The Fe films were deposited on cleaned MgO(001) substrates by molecular beam epitaxy (MBE) in an ultra-high vacuum (UHV) system with a base pressure of 2.0 × 10⁻¹⁰ mbar. The MgO(001) substrate had been first heated at 700 °C for 2 h to remove the adsorbed gas from the surface before the film was deposited. The clean surface of MgO(001) was confirmed by in situ low energy electron diffraction (LEED) equipped within the Omicron UHV system. Subsequently, the Fe (99.995% purity) film was deposited on the MgO(001) substrate by the oblique-incidence deposition method. The Fe films with thicknesses of 50 ML, 45 ML, 32 ML, and 24 ML were obtained by varying the oblique deposition angle (α) relative to the normal surface of the substrate. The Fe film deposition angles (α) were 0°, 45°, 55°, and 70°, respectively. The growth time of Fe film for all samples was kept the same (i.e., 40 min) in the deposition processes. Therefore, the deposition rate of Fe film was 0.6–1.25 ML/min, while the substrate was still kept at room temperature. Before taken out of the UHV chamber, all samples were covered with a layer of ∼ 6 nm Pd, normally deposited under pressure of 5.0 × 10⁻⁹ mbar. Figure 1(a) shows a schematic configuration of the samples synthesis.

Fig. 1.

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	Fig. 1. (color online) (a) Schematic configuration of sample growth, (b) LEED pattern of MgO(001) substrate, and (c) Fe thin film deposited on MgO(001) with α = 0° (normal deposition).

in situ low energy electron diffraction (LEED) equipped within the Omicron UHV system was employed to investigate the surface structure of the samples. The x-ray reflectivity (XRR) was performed to determine the film thickness and roughness for all samples by a Bruker D-8 x-ray diffractometer using Cu Kα radiation (λ = 0.15405 nm). The ex-situ longitudinal MOKE measurements were carried out at room temperature and described elsewhere.^[37,38] In addition, the magnetic anisotropy constants were determined quantitatively by fitting the angle-dependent anisotropic magnetoresistance (AMR) curves. The home-made AMR setup consists of a Wheatstone bridge, a lock-in amplifier (Stanford Research Systems SR830 DSP), and a rotational magnetic stage around a stationary sample. In the experiments, a sufficiently large and stable field was used to guarantee a true single-domain behavior of the specimen. The sample size was 10 mm × 3 mm × 0.5 mm for AMR measurements, which were performed with a standard four-point method.

Figure 1(b) shows the in situ LEED (2 × 2) pattern of MgO(001). The surface structure of the Fe film normally deposited is also investigated by in situ LEED, and the cubic Fe(001) layer is epitaxially grown on the MgO(001) surface as shown in Fig. 1(c). Previous study of MgO showed that it retained its bulk body centered cubic (BCC) structure due to the lattice mismatch of 4%, and there might be a tetragonal distortion in the Fe.^[39,40] As shown in Fig. 1(c), due to the epitaxial relationship, the Fe lattice is rotated by 45° relative to the MgO lattice, i.e., the well-known relation Fe〈1 1 0〉 ∥ MgO〈1 0 0〉. During the oblique deposition, a self-shadowing effect takes place, resulting in the formation of grains in the plane of the film that is elongated perpendicularly to the incident flux direction and with an aspect ratio increasing at a larger deposition angle. Therefore, all the other LEED patterns are almost similar and it is difficult to distinguish the LEED pattern of the Fe film with large oblique deposition angle. The energy provided during the LEED pattern observation is 132 eV.

The XRR usually can be performed on the grown sample to determine the film thickness, roughness, and density. Figure 2 shows the XRR experimental curve and its fitting for determining the film thickness and roughness of the sample with α = 0° (50 ML). The XRR experimental curves and their fittings for the other samples are not shown here. The fitting parameters are accurately determined by simulating (red line) the experimental curve (open circles) and are presented in Table 1. Figure 3 clearly shows that the Fe film thickness (t_Fe) decreases and the roughness (σ) increases with the increase of oblique deposition angle (α).

Fig. 2.

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	Fig. 2. (color online) X-ray reflectivity spectra recorded on 0°-Fe(001)/Pd thin film, with fitting parameters accurately determined by simulating (red line) the experimental curve (open circles).

Fig. 3.

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	Fig. 3. X-ray reflectivity measurement of Fe-film thickness (tFe) and roughness (σ) as a function of deposition angle α.

Table 1.

Table 1.

Table 1. X-ray reflectivity measurements of film thickness and roughness. . α/(°) tFe/ML σ/nm tPd/nm 0 50 0.50 6 45 45 0.84 6 55 32 1.14 6 70 24 1.78 6

Table 1. X-ray reflectivity measurements of film thickness and roughness. .

