Growth and morphology of thin Fe films on flat and vicinal Au(111): a comparative study

The epitaxial growth of Fe on flat and vicinal Au(111) was investigated with scanning tunneling microscopy (STM) and low-energy electron diffraction (LEED) in a comparative study. Below a critical film thickness we found a pseudomorphic growth behavior of Fe on flat and vicinal Au(111). Above the critical Fe overlayer thickness a phase transition from fcc(111) to bcc(110) occurs on both surfaces. As a result of this phase transition rectangular-shaped crystallites are formed on the surface. The predominant orientation of the crystallites is along all directions for Fe on flat Au(111). For Fe on vicinal Au(111), we observed that no crystallites are orientated along the step edges. For Fe on flat Au(111), we found that the phase transition starts at a higher Fe overlayer thickness but a lower Fe coverage is required before the transition is completed in comparison with Fe on vicinal Au(111). Our results obtained with STM and LEED allow us to directly link the growth directions of the bcc(110) crystallites with twofold symmetry to the crystallographic directions of the substrate surface with hexagonal symmetry.

3 than for vicinal Cu(111) of comparable terrace width [11,12]. This reflects a strong repulsive step-step interaction, probably resulting from the reconstruction.
As mentioned above, the system Fe on flat Au(111) has been studied to a great extent. The main interest was the exploration of the magnetic properties of fcc Fe which differ from the bcc bulk properties. Especially, the strong out-of-plane anisotropy of fcc Fe was considered interesting for magnetic data storage and retrieval. For the fabrication of one-dimensional (1D) magnetic nanostructures, the vicinal Au(111) surfaces are promising templates due to the stepflow like growth behavior reported for Fe on Au(788) [7].
In principle, any vicinal surface can serve as a template for growing nanostructures [13], but with vicinal Au(111) a surface with extraordinarily regular terraces is at hand. This is an important requirement for the creation of a regular array of nanostructures. Wide terraces are favorable in order to grow wide detached stripes to overcome the superparamagnetic limit at a given temperature. Due to the particular interest in wide terraces, we performed our growth study on a vicinal Au(111) surface with even wider terraces than on Au(788). We characterized both the early growth behavior and the growth behavior of thicker films on this surface. This paper is organized as follows: experimental details are given in section 2. Section 3.1 presents our results concerning the early growth behavior of Fe on flat and vicinal Au(111). Section 3.2 deals with the phase transition from fcc(111) to bcc(110). The phase transition was monitored with STM. In analogy to studies of the phase transitions of Fe on flat Cu(111) [14], we explain the observed differences in the growth behavior for Fe on flat and vicinal Au(111) beyond the phase transition with the fitting of the rectangular bcc(110) unit cells onto the hexagonal substrate surface. Low-energy electron diffraction (LEED) measurements are employed to verify the structural model.

Experiment
The experiments were performed in an ultrahigh-vacuum (UHV) multifunction apparatus with a base pressure of less than 3 × 10 −11 mbar. Details of the experimental setup are given in [15].
The flat Au(111) crystal was cleaned by Ar + -ion bombardment with an energy of 600 eV and subsequent annealing to 1000 K. The sputtering and annealing cycles were repeated until no contamination could be detected with Auger electron spectroscopy (AES) within the detection limit of 1-5% of a monolayer (ML) depending on the impurity. At this point the STM and LEED measurements revealed the typical herringbone surface reconstruction of an Au(111) surface [9,10]. STM revealed that the width of the terraces is larger than 200 nm. An STM measurement of the clean Au(111) surface is shown in figure 1.
The vicinal Au(111) crystal was cleaned by Ar + -ion bombardment with an energy of 600 eV and subsequent annealing to 815 K. We used a lower annealing temperature than in the case of the flat Au(111) surface to avoid the risk of destroying the regular step array. The sputtering and annealing cycles were repeated until no contamination was detectable with AES. The LEED pattern exhibits the characteristic splitting of the diffraction spots: the spot splitting perpendicular to the steps is caused by the miscut angle of the vicinal surface. The spot splitting along the steps is caused by the surface reconstruction [8]. The reconstructed vicinal Au(111) surface shows discommensuration lines running perpendicular to the step edges in a 'V' shape on the terraces [6]. After more than a hundred sputtering and annealing . The image exhibits the characteristic herringbone reconstruction. The bright zigzag lines are the discommensuration lines that separate the fcc-stacked regions from the fault hcp-stacked regions (tunnelling parameters: tunnel voltage U T = −0.5 V and tunnel current I T = 0.5 nA). For STM data processing we used WSxM [16] throughout this contribution.
