In this work, we investigate the structural, morphological and magnetic properties of epitaxial Cobalt ultrathin films grown on the vicinal surface Au(788). The aim was to study the magnetization reversal and determine the influence of the regular arrangement of atomic steps, typical of a vicinal surface. The influence of the Co thickness on the spin reorientation from out-of-plane to in-plane magnetization were investigated by means of the magneto-optical Kerr effect (MOKE). Preparation and surface quality of the Co films were characterized using the surface experimental techniques LEED and STM. A smooth spin reorientation transition, between 8 and 12 atomic monolayers (ML) of Co, was observed from out-of-plane magnetization, between 5 ML and 12 ML of Co, to in-plane magnetization, above 13 ML of Co. Furthermore, the angular dependence of the magnetic hysteresis loops indicates uniaxial magnetic anisotropy parallel to the atomic steps in the surface plane of the system Au/Co/Au(788) for thicknesses between 13 ML and 20 ML of Co.
The origin of magnetic anisotropy in low-dimensional systems has been explored due to a series of questions raised in systematic studies. Some of these questions are related to the intrinsic anisotropy mechanisms that contribute to in-plane magnetic anisotropy (IMA) and perpendicular magnetic anisotropy (PMA).1–3 Generally, the PMA is related to an inner strong intrinsic mechanism that overcomes the extrinsic macroscopic shape anisotropy that arises from macroscopic dipole-dipole interaction. The inner mechanism is induced by anisotropies in the crystalline lattice, including stress lattice and symmetry breaking that generates the known magnetocrystalline anisotropy (MCA). Similarly, the IMA can also originate from intrinsic, microscopic and magnetic states, besides the already known shape anisotropy. The study of systems with spin reorientation transition (SRT) is of fundamental importance for the understanding of the mechanisms that originate the magnetic anisotropies. For ultrathin films, SRT is usually related to the film thickness, temperature, or substrate morphology, which can be modified through vicinal surface and by preparation conditions.4–6
The magnetic behavior of ultrathin Co films on Au surfaces has been previously explored by several in situ studies such as, for example, Co/Au(111),7–17 Au/Co/Au(111),18–23 and vicinal surfaces.4–6 Kawakami et al. have concluded that the step-induced uniaxial magnetic anisotropy increases linearly with the step density.4 They investigated the effects of a stepped surface morphology on the magnetic anisotropy for ultrathin Co film by depositing on a curved Cu(001) substrate. Stupakiewicz et al.5 have grown Co films on an Au-buffered bifacial W(110) (atomic flat) and W(540) (vicinal surface with 6.34° miscut angle) single crystal. For Co films on Au/W(540), the out-of-plane magnetization component was maintained up to a thickness of about 8 nm (∼40 ML), showing a smooth change in the SRT (> 10 ML), while for the flat Au/W(110) a sudden magnetic transition (≤ 1.5 ML) occurred at film thickness of 3 nm (∼15 ML) of Co. Elsen et al.6 have investigated the influence of surface roughness, which is created during the growth process of Co on two different Au vicinal surfaces. Due to the competition between tilted uniaxial anisotropy and the isotropic in-plane shape anisotropy, an abrupt (≤ 0.5 ML) or smooth (3 ML) SRT was favored above a critical thickness (here defined as the film thickness to which the magnetization direction is aligned at 45° from surface normal, according to Refs. 5–8, 19, and 22) of 2.8 ML and 3.3 ML, on Au(755) and Au(233) substrates, respectively.
The magnetism of Co films grown on Au(111) and Au(788) was previously explored by Rodary et al.7 It was observed a dependence of the SRT with respect to the grain boundaries density. By increasing film thickness, the easy axis of magnetization changed from out-of-plane to in-plane of the film, at critical thickness and width of SRT of 3 ML (< 2 ML) and 4.2 ML (< 0.5 ML), for Co films deposited on Au(788) and Au(111), respectively. This behavior was correlated to a nucleation density of Co clusters on Au(788) almost four times bigger than on Au(111).9,24 To explain this behavior, they introduced a new model that takes into account the energy barrier between magnetic domains outside the plane and inside the plane created by density of grain boundaries. This approach implies that the morphological properties like structural imperfections or grain boundaries can strongly influence the SRT.
