1. Overview

Ultrathin films or multilayer systems with individual layer thicknesses down to subnanometer represent a type of material with novel properties controlled by heterointerfaces in recent decade [1]. Thus, finding new surface and interface property from the ultrathin magnetic materials becomes more important in magnetic applications. In the field of magnetism, magneto-optical effect measurement is always a powerful technique using straightforward physics (spin-orbital coupling) and an optical setup (laser and polarizers) that can acquire magnetic information. Recently, it has again become more relevant in study of popular advanced materials such as topological insulators and related spintronics application such as spin hall effects [2–6]. Focused on the characterization method, the magneto-optical response from each layer to either incident electromagnetic wave plays a crucial role. No matter the reflection or refraction of electromagnetic waves also contains magnetic information from each magnetic layer, which reflects their intrinsic and extrinsic magnetic properties [7, 8]. Therefore, determination of magneto-optical properties provides an alternative opportunity for direct exploration of the detail of magnetic material, which is controlled by the external magnetic field and light.

The angle-dependent magneto-optical Faraday effect (AMOFE) measurement was used in an ultrahigh vacuum on polar plane of the material. This method exhibits excellent examination in the magnetic properties especially for an ultrathin material only a few nanometres thick. In addition, construction of a 3D magneto-crystalline anisotropy through this technique may be possible. Compared with the azimuthal scan in the plane by rotation of the sample disc, a scan in the polar plane in optical techniques is relatively more difficult. However, this problem can be solved in an ultrahigh vacuum system.

2. Historical and motivation

In 1845, Michael Faraday observed a universal effect that a linear-polarized light travelled through a transparent material, where the polarization of light deviated from its original state if a magnetic field was introduced along the propagation path of the light [9]. The phenomenon was named the “Faraday effect” and many experimental and theoretical research papers have been studied through dielectric materials [10–12], liquids [13–15] and gases [16–18]. Applications in aerospace studies have also been addressed in particular, because only electromagnetic signals from the stars are obtained. Thus, the Faraday effect can be applied indirectly to observe the distribution of electromagnetic fields on the planet [19]. Moreover, the effect should not be discounted because it can be used for direct characterization of the magnetic response from any matter. The effect of origin, the spin-orbital coupling of electron in the magnetic material interacts with the electromagnetic radiation, is induced between the surface and interfacial structures [20].

However, most magnetic materials are opaque in latest technologies, e.g., the exchange-biased tri-layer system in spintronics [21–25] and perpendicular recording media in hard discs [26–29]. The progress of technique development for the magneto-optical Faraday effect is then limited because of large absorption by most metallic constituents. Reflection measurement is then considered for high reflectivity with mirrored surfaces, using the subsequent technique discovered by 1877, which is known as the magneto-optical “Kerr effect” and has been widely applied in many optical and material systems [2, 3, 30–50]. The polarized laser light coupled with spins in opaque materials causes a rotation, which deviates from the original polarization of incidence in the reflected beams. Through the proportional relation of the magnetization vector and polarization rotation, a typical magneto-optical hysteresis loop can rapidly reflect realistic magnetic properties. Conversely, application using the transmitted mode of the Faraday effect seems relatively rare. We are very interested in why descriptions of fundamental properties such as the hysteresis loop, evidenced by the magneto-optical Faraday effect, are few [51].

Large theoretical approaches of the magneto-optical Faraday effect in thin-film systems have been published between 1989 and 1995 [52, 53]. Prior to Faraday age, this effect has been applied only in transparent dielectric crystals. An experimental note in Faraday’s diary said that a heavy glass was used for finding the first magneto-optical effect [9]. Single crystal material such as iron garnet has demonstrated large magneto-optical Faraday rotations (FR) and applications [54–56]. The application has used this effect in many optical devices, such as Faraday rotators and Faraday isolators. It is noticed that the devices needed to provide a distinct crystal length for enhancing the polarization rotation in the magnetic field [57, 58]. In current technology, most fabrications have concentrated on the nano-scale; however, ultrathin films or nano particles are too thin or too small to have a large polarization rotation in Faraday effect. The ultrathin scale of the reaction length in these specific materials and tiny Faraday rotations may be the reason why related research has been interrupted.