cycles STM measurements showed straight and regular spaced terraces (see figure 2) with monatomic steps, which did not alter anymore by further cleaning procedures described above. The terrace width in the measurement of figure 2 is 6.3 nm on average. By analyzing many STM pictures at different positions on the crystal surface we found an average terrace width of W = 6.1 ± 0.8 nm, which corresponds to a vicinal surface with Miller indices (23 25 25) and a miscut angle of 2.3 • . The terraces of the Au(23 25 25) surface are reconstructed in the same way as on the Au(788) surface and the steps exhibit the same {111}-microfacets, but the terrace width is 6.1 nm (25 atomic rows) instead of 3.8 nm (16 atomic rows). Please note how regular the terraces are in width. This surface is therefore well suited for growing wide and well-ordered ferromagnetic 1D nanostructures.
To avoid possible contaminations from a crucible, Fe was evaporated from a high purity rod by a water-cooled electron beam evaporator. During evaporation the pressure was better than 5 × 10 −11 mbar. The sample was held at room temperature (RT) during Fe deposition. We used quantitative AES to calibrate the Fe evaporation rate by growing Fe on Cu(001). In the literature, it was observed that Fe grows not only layer-by-layer on Cu(001) but that it can also grow bilayer-by-bilayer [18,19]. After the first one to two bilayers the growth proceeds layerby-layer. In order to avoid a possible error in the calibration of the growth rate, we performed additional calibration measurements with the magneto-optical Kerr effect (MOKE) and STM. We used the well-known transition of the easy magnetization direction from out-of-plane to in-plane between 10 and 12 ML [17] in our MOKE study in order to clarify whether we evaporated layer-by-layer or bilayer-by-bilayer on Cu(001). Additionally, we determined the growth rate with STM by measuring the coverage of a submonolayer film at several positions on the sample. We found that a layer-by-layer growth is present at a deposition rate of less than 0.1 ML min −1 in contrast to a bilayer-by-bilayer growth at rates of more than 1 ML min −1 [18,19]. The low deposition rate was chosen to favor a good growth of Fe nanostructures as will be discussed below. As we will see, Fe grows on flat and vicinal Au(111) in a non-ideal layer-by-layer growth. Therefore, the thickness in ML is defined as the number of supplied Fe atoms with respect to the number of surface atoms of the substrate (ML equivalent). To transfer the calibration from Fe/Cu(001) to Fe/Au(111), the numbers of ML were multiplied by a factor of 1.11 for the coverage of Fe on Au(111) to take into account that the atomic density is 11% less (N Cu = 15.3 atoms nm −2 and N Au = 13.8 atoms nm −2 ).

Growth of fcc Fe(111) on flat and vicinal Au(111)
For the growth of Fe on flat Au(111) it was observed that Fe nucleates at the corners of the herringbone reconstruction [2]- [4]. During subsequent dosing of Fe onto the surface, monatomic high islands are formed. This can also be observed in our STM measurements shown in figure 3(a). The shape of the islands is polygonal and nearly triangular. The edges are aligned along the closed packed 011 fcc directions. The islands are atomically flat and the triangular shape reflects the fcc(111) symmetry of the substrate surface. Therefore, we observed that Fe grows pseudomorphically on the Au(111) substrate, which is confirmed by the LEED study presented in section 3.2.3 (see figures 13(a) and (b)) and was observed with STM [2,3] and TEM [1] by other authors. Due to the surface reconstruction of flat Au(111), the islands form a regular pattern (see figure 3(a)). For subsequent Fe dosing, the islands continue to grow laterally in all directions. Since the spacing between the islands along [211] fcc is smaller than along [011] fcc , the islands start to coalesce along the [211] fcc direction. This can be seen in figure 3 figure 3(c)).
