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.

Scanning tunneling microscopy experiments reported that desorption from the hydrogen-and halogenterminated Si͑001͒ surfaces exhibits frequently the two types of dangling-bond ͑DB͒ configurations. One is the intradimer configuration, where two DBs are within a single Si dimer, and the other is the interdimer configuration, where two DBs are on one side of two adjacent Si dimers. Our spin-polarized density-functional-theory calculations show that the intradimer configuration is nonmagnetic with a buckled-dimer geometry, while the interdimer configuration is antiferromagnetic with two adjacent symmetric dimers. In addition, we show that when the dissociative adsorption of hydrogen molecule occurs across the ends of two adjacent dimers on a clean Si͑001͒ surface, such an antiferromagnetic coupling between two adjacent DBs still exists, thereby giving rise to a structural transformation from buckled to symmetric dimers. 0 1 J Γ J J Γ J -1 0 1 J Γ J -1 0 1 J Γ J -1 0