Interlayer exchange coupling and interface magnetic anisotropy with crossed in-plane and perpendicular magnetic anisotropies

We investigated interlayer exchange coupling (IEC) and interface magnetic anisotropy ( K i ) between two ferromagnetic layers with crossed in-plane and perpendicular magnetic anisotropies separated by a non-magnetic spacer by using the anomalous Hall effect (AHE). The sample consisted of a Co 0.75 Fe 2.25 O 4 layer with perpendicular magnetic anisotropy and a Fe layer with in-plane anisotropy, separated by a MgO layer with variable thickness. Since Co 0.75 Fe 2.25 O 4 and MgO are insulators, the AHE signal only reflects the magnetization process of Fe. From this, we determined both IEC and K i . A strong antiferromagnetic IEC was confirmed between Co 0.75 Fe 2.25 O 4 and Fe. The strongest IEC of − 1.1 mJ/m 2 was observed for directly coupled Fe and Co 0.75 Fe 2.25 O 4 for which K i was − 1.1 mJ/m 2 .

In most cases, IEC has been investigated in a system with individual FM layers having collinear magnetic easy axes, either perpendicular or in-plane. However, few reports are available for systems where the FM materials have non-collinear or orthogonally crossed magnetic easy axes, 21,22 and more experiments are needed to gain a deeper understanding of the IEC. Recently, Fallarino et al. 22 reported the observation of IEC between a CoFeB layer with in-plane magnetic anisotropy (IMA) and a Co/Ni one with perpendicular magnetic anisotropy (PMA) by using ferromagnetic resonance (FMR). The FM-AFM oscillation behavior was also observed.
In this study, we investigated both IEC and Ki in a trilayer system composed of two FM layers having orthogonal magnetic easy axes. The structure of the trilayer system is a

II. EXPERIMENTAL METHODS
All samples were grown by reactive radio-frequency magnetron sputtering (ES-250MB by Eiko Engineering Co., Ltd.). 28 The final film structure and layer thickness (in parentheses) are MgO(001) substrate/Co 0.75 Fe 2.25 O 4 (50 nm)/MgO (0-2 nm)/Fe (1 nm)/Au (2 nm), as shown in Fig. 1. Prior to film growth, the MgO(001) substrate was sequentially cleaned by ultrasonic treatment in acetone, ethanol, and de-ionized water for 5 min each. For the fabrication of Co 0.75 Fe 2.25 O 4 (CFO), we used 2-inch alloy target with the desired composition of Co: Fe = 1:3. The film was grown at a temperature of 500 ○ C with an O 2 /Ar flow ratio of approximately 0.71. After depositing CFO, a wedge-shaped MgO interlayer with continuously increasing thickness was grown at 150 ○ C by using a moving mask and a ceramic target. Finally, the Fe and Au layers were deposited at room temperature. The multilayer structure was characterized by reflection high-energy electron diffraction (RHEED), X-ray reflectivity (XRR, by Rigaku Smart Lab, using Co Kα radiation) and X-ray diffraction (XRD). Perpendicular magnetic hysteresis (MH) loops were measured by using a vibrating sample magnetometer (VSM), which is part of a physical property measurement system (PPMS, by Quantum Design). For Hall measurements, the films were patterned into Hall bars by photolithography (200 μm width × 8000 μm length, applying 1 mA to the Hall bar) and Ar ion milling. Then, Cr and Au electrodes were sputtered on top. The current is designed to flow parallel to the MgO thickness gradient, and the Hall voltage perpendicular (vertical) to it. The final Hall bar pattern is shown in Fig. 1 Figure 2 shows the MH loop of a single-layer CFO film grown on the MgO(001) substrate. The saturation magnetization (MS) of the CFO films was approximately 330 kA/m, a value slightly smaller than its bulk counterpart (≈ 430 kA/m). This suggests the existence of a magnetic dead layer at the interface between MgO(001) and the CFO film, which can be related to the high density anti-phase boundaries in a spinel structure. 26,29 The film squareness ratio (SR), coercivity (μ 0 Hc) and saturation field (μ 0 HS) are 0.85, 0.91 T and 1.5 T, respectively. Thus, because of the large μ 0 Hc and the high SR, CFO can be considered a pinned layer.