The magnetic properties are measured by azimuthal rotation through the ex-situ MOKE at room temperature. Figure 4 shows typical MOKE hysteresis loops taken at different values of angle φ_H for all four samples. More detailed studies reveal the magnetic behaviors of these films, the conventional square hysteresis loops, and loops with multi-jumps, which are dependent on the direction of the magnetic field. The anisotropic geometry of each sample is the same as that in previous work on Fe/MgO(001).^[41] The UMA along Fe[100] is very important to create a multi-jump magnetic switching process. The experimental results of Zhan et al. showed that a considerable UMA along [100] may lead to three-jump loops in some directions of the external magnetic field.^[42] These multi-jump loops are also observed in our samples, and we have two considerable UMAs along [100]. Figures 4(c) and 4(d) show one jump at φ_H = 45°, two-jumps at φ_H = 126°, and three-jumps at φ_H = 153° given by typical MOKE; φ_H is the angle of the applied field relative to the [110] hard axis. The UMA along Fe[100] originates from oblique-incidence growth geometry. It is perpendicular to the incident flux direction and results from the self-shadowing effect. These unusual magnetic switching processes are caused by superimposed uniaxial magnetic anisotropy, which can be explained by the magnetization reversal mechanism of the 90° domain wall.^[43] Thus, the origin of uniaxial magnetic anisotropic component is the incident angle of the Fe atomic flux relative to the normal plane of the substrate. Since this effect was first observed in the Fe/Pd superlattice with a very thin Fe layer (< 20 Å), it was assumed that the magnetic anisotropy may occur, because the roughness of the Fe/Pd interface (about 5 Å) may have an anisotropic morphology, which is caused by the incident angle of the Fe atomic flux. A similar uniaxial magnetic anisotropy was also found in a single 800 Å-thick Fe film grown directly on MgO with a 15 Å Pd cap layer.^[44]

Fig. 4.

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	Fig. 4. (color online) Typical magnetic hysteresis loops of Fe films at different deposition angles: (a) 0°, (b) 45°, (c) 55°, and (d) 70°.

Therefore, on the contrary, our results show that the origin of the magnetic anisotropy is not the interface effect, nor the bulk property of the Fe layer, but it may be caused by the thickness of the Fe film changing with the oblique angle in the deposition process. The experimental dependency on the field direction of the coercive field (H_c) is plotted in Fig. 5. In order to facilitate the investigation of the anisotropic symmetry, the same data are plotted in polar coordinates in the inset. The H_c of the sample with α = 0° (50 ML) measured at φ_H = 0° is 16 Oe and shows an invariant behavior with the azimuthal angle (φ_H). When the oblique deposition angle increases to α = 45° (45 ML), the H_c measured at φ_H = 0° is increased to 25 Oe and shows a non-constant behavior with the azimuth (φ_H). Particularly in the case of the samples with α = 55° and 70°, the H_c values increase to 55 Oe and 66 Oe respectively, at the values of easy axe φ_H = 126° and 315° just as the other samples do. This implies the uniqueness of the 32 ML and 24 ML samples with α = 55° and 70°. Because of the tilting shape of the hysteresis loop, H_c drops to 21 Oe at the hard axes (φ_H = 180° and 360°), which clearly indicates the presence of uniaxial magnetic anisotropy. Quantitatively, Table 2 shows the difference , i.e., subtracting the coercivity along the easy axis () from the coercivity along the hard axis (). The values of H_c are deduced from the widths of the split half-loops. If the film had a coercive field less than the uniaxial anisotropy field, this effect would be simply regarded as a (relatively large) difference between the coercive forces in the two directions. Obviously, the larger the difference, the more alignment becomes a sign of the absence of disorder, that is, it shows single crystallinity of the sample. Also, it can be clearly seen from Table 2 that the increase of oblique deposition angle leads to more alignment and highly uniaxial magnetic anisotropy. From the longitudinal MOKE data for all samples, the angle dependent normalized remanent magnetic saturation ratio (M_r/M_s) polar plots are shown in Fig. 6. Previous work reported that the Fe thin films on MgO(001) substrates have four-fold symmetry with strong magnetic anisotropy.^[45] Figure 6(a) clearly shows that the angle dependent normalized remanence of the normally deposited (α = 0°) sample exhibits four-fold symmetry. When the Fe film thickness is large (50 ML), the four-fold cubic anisotropy is dominant to the UMA caused by oblique deposition.^[46] In the case of α = 45° (45 ML) sample, a weak four-fold symmetry is observed, as shown in Fig. 6(b). However, the samples deposited with α = 55° and 70° exhibit highly in-plane uniaxial magnetic anisotropy as shown in Figs. 6(c) and 6(d), respectively. This implies that the self-shadowing effect occurs during the oblique deposition, resulting in the formation of grains in the film plane perpendicular to the direction of the incident flux, and with aspect ratio increasing at a higher deposition angle. Therefore, the inhomogeneous distribution of the adatoms (roughness) occurs. That is why an in-plane uniaxial magnetic anisotropy is induced by the roughness caused by oblique deposition. Therefore, as the oblique deposition angle increases, the roughness also increases, resulting in the increase of UMA.^[47] These measurements also show four-fold cubic anisotropy in large Fe film thickness (50 ML) sample, but exhibit highly in-plane uniaxial magnetic anisotropy in thin films (24 ML and 32 ML) samples.

