Self-assembled alkali and alkaline earth metal nanopatterns on ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(001\right)$

We have studied the mechanism of nanopattern formation by self-assembly of impurities aggregated on the ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(001\right)$ surface. Self-assembly was controlled by thermal diffusion from the bulk of natural and artificial single crystals. We show that the diffusion of potassium and calcium is of fundamental importance to the surface dynamics of magnetite. The self-assembly of $\mathrm{Ca}$ and $\mathrm{K}$ impurities, combined with the reduction in oxygen concentration, leads to the formation of nanotrenches that can be identified as a $\mathrm{p}\left(1\times 4\right)$ structure. According to our model, the formation of nanotrenches contributes in two ways to the reduction of the surface energy. Firstly, alkali and alkaline earth impurities cause a reduction of the strain energy due to their large ionic radii. Secondly, their segregation and the reduction of the $\mathrm{O}∕\mathrm{Fe}$ ratio at the surface cause a reduction of the surface polarity. The structure of ordered nanotrenches could be used as a template for the deposition of carbon nanotubes, fullerenes, and DNA molecules.

Figure 1

Ball and stick model of the conventional unit cell of magnetite. The large gray spheres represent the oxygen anions, the small gray spheres represent the ${\mathrm{Fe}}^{3+}$ cations in tetrahedral coordination ($A$ sites) and the small black spheres stand for ${\mathrm{Fe}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ cations in octahedral coordination ($B$ sites).

Figure 2

(a) $\left(600\times 600\right){\mathrm{\AA }}^2$ STM image of an artificial ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(001\right)$ single crystal. A $\left(340\times 190\right){\mathrm{\AA }}^2$ zoom is shown. (b) $\left(300\times 200\right){\mathrm{\AA }}^2$ STM image. The atomic rows are shown in more detail. The periodicity along the [110] direction is $\sim 6\mathrm{\AA }$, and adjacent rows are separated by $\sim 18\mathrm{\AA }$.

Figure 3

(a) LEED pattern observed with a primary electron energy of $47\mathrm{eV}$. The $\mathrm{p}\left(1\times 3\right)$ reconstruction is clearly visible and is highlighted by a black rectangle. (b) AES spectrum. The potassium and calcium peaks are visible at 249 and $292\mathrm{eV}$, respectively.

Figure 4

A schematic showing the $\mathrm{p}\left(1\times 3\right)$ reconstruction due to $\mathrm{Ca}$ and $\mathrm{K}$ ions replacing $\mathrm{Fe}$ ions in octahedral coordination. The $\mathrm{p}\left(1\times 3\right)$ superlattice is marked by a dashed rectangle.

Figure 5

Dynamics of the transformation of the ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(001\right)$ surface from flat terraces to an ordered array of nanotrenches. (a) $\left(2000\times 2000\right){\mathrm{\AA }}^2$ STM image. The surface is characterized by flat terraces. (b) $\left(1000\times 1000\right){\mathrm{\AA }}^2$ STM image. Some of the trenches start to appear, as shown by the black arrows. (c) $\left(1000\times 1000\right){\mathrm{\AA }}^2$ STM image. The trenches on the surface start at one step edge to propagate along the [110] or $\left[1\overline{1}0\right]$ direction. While most of the trenches run through the full length of the terrace, some terminate in the middle of the terraces, as indicated by the white arrows. (d) $\left(1000\times 1000\right){\mathrm{\AA }}^2$ STM image. A $90°$ rotation of the trenches is observed on subsequent terraces separated by a $2.1\mathrm{\AA }$ height difference. This is consistent with the octahedrally terminated surface of magnetite.

Figure 6

Series of histograms showing the separation between trenches on the surface after 10, 17, and $65\mathrm{h}$ annealing times at $1000\mathrm{K}$. The separation decreases as the anneal time increases.