During 2004–2005, time-dependent spin oscillations in ultrafast opto-magnetic studies (inverse Faraday effect) have been greatly studied [20, 59]. This finding generates a new field of “optomagnetism” that describes how a strong electric field induces a strong magnetic field in the condensed matters. Recently, an oscillation of magneto-optical Faraday rotations as a function of the incident angle of light was observed in a (ferromagnetic-FM) film/(semiconductor-SC) substrate system [60]. Through magneto-optical signals of Faraday effect in ultrahigh vacuum, one hundredth of the optical signals respected to zero field were observed (as shown in Fig. 1). The substrate effect in the anisotropic thin crystal is critical in the further determination of interface magnetic properties. Due to the measurement in transmission mode, the received signals include independently a contribution from the magnetic film and the crystal substrate. Thus, the total Faraday rotation due to the variation of the optical phase difference from magnetic and optical parts leads to the interesting oscillation phenomenon.

 

Fig. 1 Oscillation behaviors of optical and magneto-optical Faraday intensities of the 2.3 nm Co/ZnO(0001) with the angle of incidence: (a) zero-field MOFE intensity I0 from optically anisotropic substrate and the 1 × original MOFE signal (same scale compared with the substrate); (b) oscillation behavior of MOFE signal intensity with 100 × zoom-in multiplication from (a). Here the Faraday optical intensity is measured from the hysteresis loop. The sensitivity of optical intensity in the apparatus is higher than that of FR. The scale bar of FR is indicated. Black line is a guide to the oscillation.

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The Faraday intensity (remanence, defined as two times the Faraday rotation) was measured from the negative (down spin state) to positive (up spin state) field at zero field in a hysteresis loop. Thus, the positive Faraday intensity means the rectangular hysteresis loop is typical in positive field direction (down state ↓ flipping to up state ↑) and negative intensity (↑ flipping to ↓) means the hysteresis loop is reversed in the same applied field. In Fig. 1, a 2.3-nm-thick Co film on an optically anisotropic ZnO(0001) crystal was evaluated by the MOFE. For an ordinary Faraday effect, optical beams are parallel along the magnetic field (Fig. 2). The figure of merit in device applications such as Faraday rotator is controlled by the longitudinal crystal length and rotatory power. Except for the rotatory power depending on the material, the quantity of Faraday rotation is proportional to the quantity of interaction length, if the sample is magnetized in a constant field.

 

Fig. 2 Traditional Faraday effect apparatus. P and A are polarizer and analyzer. Typical bar-shaped material is situated between two electromagnetic poles. D: is the photo detector.

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As technological requirements drive the scale of devices to become increasingly smaller, the optical path in Faraday rotation is obviously reduced. Thus, it has become difficult to measure the minute magneto-optical signals, especially for ultrathin thicknesses. After 1985, the instrument for ultrathin magnetic films was improved and given the name “surface magneto-optic Kerr effect (SMOKE)” [49]. The application of this technique then developed rapidly because of its excellent sensitivity in subsurface layers. Meanwhile, the reason of the success is also related to the sharp growth in vacuum technologies in recent three decades. High-quality surfaces with perfectly flat substrates can be applied to grow high-quality materials. In an ultrahigh vacuum environment, a substrate can be polished easily by high-temperature annealing. Without surface defects, a mirrored surface plane is suitable for the deposition of epitaxial magnetic layers. Therefore, the SMOKE technique can be applied and is efficient in probing the surface magnetic properties [49, 52, 61–71]. However, a very weak signal from the underlying substrate is usually ignored in metallic or semiconductor surfaces, such as Fe/Cu(001), Co/Cu/Co/Cu(001), Co/Fe(001), Au/Co/Si, Fe/Si(111) or Fe/GaAs(001) [34, 43, 64, 66, 67, 72, 73]. During the magneto-optical measurement, high attenuation in substrate intensity is usually treated as a minor factor in determining the magnetic properties.

However, the story is not so simple when we observe the confused various shapes of hysteresis from the same sample by MOFE, as in Fig. 3(a) and 3(b). The different result may be misled if the interpretation for oblique hysteresis shape is attributed to paramagnetic or diamagnetic contribution from the background. However, what is the cause of this?

 

Fig. 3 Hysteresis loops of 2.3-nm Co/ZnO(0001) measured at two different angles of incidence: (a) 49° and (b) 71°, for examples. The data were observed from the same sample.

