Diffusion of Fe atoms on W surfaces andFe∕Wfilms and along surface steps

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The diffusion of Fe atoms on clean W(100) and W(110) surfaces and along surface steps, and the diffusion of Fe adatoms and vacancies on $\mathrm{Fe}∕\mathrm{W}(100)$ and $\mathrm{Fe}∕\mathrm{W}(110)$ films has been investigated using ab initio DFT methods. Our results demonstrate that even a single Fe adatom on the W(100) surface induces locally a partial dereconstruction of the surface, leading to an activation energy for hopping diffusion of $1.2\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ which is lower on the reconstructed than on the ideal surface. On W(110) diffusion occurs by elementary jumps along close-packed directions, the calculated activation energies of $0.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ are in quantitative agreement with experimental estimates. Exchange diffusion of Fe is unfavorable on both surfaces. The investigations of adatom diffusion on $1\text{\ensuremath{-}}\mathrm{ML}$ Fe films reveal a delicate interplay between structural and magnetic effects. For nonmagnetic $\mathrm{Fe}∕\mathrm{W}(100)$ films, at low coverages (below $0.4\phantom{\rule{0.3em}{0ex}}\mathrm{ML}$) adatoms do not propagate the pseudomorphic structure, but occupy bridge instead of hollow sites. The site preference switches to the hollow at higher coverages. Correspondingly, the potential energy surface is rather smooth, leading to low activation energies for hopping diffusion of 0.4 and $0.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ for jumps to nearest- and next-nearest-neighbor sites, respectively. Exchange diffusion requires a larger activation energy of $0.7\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$. Antiferromagnetic ordering of the film completely changes the picture. The magnetic interactions around the adsorbate are necessarily frustrated, the adatom induces the formation of a ferromagnetic defect. As a consequence of the frustration, the potential energy is even flatter than for the nonmagnetic case with an activation energy of only $0.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$, leading to the prediction of faster diffusion below the N\'eel temperature of the film. Fe adatoms on $\mathrm{Fe}∕\mathrm{W}(110)$ induce a local transition from a pseudomorphic to a close-packed arrangement, the adatom is incorporated in the film forming a Fe-Fe dumbbell occupying a lattice site. Our studies are completed by the investigation of vacancy diffusion in $\mathrm{Fe}∕\mathrm{W}$ films and adatom diffusion along step edges. Vacancy diffusion requires a higher activation energy than adatom hopping, in particular in $\mathrm{Fe}∕\mathrm{W}(100)$ films. Diffusion along steps has been studied on a vicinal (110) surface with ⟨100⟩-type steps. The minimal activation energy is with $1.3\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ considerably higher than for diffusion on the terraces. Decoration of the steps with a row of Fe atoms lowers all activation energies, so that diffusion rates on terraces and along Fe-decorated steps are comparable. The implication of our results on the kinetics of film growth are discussed.