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

Interlayer exchange coupling (IEC) between two ferromagnetic (FM) layers separated by a non-magnetic interlayer has been intensively studied both theoretically^1–51. S. S. P. Parkin, N. More, and K. P. Roche, Physical Review Letters 64, 2304 (1990). https://doi.org/10.1103/physrevlett.64.23042. S. S. P. Parkin, Physical Review Letters 67, 3598 (1991). https://doi.org/10.1103/physrevlett.67.35983. P. Bruno, Physical Review B 49, 13231 (1994). https://doi.org/10.1103/physrevb.49.132314. P. Bruno, Physical Review B 52, 411 (1995). https://doi.org/10.1103/physrevb.52.4115. P. Bruno, Journal of Physics: Condensed Matter 11, 9403 (1999). https://doi.org/10.1088/0953-8984/11/48/305 and experimentally.^6–146. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, Physical Review Letters 57, 2442 (1986). https://doi.org/10.1103/physrevlett.57.24427. M. T. Johnson, S. T. Purcell, N. W. E. McGee, R. Coehoorn, J. aan de Stegge, and W. Hoving, Physical Review Letters 68, 2688 (1992). https://doi.org/10.1103/physrevlett.68.26888. J. Mathon, M. Villeret, A. Umerski, R. B. Muniz, J. d’Albuquerque e Castro, and D. M. Edwards, Physical Review B 56, 11797 (1997). https://doi.org/10.1103/physrevb.56.117979. J. Faure-Vincent, C. Tiusan, C. Bellouard, E. Popova, M. Hehn, F. Montaigne, and A. Schuhl, Physical Review Letters 89, 107206 (2002). https://doi.org/10.1103/physrevlett.89.10720610. H. Tokano, H. Yanagihara, and E. Kita, Journal of Applied Physics 97, 016103 (2005). https://doi.org/10.1063/1.182621211. T. Katayama, S. Yuasa, J. Velev, M. Y. Zhuravlev, S. S. Jaswal, and E. Y. Tsymbal, Applied Physics Letters 89, 112503 (2006). https://doi.org/10.1063/1.234932112. W. Skowroński, T. Stobiecki, J. Wrona, K. Rott, A. Thomas, G. Reiss, and S. van Dijken, Journal of Applied Physics 107, 093917 (2010). https://doi.org/10.1063/1.338799213. H. Yanagihara, M. Myoka, D. Isaka, T. Niizeki, K. Mibu, and E. Kita, Journal of Physics D: Applied Physics 46, 175004 (2013). https://doi.org/10.1088/0022-3727/46/17/17500414. T. Nakano, M. Oogane, and Y. Ando, Japanese Journal of Applied Physics 57, 073001 (2018). https://doi.org/10.7567/jjap.57.073001 In fact, it is an important phenomenon that is exploited in modern spintronics.^15–1715. G. Chen, A. Mascaraque, A. T. N’Diaye, and A. K. Schmid, Applied Physics Letters 106, 242404 (2015). https://doi.org/10.1063/1.492272616. Y.-C. Lau, D. Betto, K. Rode, J. M. D. Coey, and P. Stamenov, Nature Nanotechnology 11, 758 (2016). https://doi.org/10.1038/nnano.2016.8417. K. Yakushiji, A. Sugihara, A. Fukushima, H. Kubota, and S. Yuasa, Applied Physics Letters 110, 092406 (2017). https://doi.org/10.1063/1.4977565 The origin of IEC lies in the difference of spin-polarized reflection at the FM interface, as found by modelling the system as a quantum well.⁴4. P. Bruno, Physical Review B 52, 411 (1995). https://doi.org/10.1103/physrevb.52.411 If the insertion layer is metallic, the IEC oscillates between the ferromagnetic (FM) and the antiferromagnetic (AFM) coupling as a function of the interlayer thickness.^6–86. P. Grünberg, R. Schreiber, Y. Pang, M. B. Brodsky, and H. Sowers, Physical Review Letters 57, 2442 (1986). https://doi.org/10.1103/physrevlett.57.24427. M. T. Johnson, S. T. Purcell, N. W. E. McGee, R. Coehoorn, J. aan de Stegge, and W. Hoving, Physical Review Letters 68, 2688 (1992). https://doi.org/10.1103/physrevlett.68.26888. J. Mathon, M. Villeret, A. Umerski, R. B. Muniz, J. d’Albuquerque e Castro, and D. M. Edwards, Physical Review B 56, 11797 (1997). https://doi.org/10.1103/physrevb.56.11797 On the other hand, if the insertion layer is insulating, the electron Fermi wavenumber (k_F) is imaginary, and the IEC simply decays with the interlayer thickness.^9,11–139. J. Faure-Vincent, C. Tiusan, C. Bellouard, E. Popova, M. Hehn, F. Montaigne, and A. Schuhl, Physical Review Letters 89, 107206 (2002). https://doi.org/10.1103/physrevlett.89.10720611. T. Katayama, S. Yuasa, J. Velev, M. Y. Zhuravlev, S. S. Jaswal, and E. Y. Tsymbal, Applied Physics Letters 89, 112503 (2006). https://doi.org/10.1063/1.234932112. W. Skowroński, T. Stobiecki, J. Wrona, K. Rott, A. Thomas, G. Reiss, and S. van Dijken, Journal of Applied Physics 107, 093917 (2010). https://doi.org/10.1063/1.338799213. H. Yanagihara, M. Myoka, D. Isaka, T. Niizeki, K. Mibu, and E. Kita, Journal of Physics D: Applied Physics 46, 175004 (2013). https://doi.org/10.1088/0022-3727/46/17/175004 Trilayer systems comprising FM oxide layers such as Fe/MgO/Fe₃O₄,^13,1813. H. Yanagihara, M. Myoka, D. Isaka, T. Niizeki, K. Mibu, and E. Kita, Journal of Physics D: Applied Physics 46, 175004 (2013). https://doi.org/10.1088/0022-3727/46/17/17500418. H. Yanagihara, H. Kamita, S. Honda, J. Inoue, E. Kita, H. Itoh, and K. Mibu, Physical Review B 91, 174423 (2015). https://doi.org/10.1103/physrevb.91.174423 Fe/MgO/γ-Fe₂O₃,¹³13. H. Yanagihara, M. Myoka, D. Isaka, T. Niizeki, K. Mibu, and E. Kita, Journal of Physics D: Applied Physics 46, 175004 (2013). https://doi.org/10.1088/0022-3727/46/17/175004 Fe₃O₄/TiN/Fe₃O₄,¹⁹19. A. Orozco, S. B. Ogale, Y. H. Li, P. Fournier, E. Li, H. Asano, V. Smolyaninova, R. L. Greene, R. P. Sharma, R. Ramesh, and T. Venkatesan, Physical Review Letters 83, 1680 (1999). https://doi.org/10.1103/physrevlett.83.1680 and La_2/3Ba_1/3MnO₃/LaNiO₃/La_2/3Ba_1/3MnO₃,²⁰20. K. R. Nikolaev, A. Y. Dobin, I. N. Krivorotov, W. K. Cooley, A. Bhattacharya, A. L. Kobrinskii, L. I. Glazman, R. M. Wentzovitch, E. D. Dahlberg, and A. M. Goldman, Physical Review Letters 85, 3728 (2000). https://doi.org/10.1103/physrevlett.85.3728 also exhibit IEC.