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From the shape of the magneto-optic hysteresis loops, we know that the received signals are not only from the magnetic film. The signal from the substrate cannot be completely excluded. The mixed magneto-optical signals from the surface and the substrate become relevant for understanding the complete magnetic properties. Reflected signals of substrates in SMOKE measurements may be ignored because of the large absorption of metallic constituents in visible lasers. The penetration depth of evanescent waves of a visible laser, such as 633-nm He-Ne laser, is estimated at about 30 to 300 nm in solid thin films [74, 75]. This probing depth is also dependent of the refractive index and incident angle between surface and interface and it decreases when the reflection angle becomes larger. Therefore, angle-dependent detection is essential and plays a key role to provide another choice in probing magnetic properties, for example, 3D magnetic anisotropy and structurally induced magnetic properties.

3. Magnetic reversal

The reversal behavior of a hysteresis loop by magneto-optical Kerr effect had been observed when the ray of light was incident from the face and the back sides of a transparent sample [76]. But in our case, we use a similar idea in the designed magneto-optic Faraday effect to measure the magnetic properties of only one side. In Fig. 4, it was found that the hysteresis loop gradually switched its rectangular shape from spin-down state to spin-up state in a negative field and reversed in a positive field, when the sample was freely rotating in the incident plane (as detailed in the 55° to 61° evolution in the left-hand column of Fig. 4). Periodic flipping of the hysteresis loop was observed through the polar scan method [60]. A reversed behavior in ordinary Faraday effect is defined by a right-hand rule, in which the thumb of the right hand points to the direction of magnetic field H. However, in the experimental setup, the rotation of the polarizer with respect to the s-polarization is absolutely a key to the reversed loop behavior. Therefore, in author’s laboratory, the counterclockwise rotation of a linear polarization in Faraday rotation measurement is defined as a positive if the analyser in s-polarization is deviated clockwise by a small angle δ. Referring to the crystal optics and magneto-optics, the physical origin of oscillation behavior concludes in two major reasons: 1. The pure optical intensity and 2. The magneto-optic Faraday intensity varies with angle of incidence. Optical intensity oscillates due to the birefringence phenomenon of the ZnO(0001) crystal during Faraday effect measurements. The Faraday intensity I has a phase duration between parallel rays as a function of incident angle θ. The equation of crystal optics including a square of sine wave is empirically deduced as follows [60]:

 

Fig. 4 (a) Evolution of hysteresis loops from specific incident angles in the area of indicated arrow in (b). The downward arrow follows the loop data from top to bottom. (b) FR oscillation experiments as a function of incident angle for the 4-nm Co/ZnO and sputtering time of post N⁺ irradiation. Schematic digital idea described in the text is shown.

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Where d is the thickness of the birefringent crystal; λ is the wavelength of incident light; n_o and n_e are the ordinary and extraordinary refractive indices, respectively. The attenuation coefficients A and B are related to factors from materials. However, the covering of ultrathin magnetic materials alters the total optical intensities especially the attenuations. Thus, Eq. (1) can be used for analyzing the curve of I₀. According to the principle of magneto-optic Faraday effect experiment, the FR in magneto-optics physics can be simply described as [77]:

Initial optical intensity I₀ in the beginning of MOFE measurement is crucial because the analyzer should be rotating a small angle δ before experiment. Equation (2) indicates that the first-order linear Faraday rotation is proportional to the magnetization and thickness of the magnetic films. Magnetic property is completely obtained from the optical information. The order of FR in ultrathin ferromagnetic films is often less than 1°. Such small deviation in rotation angles makes ΔI become very small. If the curve of optical intensity I exhibits oscillation behavior, associate tiny magneto-optic intensity respect to the initial optical intensity in MOFE measurements should follow the same oscillation behavior but exhibits in a differential form. It is convincible and directly explains the reversal behavior of the negative Faraday rotation and a reversed hysteresis loop. The magnetic reversal of the film/crystal system may be originated from this simple inference. However, it still has many factors, such as attributed to microstructure and anisotropy issues then temporally excluding from this deduction.