For Fe on vicinal Au(111), the growth proceeds differently from the growth on flat Au(111). When adatoms are evaporated onto the vicinal surface, they start to move on the terrace until they are trapped at a step edge or meet with other diffusing adatoms. At a low evaporation rate or a high mobility, the probability for the adatoms to reach the step edge is higher than to form clusters or islands. In our case the evaporation rate of less than 0.1 ML min −1 is sufficiently low to observe a good growth of Fe nanostructures at the step edges with a minimum of unwanted clusters formed by immobilized adatoms. The Fe atoms located at the step edges act as nucleation centers for the subsequently evaporated Fe adatoms and monatomic high Fe fragments are formed. The spacing between the fragments corresponds to the periodicity of the surface reconstruction, which is 7.2 nm [8]. The Fe adatoms grow preferentially on the fcc sites. Thus, the fragments are formed on these sites and during subsequent dosing of Fe onto the surface the fragments connect finally with each other occupying also hcp sites [7]. This will be called the 1D coalescence in the following sections. The growth behavior is illustrated schematically in figures 4(a) and (b). After the first row is completed, the growth of Fe still continues preferentially on the fcc-stacked regions [7] (see figure 4(c)), which produces undulated Fe stripes. A closer look reveals that triangular-shaped islands are formed (see figure 5). The island edges are aligned along the closed packed 011 fcc directions. Between the islands the step edges are decorated with Fe stripes, which connect the islands along [011] fcc . The growth mode can be best described as a 1D Stranski-Krastanov growth and proceeds similar as on Au(788) [7]. Just as in the case of Fe on flat Au(111) proceeds the growth ) support this interpretation. The regular array of the triangular structures is eventually disturbed by the presence of Fe clusters on the terraces. We observed that, with increasing Fe overlayer thickness, the Fe starts to grow over the step edges. The coalescence with the Fe on an adjacent step edge takes place at the fcc sites of the substrate due to the preferential growth at these sites (see figure 4(d)). This will be called 2D coalescence in the following sections. We can conclude that the growth of Fe for submonolayer coverage proceeds pseudomorphically on flat and vicinal Au(111). In both cases, triangular-shaped islands are formed. The observed Fe overlayer thicknesses required for the coalescence of the triangularshaped islands are different on flat and vicinal Au(111) due to the different island spacings. While the spacing of the nucleation centers on flat Au(111) is 7.5 nm along [211] fcc and is given by the surface reconstruction, the spacing on vicinal Au(111) is given by the terrace width (here: 6.1 nm). Furthermore, the growth proceeds preferentially on the fcc sites of the reconstructed terraces. Thus, the Fe islands reach the step edges faster than for an equal growth on fcc and hcp sites. Along the [011] fcc direction the spacing is given by the surface reconstruction on both surfaces (≈11.5 nm for flat Au(111) and 7.2 nm for all vicinal Au(111) surfaces exhibiting discommensuration lines perpendicular to the step edges).

Phase transition from fcc(111) to bcc(110) Fe
As described in the previous section, Fe starts to grow pseudomorphically on Au(111). The fcc structure is a metastable phase for Fe at RT. The native RT structure of Fe is bcc.

9
The stress building up during the pseudomorphic growth results in a phase transition from fcc(111) to bcc(110) for larger overlayer thicknesses [1]- [3]. This structural phase transition and the corresponding disruption of the pseudomorphic growth mode was observed with STM [2,3]. The following sections deal with this phase transition. In section 3.2.1, we present our results obtained with STM, where we observed the phase transition in a change of the topography by the appearance of rectangular-shaped structures, so-called crystallites. From our STM measurements we deduced, how the rectangular bcc (110) (d)). The numbers of layers contributing to the film surface is similar to other systems, which grow quasi-layer-by-layer, e.g. Co/Cu(001) for Co films grown at RT [20]. Furthermore, the crystallites are atomically flat. This shows that the Fe still grows in layers, with atomically flat terraces with the size of the crystallites. This was also observed in an STM study of up to 3 ML [3]. Ideal layer-by-layer growth reproduces the topographic properties of the substrate. This is not the case here, since the pseudomorphic growth is disrupted and the crystallites begin to form, but the rectangular shape of the crystallites is reproduced layerafter-layer. The growth of Fe on flat Au(111) can be best described as a non-ideal layer-by-layer growth because a new layer starts before the previous layer is completed. We observed this growth mode for the entire Fe film thickness region studied (up to 10 ML).