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,^21,2221. D. Navas, J. Torrejon, F. Béron, C. Redondo, F. Batallan, B. P. Toperverg, A. Devishvili, B. Sierra, F. Castaño, K. R. Pirota, and C. A. Ross, New Journal of Physics 14, 113001 (2012). https://doi.org/10.1088/1367-2630/14/11/11300122. L. Fallarino, V. Sluka, B. Kardasz, M. Pinarbasi, A. Berger, and A. D. Kent, Applied Physics Letters 109, 082401 (2016). https://doi.org/10.1063/1.4960795 and more experiments are needed to gain a deeper understanding of the IEC. Recently, Fallarino et al.²²22. L. Fallarino, V. Sluka, B. Kardasz, M. Pinarbasi, A. Berger, and A. D. Kent, Applied Physics Letters 109, 082401 (2016). https://doi.org/10.1063/1.4960795 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 K_i in a trilayer system composed of two FM layers having orthogonal magnetic easy axes. The structure of the trilayer system is a MgO substrate/Co_0.75Fe_2.25O₄/MgO/Fe. An epitaxial Co_0.75Fe_2.25O₄ (CFO) film grown on MgO(001) exhibits large coercivity and PMA due to t_2g-level splitting caused by a local lattice symmetry enhancing the spin-orbit interaction.^23–2623. M. Tachiki, Progress of Theoretical Physics 23, 1055 (1960). https://doi.org/10.1143/ptp.23.105524. J. C. Slonczewski, Physical Review 110, 1341 (1958). https://doi.org/10.1103/physrev.110.134125. J. Inoue, H. Itoh, M. A. Tanaka, K. Mibu, T. Niizeki, H. Yanagihara, and E. Kita, IEEE Transactions on Magnetics 49, 3269 (2013). https://doi.org/10.1109/tmag.2013.224370326. T. Niizeki, Y. Utsumi, R. Aoyama, H. Yanagihara, J. Inoue, Y. Yamasaki, H. Nakao, K. Koike, and E. Kita, Applied Physics Letters 103, 162407 (2013). https://doi.org/10.1063/1.4824761 While CFO and MgO are good insulators, Fe is a metal; thus, only the changes in magnetization of the latter can be detected by the anomalous Hall effect (AHE).²⁷27. N. Nagaosa, J. Sinova, S. Onoda, A. H. MacDonald, and N. P. Ong, Reviews of Modern Physics 82, 1539 (2010). https://doi.org/10.1103/revmodphys.82.1539