According to the result of Fig. 4, variation of hysteresis loops is distinct even in 1° resolution of incident angle. Different shape and coercivity corresponds to the optical responses from the crystal and the magnetic film, respectively. Variation of coercivity corresponds to magnetic anisotropy of the film and variation of Faraday rotation is attributed to birefringence of the substrate crystal in the angle-dependent measurement. Each hysteresis loop consists of two contributions from the optical effect and the magnetic effect. The optical effect originates from the uniaxial optical ZnO(0001) substrate and the magnetic effect originates from the ultrathin magnetic film. The advantage of this experiment is that the Faraday effect observes both even may cancel entirely (zero rotation). In magnetic point of view, the variation of coercivity is related to the magnetic anisotropy of the film. Figure 4(a) shows the squared loop close to perpendicular magnetic field that corresponds to large out-of-plane anisotropy at around 60 degree. The rectangular loop is mainly from magnetic signals while oblique loop is formed by Faraday effect of the crystal. If the various rectangular loops and oblique loops forming different optical amplitudes are treated as continuous signals (analog), and switching of the loop corresponding to the spin transition are treated as discontinuous signals (digital), it has a great potential in advanced signal processing using magnetic technology in the evolution of hysteresis loops.

In Fig. 4(b), the oscillation behavior in the angle-dependent measurement is performed on the same substrate condition with short-time sputtering of 1 keV N⁺. Three curves seem like overlapping with others. However, only Co/ZnO and 113 s N⁺ Co/ZnO almost overlap each other. Small reduction in Faraday rotation was detected in 225 s N⁺ Co/ZnO, obviously in peaks. The N doping effect dominates in the first data and N sputtering effect begins in the second data. Few N doping did not alter the Faraday rotation but alters coercivity. More N dose causes surface sputtering. Meanwhile, both Faraday rotation and coercivity greatly reduced. In the experiment, the ultrathin magneto-optic material is expected to retain on the surface. Short sputtering time is to prevent all atoms removing from the surface. Owing to the oscillation of magneto-optic Faraday rotation 1/100 smaller than that of the optical intensities due to crystal birefringence, that's why an overlapping behavior in the experiment was observed.

4. Equipment and preparation of ultrathin film material

The setting of optical devices and the magnetic field on an ultrahigh vacuum system is a significant challenge. Two electromagnets mounted on the UHV system were specifically designed by Omicron Technology Co. Ltd., Taiwan. Referring to the diagram in Fig. 5, the incident angle with respect to the normal of surface is 30°, if the sample plane is rotated to the magnetic field. According to the principles described in Eq. (1), the magnetic field component of the ordinary Faraday effect is aligned to the propagation of light. However, in the UHV-MOFE system, it is an obstacle for the pair of electromagnets to have hollows in the optical setup in a vacuum. This is an unsolved problem but here, the main modification in this magneto-optical measurement, excluding this point, is that light has to propagate along the magnetic field. Therefore, the sample is situated at the cross point of the magnetic field and light path. The incident angle with respect to surface normal is 30° for the L-MOFE and 60° for the P-MOFE [78]. The ordinary Faraday effect measurement can be extended with an α-angle correction (see the corrected formula in Ref [79].).

 

Fig. 5 Schematic diagram of UHV-MOFE apparatus in author’s laboratory.

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Preparation of the ultrathin materials is important in MOFE studies. The ZnO(0001) crystal with hexagonal structure (hydrothermal growth; cubic dimension: 10 × 10 × 0.5 mm; light yellow appearance) was used as the substrate because of its excellent optical anisotropy in the c-axis and over 95% high transmittance. Cobalt is a ferromagnetic material that also has a hexagonal structure with high stability in a vacuum. The use of ZnO is designed for developing further high-quality hexagonal Co thin films. The atomic flux of wound Co filament was evaporated in UHV by resistive heating. The stable flux was controlled externally by a power supply with constant current. The deposition rate was estimated at around 0.5 nm per hour. The two materials have high planar lattice mismatch (~22.8%) according to the lattice constants of Co and ZnO, which are 0.251 and 0.325 nm, respectively [80, 81]. Strain in the hexagonal bulk structures may exists in the development of crystalline Co. Indeed, no surface structure pattern was detected by the low-energy electron diffraction technique. The variation of strain-induced magnetic crystalline anisotropy is expected to be observed in this polar scan method.