III. RESULTS AND DISCUSSION
In order to evaluate size effect in MS of the Fe layer, we fabricated a MgO sub./Fe (1 nm)/Au multilayer by depositing the metals at room temperature and measured the magnetization by VSM at 300 K. 30 The MS at 300 K is 1360 kA/m, approximately 0.80 times that of bulk Fe. Figure 3 shows the ρ AHE (H) loop of MgO sub./CFO/Fe/Au. In the magnetization loop perpendicular to the Fe layer plane, a clear hysteresis is opened even for the hard axis of the Fe layer. This means that Fe layer feels an exchange field (Hex) originated from the IEC in addition to the external magnetic field (Hext). Therefore, the effective magnetic field (H eff ) acting on the Fe layer can be described as H eff = Hext + Hex. When the magnetic field goes to zero from positive high values, the remanent state ρ AHE (0) is negative, meaning that Hex < 0 and that antiferromagnetic coupling (J < 0) exists between the Fe and CFO layers. In other words, IEC can make the preferential axis of the Fe layer perpendicular to the plane if the Fe layer is sufficiently thin, since the exchange field at the interface acts along the out of plane direction.
The IEC energy (J) and the interface magnetic anisotropy (Ki) can be determined from the equations 31-33 where t Fe and MS ,Fe are the Fe layer thickness and saturation magnetization, respectively. Since a single Fe layer has no coercivity for out-of-plane magnetization, −μ 0 Hex is equal to the x-axis intersect of ρ AHE (H). Therefore, J corresponds to the red-shaded area of Fig. 3.
Here, we assumed that the Fe layer has only the shape magnetic anisotropy as the bulk component of the magnetic anisotropy, Ku = − 1 2 μ 0 M 2 S,Fe . Thus, Ki is determined by the difference in anisotropy energy and corresponds to the blue-shaded area of Fig. 3. Note that if FM coupling exists, μ 0 Hex is positive. Note also that Eq.(1) is valid for both AFM and FM coupling.
The dependence of J and Ki (Eqs. (1) and (2)) on the thickness t MgO of the MgO interlayer between the CFO and Fe layers is shown in Fig. 4 and Fig. 5, respectively. We first consider IEC. A positive J value corresponds to FM coupling, while a negative one corresponds to AFM coupling. In our system, two types of IEC can exist: (i) direct coupling between CFO and Fe, and (ii) indirect coupling between CFO and Fe through MgO. From Fig. 4, it is seen that the coupling is AFM for almost all t MgO . Furthermore, J increases linearly with t MgO from its lowest value of −1.1 mJ/m 2 . This indicates that both direct and indirect coupling are AFM. In the quantum well model of Ref. 4, J changes monotonically for an insulating interlayer, which is at least qualitatively consistent with our results. However, around t MgO = 1 nm, we observed a weak FM coupling. A similar phenomenon has been reported by Katayama et al. 11 for Fe/MgO/Fe. The authors attributed this behavior to the oxygen vacancies in the MgO interlayer. Another possible origin of the weak FM coupling observed is the orange peel effect. 34 In addition, J changes almost linearly with t MgO . These results indicate that the growth mode of the MgO interlayer is island growth like.
Next, we consider the interface magnetic anisotropy Ki determined by Eq. (2). As seen from Fig. 5, Ki is initially negative and changes sign as the MgO film thickness increases. This means that although the interface anisotropy between CFO and Fe is negative, it is positive between MgO and Fe. A large interface PMA has been previously reported between a Fe and MgO layer, 35 consistent with our results. In general, determining Ki between two FM layers is not straightforward, because it is difficult to measure the magnetic hysteresis of only one FM layer. However, in our system one FM layer is an insulator characterized by PMA, and the other one is a conductor characterized by IMA. The magnetic anisotropy energy of the metal layer corresponds to the area of the out-of-plane MH loop. Thus, we can determine Ki from the area difference between the two, finding that it is negative at the CFO-Fe interface, with a value of −1.1 mJ/m 2 .

IV. CONCLUSIONS
In summary, we investigated the interlayer exchange coupling and the interface magnetic anisotropy in Co 0. 75