All samples were grown by reactive radio-frequency magnetron sputtering (ES-250MB by Eiko Engineering Co., Ltd.).²⁸28. H. Koizumi, S. Sharmin, K. Amemiya, M. S. Sakamaki, J. Inoue, and H. Yanagihara, Physical Review Materials 3, 24404 (2019). https://doi.org/10.1103/physrevmaterials.3.024404 The final film structure and layer thickness (in parentheses) are MgO(001) substrate/Co_0.75Fe_2.25O₄ (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_0.75Fe_2.25O₄ (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 O₂/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. The AHE was measured by PPMS using a Keithley 6221 DC current source and a Keithley 2182 nanovoltmeter. Both VSM and AHE experiments were carried out at room temperature with an external magnetic field of up to 7 T along the MgO[001] direction.

Figure 2 shows the MH loop of a single-layer CFO film grown on the MgO(001) substrate. The saturation magnetization (M_S) 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.^26,2926. T. Niizeki, Y. Utsumi, R. Aoyama, H. Yanagihara, J. Inoue, Y. Yamasaki, H. Nakao, K. Koike, and E. Kita, Applied Physics Letters 103, 162407 (2013). https://doi.org/10.1063/1.482476129. D. T. Margulies, F. T. Parker, M. L. Rudee, F. E. Spada, J. N. Chapman, P. R. Aitchison, and A. E. Berkowitz, Physical Review Letters 79, 5162 (1997). https://doi.org/10.1103/physrevlett.79.5162 The film squareness ratio (SR), coercivity (μ₀H_c) and saturation field (μ₀H_S) are 0.85, 0.91 T and 1.5 T, respectively. Thus, because of the large μ₀H_c and the high SR, CFO can be considered a pinned layer.

In order to evaluate size effect in M_S 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.³⁰30. R. Zhang and R. F. Willis, Physical Review Letters 86, 2665 (2001). https://doi.org/10.1103/physrevlett.86.2665 The M_S 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 (H_ex) originated from the IEC in addition to the external magnetic field (H_ext). Therefore, the effective magnetic field (H_eff) acting on the Fe layer can be described as H_eff = H_ext + H_ex. When the magnetic field goes to zero from positive high values, the remanent state ρ_AHE(0) is negative, meaning that H_ex < 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 (K_i) can be determined from the equations^31–3331. P. J. H. Bloemen, H. W. van Kesteren, H. J. M. Swagten, and W. J. M. de Jonge, Physical Review B 50, 13505 (1994). https://doi.org/10.1103/physrevb.50.1350532. M. T. Johnson, P. J. H. Bloemen, F. J. A. den Broeder, and J. J. de Vries, Reports on Progress in Physics 59, 1409 (1996). https://doi.org/10.1088/0034-4885/59/11/00233. H. Koizumi, S. Kobayshi, M. Hagihara, and H. Yanagihara, (2019), manuscript in preparation.