Furthermore, typical ferromagnetic metals, such Fe, Co and Ni, all have large specific Faraday rotations. Because of the large absorption coefficients among these materials, the first choice in opto-communication applications that require high transmission is excluded [82]. The reason for use of Co films with a thickness down to around 2 nm is to prevent huge absorption and to retain the transparency of the sample. The thickness of the magnetic layer is just the order of several interatomic distances. Such a scale, beyond the scope of macroscopic phenomena, may have new physics. This is the point that is expected to show novel properties through MOFE observation in the ultrathin material system.

5. Problems and discussion

5.1. Magneto-optical physics in UHV and compensation effect of optical components

The MOFE measurement in UHV was conducted by an incidence of the p-polarization (TM) wave, where the polarization of an electromagnetic wave interacts with the magnetized surface/interface at which the electric field vector lies on the plane of incidence [83]. Similar to the setup of the SMOKE technique, the analyzer detected the intensity deviated from the s-polarization (TE) wave, where the polarization of an electromagnetic wave received from the magnetized surface/interface at which the electric field vector is perpendicular to the plane of incidence [49].

In addition, many view ports consisting of crystalized glass, i.e. quartz, produce a background birefringence when the laser light passes from the ambient conditions to the vacuum and then out of the chamber. To eliminate the birefringence, a quarter-wave plate is generally placed in front of the optical detector for typical SMOKE apparatus. However, the retardation of electromagnetic waves is varied with the angle of incidence. This effect can be eliminated by tuning the analyzer. The search for the s-minimum intensity for the analyzer is the key point. In optics, most of the p-component intensity is eliminated when a minimum intensity is reached in the detection of the analyzer. This is not only the case if the incident angle is changed. It can be seen clearly that the compensation effect is independent of the initial surface condition used in the subsequent growth of the Co films and the sputtering of the Co film by N⁺ plasma, as shown in Fig. 6.According to the oscillation curves shown in Fig. 6, the compensation effect of the analyser depends only on the initial clean ZnO surfaces. This effect was compared by two series experiments: growth process of ultrathin film and sputtering process of N⁺. Until the end, the substrate was the same one. It is worth to notice that the surface condition depends on the cleaning process. Although the ZnO(0001) substrate is the same, surface condition in 6(a) and 6(b) is different. The surface condition affects the further received optical signals. But it did not alter the optical properties of originally anisotropic crystal. The optical periodicity depends on the substrate thickness as indicated in Eq. (1). This interesting phenomenon can be further checked and may have potential to evaluate any substrate before used. Therefore, this phenomenon reminds us again the importance of the substrate. The deviation angle, shifted from the s-minimum intensity (0° corresponds to the analyzer at normal incidence), is independent of further growth of Co (Fig. 6(a)) and post-sputtering of Co (Fig. 6(b)).

 

Fig. 6 Deviation angle shifted to the s-minimum analyzer at normal incidence. The data are acquired from the sample conditions: (a) deposition of Co film and increase of thickness up to 2.3 nm and (b) the 4-nm Co film was sputtered by 1-keV N⁺ plasma (with time of 113 and 225 s). Dash lines L and P are corresponding to the longitudinal and perpendicular field configurations.

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5.2. Layered dependent magnetic anisotropy of multilayered structure

Multilayered types of metallic or semiconductor films are required in modern electronic devices. One of the key technologies, ion implantation, is usually used to adjust the electronic, optical and magnetic properties. Recently, the formation of high stiffness cobalt nitride (CoN_x) magnetic films has been evaluated by MOFE [77]. The magnetic phase of Co is gradually transformed to CoN_x for the top surface layers by nitrogen ion irradiation. The material exhibits high perpendicular magnetic anisotropy, although the evolution of in-plane anisotropy has been observed in a previous study of the initial growth of Co film [78]. The thickness over 2 nm switches to out-of-plane in magnetic anisotropy. It emerges a debate that the coexistence of the saturation hysteresis loops in the plane and out of the plane was simultaneously detected. Thus, the determination of the magnetic easy axis becomes a problem. In order to further prove the details of magnetic anisotropy from the surface, further studies about the 3D anisotropy determined by AMOFE are imperative.