Figure 7

(a) $\left(500\times 500\right){\mathrm{\AA }}^2$ STM image. (b) $\left(1000\times 1000\right){\mathrm{\AA }}^2$ STM image. Terraces separated by an odd multiple of $2.1\mathrm{\AA }$ exhibit a $90°$ rotation of the rows that are oriented along the [110] or $\left[1\overline{1}0\right]$ direction. The periodicity of the rows ranges between 24 and $26\mathrm{\AA }$. A $\mathrm{MnNi}$ tip was used to scan the surface. (c) $\left(2000\times 2000\right){\mathrm{\AA }}^2$ STM image of a natural crystal of magnetite displayed in derivative mode. (d) $\left(500\times 500\right){\mathrm{\AA }}^2$ STM image of a natural crystal of magnetite. The step height between the two terraces is $2.1\pm 0.2\mathrm{\AA }$ along the $z$ direction. An $\mathrm{Fe}$ tip was used to scan the surface.

Figure 8

Auger spectra corresponding to the first (a), second (b), and fourth annealing cycle (c). The potassium and calcium peaks are visible at 249 and $292\mathrm{eV}$, respectively. (d) indicates the change in the $\mathrm{K}$ and $\mathrm{Ca}$ concentrations after the four annealing cycles.

Figure 9

First annealing cycle: LEED pattern observed with a primary electron energy of $93\mathrm{eV}$. Satellite spots are visible around the primary spots along the [110] and $\left[1\overline{1}0\right]$ directions. Faint spots corresponding to a $\left(\sqrt{2}\times \sqrt{2}\right)R45°$ reconstruction are indicated by white arrows. (b) Schematic of the $\mathrm{p}\left(1\times 4\right)$ reconstruction. (c) Second annealing cycle: LEED pattern observed with a primary electron energy of $93\mathrm{eV}$. Satellite spots are still visible around the primary spots, but some of them form streaked lines along the [110] and $\left[1\overline{1}0\right]$ directions. The $\left(\sqrt{2}\times \sqrt{2}\right)R45°$ mesh is now clearly visible. (d) Fourth annealing cycle: LEED pattern observed with a primary electron energy of $66\mathrm{eV}$. No superlattice is visible on the surface.

Figure 10

(a) $\left(2000\times 2000\right){\mathrm{\AA }}^2$ STM image of an artificial ${\mathrm{Fe}}_3{\mathrm{O}}_4\left(001\right)$ single crystal after the first annealing cycle. (b) $\left(400\times 400\right){\mathrm{\AA }}^2$ STM image. Two terraces separated by $2.1\pm 0.2\mathrm{\AA }$ along the $z$ direction are visible; the rows on the two terraces are rotated by $90°$ with respect to each other. All images were acquired at a sample bias of $1.0\mathrm{V}$ and a tunneling current of $0.1\mathrm{nA}$ using a $\mathrm{W}$ tip.

Figure 11

(a) $\left(700\times 750\right){\mathrm{\AA }}^2$ STM image taken after the second annealing cycle. Terraces labeled as “$B$” correspond to octahedral planes and are characterized by rows running along the [110] direction, while terraces labeled as “$A$” correspond to tetrahedral planes and are flat. The step height between terraces $B$ and $A$ is $\sim 1\mathrm{\AA }$. The step height between $B$ terraces is $4.2\pm 0.4\mathrm{\AA }$. (b) Line profile showing a $\sim 1\mathrm{\AA }$ step height between terraces $B$ and $A$.

Figure 12

(a) Surface after the third annealing cycle: $\left(2000\times 2000\right){\mathrm{\AA }}^2$ STM image. Terrace edges have become rough and the rows are no longer visible. (b) Surface after the fourth annealing cycle: $\left(2000\times 2000\right){\mathrm{\AA }}^2$ STM image. The terrace definition is almost completely lost. A $\mathrm{p}\left(1\times 1\right)$ LEED pattern [see Fig. 9d] was observed.

Figure 13

A schematic of the $\mathrm{p}\left(1\times 4\right)$ reconstruction. Oxygen vacancies are created at the surface by the extended anneal.