Scanning tunneling microscopy (STM) measurements of the step structure on natural single-crystal samples of ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(100\right)$ have been performed. Step edges are found to occur along both $\left[110\right]$ and $\left[1\overline{1}0\right]$ directions. For step heights of $4.2\pm 0.3\mathrm{\AA }$, the step edges are found to be straight, whereas for step heights of $2.1\pm 0.2\mathrm{\AA }$, alternate step edges are straight and jagged. The straight (jagged) step edges are parallel (perpendicular) to the octahedral iron rows on the upper terrace. The concepts of coordinative unsaturation and excess surface charge are used to predict which atomic geometries are likely to be most stable along step edges. Our calculations show that steps parallel to the octahedral iron rows on the upper terrace are expected to be more stable than those perpendicular to them, in agreement with our STM observations. This step stability is found to be independent of both terrace structure and step height.

• Received 6 March 2006

DOI:https://doi.org/10.1103/PhysRevB.73.235418