The evolution of coercivity (H_c) can help focus this issue. Returning to the initial conditions of 4-nm Co film, it is deposited via step deposition with eight-hour breaks. The purpose of the break is for the MOFE measurements. Each deposition continues for one hour, therefore, the deposition rate is estimated at 1 nm per hour. Thickness-dependent coercivity was once observed during the growth of Co films. Figure 7 shows the evolution of H_c values versus the Co thickness by L-MOFE and P-MOFE measurements. It is apparent that the critical thickness is located at around 2 nm. Below 2 nm, in-plane anisotropy is dominated. Out-of-plane signal greatly enhanced when thickness is larger than 2 nm. Instead, unusual in-plane anisotropy saturates. Formation of a layer-dependent anisotropy may approach this problem. The transmitted Faraday effect measurement observes all layers with angle of incidence and rotation of field direction. If bottom layer prefers in-plane anisotropy with low coercivity and top layer gradually prefers out-of-plane anisotropy with high coercivity. According to the thermally activated studies at Co/ZnO interfaces, few nano-scale clusters may form when thickness of Co is small than 1 nm [84]. The result is fit to our observation due to the absence of magnetic behavior under 1 nm [78]. We speculate the Co growth may coherently follow the lattice of ZnO and the surface morphology of that condition is similar to the striped structure of Co on the m-plane ZnO crystal [85]. Therefore, room temperature coherent growth of Co prefers and exhibits in-plane anisotropy in the L-MOFE experiment. Beyond 2 nm, H_c value along out-of-plane direction grows rapidly. Large bulk-like clusters with perpendicular anisotropy along c-axis may form on the surface. Under the break condition during the measurements, the film may form a discontinuous multilayered structure. Due to the transmission signals totally received by the Faraday effect, progressive magneto-optic property can be monitored. Through the deviation of angle dependence, we have found that the coercivity along out-of-plane direction enhanced beyond 2 nm. That is why we boldly assume an out-of-plane anisotropy on the top surface. The schematic diagram for the multilayer system with different easy axes is proposed in Fig. 8.The structure with four slabs is assumed. Each slab has different magnetic anisotropy. In-plane anisotropy dominates under 2 nm and out-of-plane anisotropy dominates over 2 nm. Magnetic dead layer or the Curie temperature lower than room temperature may result in the absence of magnetic behavior. The microstructure needs further systematic studies and is beyond this study. However, each layer thickness is only 1~2 monolayers thick in the multilayer model. According to the literature, domain size about one-sixth laser wavelength or larger can be resolved without interference for magneto-optic measurements [86]. If total layer thickness is down to 1 nm or less, magnetic domain is not easy to form and cannot be resolved by any magneto-optic measurements. We assume that each slab has different easy axis orientation according to the result of experiment procedure. The magnetic anisotropy in each slab is therefore sensitive to surface composition. N⁺ ions were used to observe this variation of magnetic anisotropy on top of the surface. In the AMOFE observation, Fig. 8(a) shows high H_c values that obviously enhance at the P-MOFE side. The configuration just corresponds to the perpendicular field applied normal to the surface. When sputtering time increases, the coercivity in this region obviously declines. It can be speculated that the large enhancement in out-of-plane coercivity originates from the top layer of Co. Because of the low surface energy preferring the surface, the topmost surface layer exhibits nucleation behavior that reflects the large coercivity [87]. Recently, we observed the magnetic phase transition of CoN_x material and concluded the phase transforming to paramagnetic phase if nitrogen constituent is higher [77]. The continuous reduction in H_c means high possibility of CoN_x composition is in the interstitial alloy phases. An argument originates from the in-plane and out-of-plane hysteresis loops as thicknesses larger than 2.3 nm are all squared [60]. Typically, it is hard to define the exact location of easy axis. The only difference is that the coercivity measured in the perpendicular field is larger than that in the longitudinal field. About one-fourth wide of angles with high H_c values focusing at the P-MOFE side was observed. The coercivity value only in the out-of-plane field grows with thickness.

 

Fig. 7 Thickness-dependent coercivity measured from MOFEs along in-plane and out-of-plane magnetic field under the Co growth. Critical thickness is apparent at 2 nm. Below 2 nm, only in-plane magnetic anisotropy was observed and coercivity can be measured.

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Fig. 8 (a) Angle-resolved coercivity of 4 nm of Co recorded in different sputtered condition by N⁺ ion irradiation over a short period (sputtering energy and time are indicated on the figure). Parts of data without H_c are also indicated. (b) Possible model of multilayered structure with layer-dependent anisotropy by MOFE. Bottom magnetic layer close to substrate with low H_c values along in-plane magnetic easy axis and surface magnetic layer with high H_c values along out-of-plane easy axis form a layered magnetic structure.