$$J={\int }_0^{M_{S,\mathrm{F}\mathrm{e}}}{\mu }_0{H}_{\mathrm{e}\mathrm{x}}{t}_{\mathrm{F}\mathrm{e}}dM={\mu }_0{H}_{\mathrm{e}\mathrm{x}}{t}_{\mathrm{F}\mathrm{e}}{M}_{S,\mathrm{F}\mathrm{e}},$$

(1)

$$K_i=-{\int }_0^{M_{S,\mathrm{F}\mathrm{e}}}{\mu }_0\left(H\left(M\right)+H_{\mathrm{e}\mathrm{x}}\right)t_{\mathrm{F}\mathrm{e}}dM+\frac{1}{2}{\mu }_0{M}_{S,\mathrm{F}\mathrm{e}}^2{t}_{\mathrm{F}\mathrm{e}},$$

(2)

where t_Fe and M_S,Fe are the Fe layer thickness and saturation magnetization, respectively. Since a single Fe layer has no coercivity for out-of-plane magnetization, −μ₀H_ex 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, $K_u=-\frac{1}{2}{\mu }_0{M}_{S,\mathrm{F}\mathrm{e}}^2$. Thus, K_i is determined by the difference in anisotropy energy and corresponds to the blue-shaded area of Fig. 3. Note that if FM coupling exists, μ₀H_ex is positive. Note also that Eq.(1) is valid for both AFM and FM coupling.

The dependence of J and K_i (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/m². This indicates that both direct and indirect coupling are AFM. In the quantum well model of Ref. 44. P. Bruno, Physical Review B 52, 411 (1995). https://doi.org/10.1103/physrevb.52.411, 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.¹¹11. T. Katayama, S. Yuasa, J. Velev, M. Y. Zhuravlev, S. S. Jaswal, and E. Y. Tsymbal, Applied Physics Letters 89, 112503 (2006). https://doi.org/10.1063/1.2349321 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.³⁴34. L. Néel, Comptes Rendus Hebdomadaires des Seances de l Academie des Sciences 255, 1545 (1962). 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 K_i determined by Eq. (2). As seen from Fig. 5, K_i 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,³⁵35. J. W. Koo, S. Mitani, T. T. Sasaki, H. Sukegawa, Z. C. Wen, T. Ohkubo, T. Niizeki, K. Inomata, and K. Hono, Applied Physics Letters 103, 192401 (2013). https://doi.org/10.1063/1.4828658 consistent with our results. In general, determining K_i 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 K_i from the area difference between the two, finding that it is negative at the CFO-Fe interface, with a value of −1.1 mJ/m².

In summary, we investigated the interlayer exchange coupling and the interface magnetic anisotropy in Co_0.75Fe_2.25O₄/MgO/Fe(001) by measuring the anomalous Hall effect. Since we can measure the MH loop only in the Fe layer by AHE, J and K_i are determined from the exchange field and the evolution of the MH loop of the Fe layer, respectively. By studying the IEC dependence on the interlayer MgO thickness, a strong AFM coupling was observed between Co_0.75Fe_2.25O₄ and Fe. The strongest coupling was found in the absence of the MgO interlayer, with a value of −1.1 mJ/m². Finally, we measured a K_i of −1.1 mJ/m² between the Co_0.75Fe_2.25O₄ and the Fe layer, being one of the few magnetic anisotropy measurements reported between two ferromagnetic layers. In the system with crossed IMA and PMA, strong exchange coupling at the interface can lead to PMA for IMA film. However, in our system, exchange coupling is not enough for the Fe layer to exhibit PMA.