ly, a generalization of Hund's third rule on spin-orbit coupling to it inerant ferromagnets is proposed.