For Fe on vicinal Au(111), the growth front was also analyzed by STM and the same growth behavior as for Fe on flat Au(111) was found (see figure 9). For 3.7 ML, the growth front exposes three layers. Similar to Fe on flat Au(111), the number of exposed layers increases with increasing coverage. For 20 ML Fe on vicinal Au(111), five layers are exposed (see figure 9(e)). As observed for Fe on flat Au(111) the crystallites are atomically flat. From this observation and the analysis of the exposed layers, it can be concluded that the growth also proceeds in a non-ideal layer-by-layer growth after the 2D coalescence (up to 20 ML, which is the highest Fe overlayer thickness studied).

Structural model of the phase transition from fcc(111) to bcc(110).
The stress, which results from the mismatch between the pseudomorphic fcc Fe on Au(111) and the stable bcc(110) phase, can only be accumulated for a few atomic layers. Consequently, the pseudomorphic fcc(111) Fe film can only be maintained for few layers. This is the driving force for the phase transition from fcc(111) to bcc(110). As depicted in section 3.2.1, the growth is not pseudomorphic any more and the described rectangular-shaped crystallites appear, which represent relaxed bcc Fe with (110) surface orientation. But how does the rectangular bcc(110) unit cell fit onto the hexagonal substrate? The bcc(110) Fe unit cells can fit in the so-called Nishiyama-Wassermann (NW) orientation onto the fcc(111) substrate [21,22] as illustrated in figure 10. The planes of substrate and film are parallel to each other, thus (110) bcc (111) fcc . Furthermore [001] bcc is parallel to 011 fcc and [110] bcc is parallel to 2 11 fcc (2D matching). The smallest lattice mismatch between bcc(110) and fcc(111) Fe on Au(111) is realized in this orientation. The lattice mismatch is only 0.5% along [001] bcc corresponding to 011 fcc (in-plane nearest-neighbor distance 0.288 nm for bcc Fe  [21,22]. and 0.287 nm for pseudomorphic fcc Fe), but 18.7% along the [110] bcc corresponding to 2 11 fcc (0.406 nm for Fe and 0.499 nm for the second nearest-neighbor spacing of pseudomorphic fcc Fe) [3].
Another orientation of bcc(110) onto fcc(111), called Kurdjimov-Sachs [22,23], is illustrated in figure 11. For this orientation, the planes of substrate and film are also parallel and the [111] bcc direction is parallel to the 011 fcc directions (1D matching). The angle between the [110] bcc and the 2 11 fcc directions for the KS matching is 5.25 • .
In the NW orientation, the Fe bcc(110) unit cell fits onto the flat Au(111) substrate in three equivalent orientations (see figure 12(a), white atoms) and in the KS orientation in six orientations (see figure 12(a), black atoms) 2 . This picture illustrates the origin of the three dominant orientations of the Fe crystallites on flat Au(111). The orientations given by the KS orientation deviate only by ±5.25 • . Deviations of the crystallites from the preferential growth direction of the order of a few degrees can be found in the STM measurements, but it cannot be decided from these measurements, to which extent this is the result of the KS orientation or a result of the statistic variations of the growth process. TEM measurements [1] and combined reflection high-energy electron diffraction and grazing-incidence surface x-ray diffraction [5] confirm the coexistence of NW-and KS-orientated bcc(110) unit cells on Au(111). The amount of NW-and KS-orientated domains is not accessible from our STM measurements, but the KS-orientated unit cells (1D matching) builds up more stress in the film than the NW-oriented unit cells (2D matching). Therefore, the KS domains should be less favorable than the NW domains as suggested for Fe/Cu(111) [14].
On the vicinal Au(111) surface, crystallites are present for 1.0 ML of Fe and above (see section 3.2.1). The orientation of the crystallites is the same as for Fe on flat Au(111) except for the growth direction [011] fcc , i.e. along the step edges, which is not present for Fe on Au(23 25 25). Nevertheless, the appearance of the crystallites on the vicinal Au(111) surface is an indication of the phase transition because the rectangular shape and the growth along the [101] fcc and the [110] fcc directions can be explained by the NW and/or KS fittings of the bcc(110) to fcc(111) (see figures 10 and 11). This means that, for the vicinal Au(111) surface, one NW orientation of the bcc(110) unit cells and two corresponding orientations in the KS mode are not present as illustrated in figure 12(b).