Many other works also highlight the magnetic anisotropy of thin films grown on Au(111) substrates. Ayadi et al.22 investigated the magneto-optical properties of Co grown on an Au(111)/glass substrate and compared HCP structure to the FCC structure produced by an annealing procedure. For HCP structure, the SRT occurs at critical thickness of 2.1 nm (∼10 ML) of Co, and presents canted spin configuration, throughout the smooth SRT (∼2 ML), due to a progressive reorientation of the magnetization towards the film plane. For FCC structure, the saturation state is almost never reached even for the thinner film in high magnetic fields (up to 8 kOe) and the saturation field increases with Co thickness. For this case, the SRT was not complete even after 6 ML of transition (between 4 ML and 10 ML). The explanation for the distinct magnetization reversal observed for each structure was related to the shape of the nucleation of the domains. In the HCP case, after nucleation at one site, magnetization reverses by rapid domain wall motion, but in the FCC case jagged domain walls develop around many nucleation centers. Weller et al.25 studied the Au/Co/Au/glass system by XMCD, perceiving a smooth SRT between 3 ML and 10 ML with a complete easy axis transition from out-of-plane to in-plane anisotropy that occurs at 11 ML. The Au buffer on the glass substrate provides an atomically flat and fully (111) textured template for the grown Co films.
In another study, it was reported the in-plane magnetic anisotropy for Au(7 ML)/Co(5 ML)/Au(322) system.26 The results revealed an uniaxial magnetic anisotropy in the plane of the Co film, with an easy axis of magnetization oriented parallel to the atomic steps of the Au(322) vicinal surface.
Here, we revisited the magnetic properties of ultrathin Co films. Magneto-optical Kerr effect (MOKE), low energy electron diffraction (LEED), and scanning tunneling microscopy (STM) were employed to characterize epitaxial monoatomic overlayers of Co on the vicinal surface Au(788). We have explored the influence of the surface structure and morphology induced by a regular matrix of atomic steps on the spin reorientation transition of ultrathin Co films on Au(788). The experimental results suggest a smoother spin reorientation as compared to Co film deposited on flat Au(111), with critical film thickness of 12 ML. For thicker Co films (t > 13 ML), the angular dependence of the magnetic hysteresis loops indicates an in-plane uniaxial magnetic anisotropy parallel to the atomic steps of the substrate vicinal surface, for the system Au/Co/Au(788).
The Au(788) substrate is a vicinal surface with 3.51° of miscut angle relative to the  direction. This vicinal surface presents a regular pattern of monoatomic steps with an average terrace width of 38.3 Å, with an average number of 16 adjacent lines of Au atoms.27 The preparation and characterization of the substrate Au(788) and ultrathin Co films on Au(788) were carried out in an ultrahigh vacuum (UHV) chamber equipped with thin film preparation and characterization resources.
In order to obtain a clean and well-ordered surface, the sample was cleaned by 2-hour Ar+ sputtering, with 2.5 keV ion beam energy and sample current of 10 uA, followed by a thermal annealing at 550 °C for 30 min and slow decrease, at a rate of 5°C per minute, down to 400 °C. The sputtering ion energy was progressively reduced from 2.5 keV to 1.0 keV (by 0.5 keV steps), while the annealing temperature was kept at 550°C for 30 min. Subsequently, several sputtering and annealing cycles were carried out at ion beam energy of 1 keV followed by the same annealing procedure. After many cycles, the surface reconstruction was checked by LEED. Preparation procedure was repeated until a well-ordered surface was achieved.
Epitaxial ultrathin Co films on Au(788) were prepared under molecular beam epitaxy (MBE) conditions at room temperature (300 K), with thickness in the range of 5 and 20 ML. The deposition rate was calibrated for ∼3 ML for 1 min by using STM images of Co deposited on Ni(111) at sub-monolayer regime.28 The epitaxial growth of the Co films on Au(788) was evaluated by LEED, while surface morphology was explored in situ by STM.
The magnetic properties of the Co/Au(788) system were investigated by MOKE in longitudinal (LMOKE) and polar (PMOKE) geometry. The experimental setup consists of a 635.2nm stabilized He-Ne laser incident at 45° to the sample normal, a Glan-Thomson polarizer/analyzer, a photo-elastic modulator (Hinds, PEM-90, modulation frequency f = 50 kHz), and Si-photodiode detectors. The Si-detector AC-signal is registered by a digital Lock-In amplifier at f and 2f (f = reference signal frequency) and divided by the DC-signal. Additionally, an external magnetic field of up to 150mT can be applied at a continuously varying angle in polar, longitudinal, or transverse geometries.
RESULTS AND DISCUSSION
Figure 1 shows LEED and STM results for the Au(788) substrate after preparation procedure. The results demonstrated a clean and well-ordered Au(788) surface: the LEED pattern in Figures 1a and 1b reveal the hexagonal reflections of the (111)-type terraces, confirming the long range order of the surface. The STM image after surface preparation (Fig. 1c) shows a typical pattern of regular steps due to the vicinal surface Au(788). The experimental mean values found for the step height and the terrace width were 2.5 Å and 42 Å, respectively. These values are in good agreement with those found in the literature27 for the vicinal surface Au(788).
