Nonperturbative theory of magnetocrystalline anisotropy energy for wires and rings of Fe adatoms

The magnetocrystalline anisotropy energy E(anis) for free-standing chains (quantum wires) and rings of Fe adatoms N=(2,...,48) is determined using an electronic tight-binding theory. Treating spin-orbit coupling nonperturbatively, we analyze the relationship between the electronic structure of the Fe d electrons and E(anis)(n(d)), for both the chain and ring conformations. We find that E(anis)(N) is larger for wires than for rings or infinite monolayers. Generally E(anis)(n(d)) decreases in chains upon increasing N, while for rings E(anis)(n(d)) is essentially independent of N. For increasing N, E(anis)(n(d)) in rings approaches the results for free-standing monolayers. Small rings exhibit clear odd-even oscillations of E(anis)(N). Within our theoretical framework we are able to explain the experimentally observed oscillations of E(anis)(nd) during film growth with a period of one monolayer. Finally, a generalization of Hund's third rule on spin-orbit coupling to itinerant ferromagnets is proposed.