Quantum size effects in competing charge and spin orderings of dangling bond wires on Si(001)

Abstract

Using spin-polarized density-functional theory calculations, we investigate the competition between charge and spin orderings in dangling-bond ͑DB͒ wires of increasing lengths fabricated on an H-terminated Si͑001͒ surface. For wires containing less than ten DBs as studied in recent experiments, we find antiferromagnetic ͑AF͒ ordering to be energetically much more favorable than charge ordering. The energy preference of AF ordering shrinks in an oscillatory way as the wire length increases and preserves its sign even for DB wires of infinite length. The oscillatory behavior can be attributed to quantum size effects as the DB electrons fill discrete quantum levels. The predicted AF ordering is in startling contrast with the prevailing picture of charge ordering due to Jahn-Teller distortion or Peierls instability for wires of finite or infinite lengths, respectively.

Antiferromagnetic ordering of dangling-bond electrons at the stepped Si(001) surface

“…We find that the NM configuration is more stable than the AFM configuration by 28 meV/DB. This result is different from our previous 22 result for the DB wire formed on the H-passivated Si(001) surface, where the AFM configuration is slightly favored over the NM configuration by 8 meV/DB. This different energetics of the NM and AFM configurations between the D B step and the H-passivated Si(001) surface may be attributed to more delocalized character of DB electrons at the D B step, as discussed below.…”

“…Okada et al 26 predicted a ferrimagnetic spin ordering in various DB networks created on an H-passivated Si(111) surface. Similarly, Lee et al 22 predicted an AFM spin ordering in DB wires fabricated on an H-passivated Si(001) surface. On the basis of these previous studies, we speculate that the delocalization of DB electrons at the D B step could be prevented by passivating the terrace with atomic H [see Figs.…”

“…22,25,26 Amanna et al 25 reported an H-induced magnetic order on the Pd(110) surface. Okada et al 26 predicted a ferrimagnetic spin ordering in various DB networks created on an H-passivated Si(111) surface.…”

“…17,22,23 To find the on-site electronelectron interactions in the DB wire [ Fig. 1(d)] formed on the D B step, we evaluate the Hubbard correlation energy U by using the constrained DFT calculations.…”

“…Thus, it is most likely that an individual DB is fully spin-polarized by an intra-atomic exchange, and such magnetic moments of S atoms are antiferromangnetically coupled with each other via the superexchange mechanism, similar to the case of the DB wires formed on the H-passivated Si(001) surface. 17,22,23 In order to see how the magnetic stability of the DB wires varies with respect to the wire length, we determine the atomic structures of finitely long DB wires within the NM, FM, and AFM configurations. Here, we consider finitely long DB wires containing up to six DBs (designated as DB-2, DB-3, DB-4, DB-5, and DB-6, respectively).…”