The growth of Co on Au(788) was previously studied in details,7,24 which is far beyond the scope of this work. The reconstructed vicinal surface of the Au(788) substrate works as a template for 2D self-organized growth of Co nanodots. Co submonolayer coverage displays a quasi-ordered dot array in a wide temperature range. By increasing film thickness, Co bilayer islands grow laterally in size, and partially coalesce along the atomic steps. At higher coverages, a continuous film is constituted of grains separated by grain boundaries with a density controlled by the initial nucleation pattern. STM image (Fig. 2) collected after deposition of 5 ML of Co on Au(788) at RT shows irregular islands with a random size distribution.
PERPENDICULAR MAGNETIC ANISOTROPY
In order to explore the magnetic anisotropy of Co/Au(788) system and especially to unravel a spin reorientation as a function of Co film thickness (5 ML to 20 ML range), in situ MOKE experiments were performed both in polar (PMOKE) and longitudinal (LMOKE) geometries. The MOKE hysteresis curves for different Co film thickness on Au(788) are presented in Figure 3 (LMOKE) and Figure 4 (PMOKE).
A perpendicular magnetization component was found over the entire Co thickness range, which suggests that the film magnetization is canted. For canted magnetization, the switching could be realized by applying a magnetic field perpendicular or parallel (H//) to the film surface. For magnetization reversal induced by H//, the coercive field HC (as defined in the inset of Figure 3b), decreases from 1760 Oe for 5 ML Co film, with almost pure perpendicular magnetization, to about 42 Oe for the canted magnetization state observed at 12 ML of Co (see Figure 3b). It was noticed that the value of the coercive field became smaller with increasing thickness between 5 ML and 12 ML until it reached a lower and constant value (∼30 Oe), when the SRT was complete at 13 ML.
Figure 4 shows the out of plane magnetization behavior for Co films with thickness varying from 5 ML to 15 ML of Co. It was observed that by using an out of plane magnetic field (PMOKE) to reverse the magnetization state, as the film thickness increases, the coercive field decreases until the critical thickness of 12 ML. For the thickest Co films (t ≥ 13 ML), the MOKE measurements suggest typical shape of hard axis hysteresis loop.
By analyzing the graphics of Figures 3 and 4, it is observed that the Co film presents an out of plane easy magnetization axis for Co film thickness between 5 ML and 12 ML, when a smooth SRT occurs (between 8 ML and 12 ML), changing the easy magnetization axis to the film plane for Co film thickness with 13 ML and above. Figure 4 shows that above the critical thickness (12 ML) the hysteresis loops for the hard magnetization axis maintained a similar behavior. The same occurs with the easy axis, probed through LMOKE hysteresis loop that show a lower and constant value for coercive field (∼30 Oe) as from 13 ML.
The smooth SRT transition for Co/Au(788) system (4 ML wide) is quite different as compared to the other systems such as Co/Au(755) (≤ 0.5 ML) and Co/Au(233) (3 ML)6 or Co/Au(111) (< 0.5 ML) and Co/Au(788) (< 2 ML).7 A possible explanation for this distinct behavior of magnetization reorientation is related to the different magnetic film morphology of the Co films on flat and vicinal surfaces, Au(111) and Au(788), respectively. It has been already reported that the structural inhomogeneity of the magnetic film caused by grain boundaries induces the presence of a new characteristic volume, or length, which is added to the common exchange length.
Weller et al.25 reported a smooth SRT between 3 and 10 ML with a complete easy axis transition to the film plane at 11 ML of Co on Au/glass. The substrate (glass) is polycrystalline, which causes the deposited Au film to become textured in the  direction, which can explain the smoother transition generated by grain boundaries and other structural inhomogeneities.
Ordinarily, for a magnetic thin film grown on a flat surface, PMA dominates and drives the film magnetization out of plane, whereas for thicker films, shape anisotropy dominates and pulls the magnetization towards the film plane, often abruptly (SRT). However, on a vicinal surface, due to the misfit cut angle, the terrace plane and film plane are tilted from each other, which can contribute to a continuous rotation of the easy magnetization axis instead of an abrupt magnetic transition.29 The SRT process could occur by changing continuously the inclination state or by coexistence of phases. Recent studies in Co/Au(111)16 by using Kerr microscopy have observed that the inner mechanism that drives the SRT is related to a competition of two coexisting magnetic phases with preferred in-plane and out-of-plane magnetization orientation, known as orthogonal bistable magnetic domains. The overall magnetization reversal behavior is explained by thermal activation of magnetic domains.