Fig. 5.

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	Fig. 5. (color online) Experimental dependency on the field direction of coercive field (Hc), with the same data plotted in polar coordinates in the inset.

Fig. 6.

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	Fig. 6. Angular dependent normalized residual polar plots of longitudinal MOKE data for all four samples.

Table 2.

Table 2.

Table 2. Magnetic anisotropy constants (Kl and Ku) and coercivity field (Hc) measured by using torque curves and MOKE, respectively. . tFe/ML Kl/J·m−3 Ku/J·m−3 Hc/Oe (–) 50 5.2 × 104 5.1 × 103 10.3 10.3 45 5.2 × 104 7.6 × 103 14.5 20.9 6.4 32 5.2 × 104 5.1 × 104 11.3 23.1 11.4 24 5.2 × 104 7.1 × 104 38.7 51.5 12.8

Table 2. Magnetic anisotropy constants (Kl and Ku) and coercivity field (Hc) measured by using torque curves and MOKE, respectively. .

In order to quantitatively determine the constants of magnetocrystalline anisotropy K_l and uniaxial magnetic anisotropy K_u for all four samples, the torque curves are obtained.

The resistance in ferromagnetic metallic film is a function of angle φ_M, which is the angle between the magnetization and current (inset of Fig. 7(b)), and can be written as^[48,49]

Fig. 7.

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	Fig. 7. (color online) (a) Angle-dependent MR measurement (H = 500 Oe) at different deposition angle α and with cos2(φH) as a reference for comparison. (b) Correlation between φH and φM at different deposition angle α. Inset shows schematic configuration of sample resistance measurement as a function of angle φM, which is between the magnetization (M) and current (I).

For real single domain rotation and excluding ordinary magnetoresistance effect, it is necessary to impose a higher external magnetic field than the saturation field.

The AMR curves of all four samples are plotted in Fig. 7(a). By changing the direction of the external magnetic field H, the magnetization M follows the orientation of the external applied field, so that the value of AMR exhibits an oscillatory behavior. However, due to magnetic anisotropy, M_Fe is no longer consistent with the external field (H) in the rotation process, that is, φ_M ≠ φ_H. Therefore, the AMR curve does not follow this cos²φ_H relationship. The correlation between φ_H and φ_M can be obtained from Fig. 7(a) and drawn in Fig. 7(b). Obviously, it can be expressed as

In order to compare the above two types of torques, the normalized torque is introduced below

The normalized magnetic torque curves for all four samples are shown in Fig. 8. The values of magnetic anisotropy constants K_l and K_u are determined by fitting the normalized torque curves with Eq. (7). It is obvious that the sample deposited with α = 0° (normal deposition) shows the minimum value of UMA, K_u = 5.0 × 10³ J/m³, with dominant four-fold MCA K_l = 5.2 × 10⁴ J/m³, and with higher deposition angle α = 70°, UMA obviously reaches the maximum value K_u = 7.1 × 10⁴ J/m³. The values of magnetic anisotropy constants K_u and K_l under variant external magnetic fields are plotted in Fig. 9. Both K_u and K_l show the almost invariable behaviors of the magnetic fields applied externally, which are in good agreement with those of the Fe/Si(001) films.^[50] The determined values of K_u and K_l for all samples are also plotted against the deposition angle (α) as shown in Fig. 10. Table 2 shows the values of K_u and K_l obtained from the AMR measurements. It can be clearly observed that K_u increases with the increase of oblique deposition angle, while K_l shows an invariant behavior. In addition, K_u decreases with increasing Fe film thickness (t_Fe) as shown in Fig. 11. Our measurements show four-fold cubic anisotropy in a large Fe film thickness (50 ML) sample and the recognition of superimposed highly in-plane uniaxial magnetic anisotropy in thin film (24 ML and 32 ML) samples. Thus, it is concluded that UMA may also be induced by oblique deposition with smaller film thickness.

Fig. 8.

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	Fig. 8. (color online) Normalized magnetic torque curves of Fe films deposited on Mg(001) substrate at different deposition angles: (a) 0°, (b) 45°, (c) 55°, and (d) 70°.

Fig. 9.

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	Fig. 9. Anisotropy constants Ku and Kl versus applied magnetic field (H) of Fe thin films deposited at different deposition angles: (a) 0°, (b) 45°, (c) 55°, and (d) 70°.

Fig. 10.

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	Fig. 10. Plots of Ku and Kl versus deposition angle α.

Fig. 11.

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	Fig. 11. UMA Ku versus Fe-film thickness tFe.