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To verify the assumption that the top layer anisotropy is different from the underlying one, we tried an experimental method via N⁺ sputtering to affect the top surface properties. It is quite effective. In our previous study, implantation of N⁺ into Co to form magnetic nitrides depending on the ion energy and irradiation time was found [88]. An increase in the amount of N in the Co films by N⁺ dc plasma contributes to a magnetic phase transforming from ferromagnetic to paramagnetic [77]. In this case, more ions interact with the top of the surface Co and gradually form the CoN_x phase as the irradiation time increases. That is why the curve of coercivity greatly enhanced in P-MOFE side shows a stepped decrease with sputtering time. The coercivity other than by P-MOFE measurement finally saturates at around 50 Oe till the L-MOFE side. The boundary thickness of perpendicular magnetic anisotropy is around 2 nm, which is according to the recent results of epitaxial growth of Co on ZnO(0001) [78]. In-plane anisotropy is strongly dominant in the initial growth when the film thickness is less than 2 nm. Large spin pinning effect dominates this regime, which the spins prefer along the in-plane easy axis in the underlayer of multilayered model. Perpendicular spins corresponding to the out-of-plane easy axis then locate on the top layer. According to the MOFE measurement, a schematic diagram is modelled in Fig. 8(b).

The enhancement of coercivity may originate from the surface anisotropy, even though it seems to conflict with one sentence that have been mentioned: “Faraday effect in a particular material is independent of the direction of wave propagation” [82]. According to our observation from longitudinal to perpendicular magnetic field with 1° incidence, this description has been excluded. We propose a model of possible magnetic structure to simulate that the in-plane anisotropy dominates the bottom layer and out-of-plane anisotropy dominates the surface layer. The bottom layer prefers in-plane anisotropy because of the pinning layer effect and the surface layer prefers out-of-plane anisotropy because of the bulk nucleation effect. The film established a multilayer structure when the film deposition was interrupted for the purpose of in situ measurement in a vacuum. Saturation of the constant coercivity around 50 Oe in Fig. 8(a) occupies almost two third of the 120 measured angles. This means that the number of in-plane spin layers is greater than that of out-of-plane spin layers. The background coercivity originates from the in-plane spin layers. In magnetic geometry, spin domains in the plane may be highly isotropic because of the large symmetry extending infinitely on the surface plane. Most of the spin domains and Néel walls rotate freely on the in-plane field in the ultrathin length scale. However, the perpendicular domains with 180° Bloch domain walls should gradually grow if the bulk phase of thick Co film is formed. The easy axis of bulk-like Co is proposed along the c-axis. This is consistent with our inference that thick film approaches the bulk nucleation effect. The formation of out-of-plane anisotropic spins, following the crystallinity of Co, emerges rapidly with thicker films. In the 4 nm Co/ZnO(0001) sample, perpendicular anisotropy with hexagonal structure on the in-plane anisotropic layers is possible. That is why we observe the saturation hysteresis loops occurring at two easy-axis directions. It can simultaneously explain why the coercivity grows at the P-MOFE side when thicknesses are greater than ~2 nm (Fig. 7 and in Ref [78].).

6. Conclusion

Angle-dependent magneto-optic Faraday effect measurements has successfully performed in the ultrahigh vacuum system for the ultrathin magnetic Co film on an optically anisotropic ZnO(0001) substrate. The success includes the following two points: 1. ultrathin film on an optically transparent substrate is suitable for a study by MOFE and 2. magneto-optic effect of film coupled with optical properties of substrate induces the reversal behavior of hysteresis loops. Through the observation of incident angle measurement, we can understand more about the magnetic anisotropy information other than the typical configurations, longitudinal and polar field directions. The result is conducive to verify the uniaxial magnetic anisotropy and interface properties between optical substrates in similar systems. It can also help to understand the unsolved problem from surfaces and interfaces of ultrathin type of materials. Due to the total optical signals received from Faraday effect measurement, an oscillation behavior of optical and magneto-optical behaviors due to the variation of phase retardation from magnetic film and optical substrate is observed. The result can be considered to apply for any system which needs to combine the magnetic and optical information.