Additional evidence of this mechanism was observed by MOKE in the Co/Au(111) system.17 In this work, by decomposing the magnetization into orthogonal components in the SRT region, it was observed hysteresis loops with no vanishing remanence in all three components when an external field is applied in the film plane. On the other hand, when an out-of-plane external field is applied, the same film is driven to a single domain state with full remanence. Since remanence was found in all magnetization components for in-plane applied field, and full remanence is obtained for an out-of-plane applied field, it rules out that the magnetization reversal proceeds via a state of canted magnetization and suggests that it proceeds via a state of coexisting phases.
The PMOKE results (Figure 4), obtained with perpendicular external field, present square hysteresis loops (almost total remanence), for Co thickness between 8 ML and 12 ML, which is in agreement with a single domain state. Additionally, in that same thickness range, the hysteresis loops obtained by LMOKE show a reduced remanence, which indicates magnetic remanence components in other directions.
Therefore, the observations suggest that the competition of the populations of the magnetic phases in the Co film is the mechanism responsible for the SRT transition in the Co/Au(788) system.
IN-PLANE MAGNETIC ANISOTROPY
The in-plane magnetic anisotropy of ultrathin Co films on Au(788) was investigated for two different film thickness (15 ML and 20 ML of Co). Hysteresis loops were collected for different directions of the applied external magnetic field, by means of ex situ LMOKE experiments (α angle is the in-plane angle between the applied external field and the axis perpendicular to the surface steps). Before removing from the experimental UHV chamber, these samples were covered by a Au capping layer (20 ML thick), in order to avoid contamination and film oxidation. Two different Co films, with thicknesses of 5 ML and 20 ML, with Au capping layer were measured (not shown) and no significant change of hysteresis loop was observed.
The analysis of ex situ LMOKE results indicate an uniaxial in-plane magnetic anisotropy for the Au/Co/Au(788) system, with easy axis of magnetization oriented along the direction parallel to the atomic steps and hard axis in the direction perpendicular to the atomic steps. Figure 5 shows the dependence of the coercive field (Hc) as a function of α angle, for Au(20 ML)/Co(t)/Au(788), for t = 15 ML and t = 20 ML, plotted in polar coordinates. This result is consistent with previous results obtained for similar systems as, for example, Co/Cu(1 1 13)30 and Co/Cu(001).31
A non-linear fitting of the coercive field as a function of the applied field for Au(20ML)/Co(t)/Au(788) was performed, by considering
where H0 is a constant that represents the projection of the coercive field in the direction of the easy axis. H0 comes in agreement with the uniaxial anisotropy model, where the coercive field varies satisfying Equation 1. In our system, this equation will diverge at α = 0° or α = 180o, when H is perpendicular to the steps. Figure 6 shows the experimental data (Hc x α) for 15 ML and 20 ML of Co on Au(788) and the respective fitting curves.
From fitting procedure, H0(15 ML) = 82 ± 3 Oe and H0(20 ML) = 57 ± 2 Oe. These values show that the coercive field projection on the easy axis is stronger in the 15 ML film than the thicker one (20 ML), which was expected, so as the film thickness increases the magnetic anisotropy generated by the film/step interface becomes weaker. Atomic steps can influence the crystallographic orientation with which the first layers of the film grow, being able to cause the axis of easy magnetization to be induced along the direction of these same atomic steps.32 The fitting values are in agreement with the H0 (55 Oe) founded in the Au(7ML)/Co(5ML)/Au(322) system.26
The analysis of in situ PMOKE and LMOKE measurements as a function of the film thickness for Co/Au(788) showed a spin reorientation of film magnetization, from out-of-plane to in-plane, concluded for a Co film thickness of 13 ML. We observed a smooth SRT with increasing Co thickness between 8 ML and 12 ML, with strong evidence that the transitions are driven through competition of coexistence of magnetic phases.
This transition behavior may have occurred due to the influence of atomic steps on the vicinal surface, as suggested by Rodary et al.7 Other morphological properties like structural imperfections or grain boundaries can also strongly influence the SRT, and the STM images indeed show irregular islands with a random size distribution, which suggest this contribution. The authors of this article report that the grain sizes formed during the growth of the film strongly influence the magnetic properties of Co/Au(788).
The analysis of ex situ LMOKE measurements as a function of the orientation of applied external field, indicates an uniaxial magnetic anisotropy in the film plane for 15 ML and 20 ML thicknesses, with easy axis of magnetization oriented along the direction parallel to the atomic steps of the Au(788) vicinal surface.
Through the detailed preparation conditions of Co on Au(788), it is observed a smoother SRT as compared to similar systems, which reinforce the argument that the transition occurs due to coexistence of phases.
The authors thank the financial support from FAPEMIG (grants APQ-00460-15 and APQ-02087-16), CNPq and CDTN/CNEN (project 614.22/2019).
The data that support the findings of this study are available from the corresponding author upon reasonable request.