This circumstance allows us to gain insight into the crystallographic properties of the crystallites: from the STM measurements we know that the crystallites are orientated under an angle of ±30 • toward the step edge normal. The long side of the crystallites could by be either parallel to the [001] bcc or to the [110] bcc direction, but only the growth along the [001] bcc direction allows the formation of the crystallites, which exhibit an elongation of ±30 • toward the step edges. This seems reasonable since the mismatch for [001] bcc parallel to 011 fcc is only 0.5% instead of 18.7% for [110] bcc parallel to 2 11 fcc (see figures 10 and 11). The growth proceeds therefore along the direction in which the minimum of stress is built up. For the system Fe on flat Au(111) this was also suspected by Voigtländer et al [2] but with the use of a vicinal Au(111) substrate we were able to directly identify the crystallographic growth direction of the crystallites. With increasing Fe overlayer thickness the spots broaden. The shape of the spots changes from round spots to crescent-shaped stripes with a curvature toward the (0,0)-spot for an Fe coverage larger than 2.0 ML (see figure 13(c)). This is interpreted as an appearance of (unresolved) satellite spots. 3. The transformation of the LEED spots into stripes is completed at a coverage of 4.5 ML (see figure 13(f)). Above this coverage only the intensity of the LEED streaks increases. are as long as in the case of Fe on flat Au(111) but the other four LEED streaks are shorter. The origin of this difference is the missing orientation of the crystallites along [011] fcc as will be demonstrated in the following.
The LEED patterns were simulated using the lattice parameters for Au(111) and bcc Fe(110). Figure 15    From the comparison between the LEED measurements and simulations, we conclude that the measured streaks are too wide to be explained only by the NW-orientated growth of the bcc(110) unit cells. Therefore, we assume that the bcc(110) unit cells are present either in the KS-or in the NW+KS-orientated growth mode. Our growth study demonstrates the surplus of combined LEED and STM investigations.

Summary and conclusion
In this contribution, we characterized the development of the topography of submonolayer and ML Fe films on Au(111) and Au(23 25 25). We observed a pseudomorphic growth behavior of Fe on the flat and vicinal Au(111) up to a critical Fe overlayer thickness. For Fe on flat Au(111) the critical thickness is ≈1.7 ML and for Fe on vicinal Au(111) it is ≈ 1.0 ML. Since Fe grows in the same way on Au(23 25 25) as on Au(788) below the critical thickness [7], we assume that the growth behavior is the same on all vicinal Au(111) substrates with reconstructed terraces and {111}-microfacets steps.
Above the critical thicknesses we observed a phase transition from fcc(111) to bcc(110) with STM and LEED. In STM, the appearance of Fe crystallites marks the end of the pseudomorphic growth and, in LEED, satellite spots arise from these crystallites. The critical thicknesses for the phase transition, which we deduced from STM and LEED for the onset and end of the phase transition, are summarized in table 1. We found that the onset of the phase transition from fcc(111) to bcc(110) of Fe on Au(23 25 25) starts at a lower Fe coverage than for Fe on flat Au(111), but the development of the phase transition is impeded and therefore is completed at a higher Fe overlayer thickness on the vicinal surface.
From the STM and LEED measurements, we were able to deduce the orientation of the crystallites on the flat and vicinal Au(111) surface: while for Fe on flat Au(111) all 011 fcc directions are preferential growth directions of the Fe crystallites, no crystallites were found along [011] fcc for the system Fe on Au(23 25 25). That means that not all orientations for the bcc Fe(110) unit cells are present on the vicinal surface. This circumstance allows us to directly link the elongation direction of the crystallites to the Fe bcc(110) unit cell. The crystallites grow along the [001] bcc direction. The unit cells are either orientated in a KS orientation or in a combination of NW and KS orientations.
It will be interesting to link the results obtained for the growth and morphology of Fe on flat and vicinal Au(111) to the magnetic properties of the studied systems for two reasons: firstly, the well-known spin reorientation transition for Fe on flat Au(111) is accompanied by the phase transition from fcc(111) to bcc(110). If the phase transition is impeded, the spin reorientation transition for Fe on Au(23 25 25) may be impeded as well. Secondly, the easy in-plane magnetization direction should be different for both systems. Fe films on flat Au(111) exhibit a sixfold symmetry due to the alignment of the crystallites along all 011 fcc directions, while the surface of Fe on Au(23 25 25) is twofold due to the missing growth along the [011] fcc direction. These questions will be addressed in a future work.