Perpendicular magnetic anisotropy of an ultrathin Fe layer grown on NiO(001)

First, we investigated the valence states and composition, as well as the lattice parameters of NiO, depending on the O₂ flow rate during the growth processes. As shown in Fig. 2(a), clear Laue fringes are observed around the 002 diffraction of the XRD patterns, indicating that the NiO films are epitaxially grown with a (001) orientation and had a sufficiently smooth surface without incoherent lattice distortion at any O₂ flow rate. In addition, the RHEED images of all samples exhibited typical streak patterns (Fig. 2(b)), implying that the film surfaces are atomically flat and barely distorted, which is consistent with the observation of the Laue fringes. Figure 2(c) summarizes the lattice constants normal to the film plane of $c_{\mathrm{NiO}}$ as a function of the O₂ flow rate, as determined by 002 reflection positions of the XRD patterns. $c_{\mathrm{NiO}}$ is largely the same as that of the bulk value of NiO (4.176 Å)Navrotsky (1973) for O₂ flow rates $\leq$ 1.0 sccm, and $c_{\mathrm{NiO}}$ becomes greater than that of the bulk value of MgO (4.216 Å) for O₂ flow $\geq$ 2.0 sccm, as shown in Fig. 2(c).

As shown in Fig. 2(d), the RSM measurements indicate that the lattice constants along the in-plane direction of NiO(001) mostly matched that of MgO of the substrate at any O₂ flow rate, implying $a_{\mathrm{NiO}}\approx$4.22 Å. Moreover, clear fringe patterns were observed around NiO 113 in both the films, suggesting that all the NiO films were coherently distorted owing to epitaxial stress. Moreover, the critical thickness of the misfit relaxation was greater than 20 nm for all the films. Because the in-plane lattice constants are locked to the MgO(001) substrate, the volume of the unit cell varies with the O₂ flow.

Similar results have been reported in previous studies Chen et al. (2010); Wang et al. (2017); Ferreira et al. (1996). With increasing oxygen in the film growth process, Ni²⁺ ions are replaced by Ni³⁺ ions and vacancies at the Ni-sites, resulting in the growth of non-stoichiometric NiO(001) films. We also performed XPS measurements of the NiO(20 nm)/MgO(001) films without Fe or Cr layers grown at various O₂ flow rates. The relative composition of oxygen and a trace of Ni³⁺ in NiO increased with the increase in the O₂ flow rate, consistent with previous XPS measurementsOswald and Brückner (2004) and the structural analysis mentioned.

To study the magnetic anisotropy at the Fe/NiO(001) interface, we fabricated Fe/NiO multilayers on MgO(001) substrates with different O₂ flow rates for NiO(001) layer growth. Figure LABEL:VSM1(a) shows the out-of-plane magnetization processes of 0.63 nm-thick Fe thin films grown on 20 nm-thick NiO(001) layers. Clearly, the magnetization processes are sensitive to the growth conditions of NiO(001), and the Fe layer becomes perpendicular magnetization. Therefore, PMA was dominant when the O₂ flow rate $\geq$ 2.0 sccm. The in-plane lattice constant of NiO(001) was largely the same as that of the MgO(001) substrate, irrespective of the growth condition of the NiO layer, as mentioned in Sec. III.1. The observed PMA dependence on the growth condition of the NiO(001) layer originates from an interfacial effect rather than an epitaxial strain. Next, we fabricated a Cr/Fe/NiO (O₂ flow rate = 2.0 sccm) structure employing a post-annealing process at different temperatures ($T_{\rm{anneal}}$) following the growth of the capping layer of Cr. Figure LABEL:VSM1(b) shows the out-of-plane magnetization processes of the films annealed at different $T_{\rm{anneal}}$. The samples were perpendicular magnetization films at $T_{\rm{anneal}}$ = 350 and 450^∘C . In the case of $T_{\rm{anneal}}$ = 550^∘C, a clear peak shift of NiO 002 was observed in XRD patterns (not shown), suggesting considerable atomic mixing at the interface.

We performed AHE measurements on multilayer Cr-cap (2 nm)/Fe (0.5-4.0 nm)/NiO (20 nm)/MgO(001)(substrate) to quantitatively separate the observed magnetic anisotropy into the interfacial magnetic anisotropy and volume contribution. The sample with the Fe layer thickness of $t_{\rm{Fe}}$ = 0.5 nm is perpendicular magnetization. In contrast, the saturation field increased with increase in $t_{Fe}$, indicating that the shape anisotropy became dominant, and that the preferential direction of the magnetization changed from normal to the film plane and finally to the in-plane direction. These results indicate that the origin of PMA is the interfacial effect rather than the bulk effect.

The areal magnetic anisotropy ($K_{u}t_{\rm{Fe}}$) as a function of $t_{\rm{Fe}}$, $K_{u}t_{\rm{Fe}}=K_{v}t_{\rm{Fe}}+K_{i}$ den Broeder et al. (1991), is plotted in Fig. 4 . Here, $K_{v}$ is the volume contribution to magnetic anisotropy, for example, magneto-crystalline, strain induced, and shape anisotropies, while $K_{i}$ is the interface contribution. $K_{i}$ at room temperature was determined as $0.93\pm 0.03$ mJ/m². This is of the same order as the previously reported $K_{i}$ for the Fe/MgO interface Koo et al. (2013); Okabayashi et al. (2014). In contrast, $K_{v}$ was estimated to be $-1.46\pm 0.01$ MJ/m³, which is reasonably close to the demagnetization energy or shape anisotropy energy for the film form a sample with $-\frac{1}{2}\mu_{0}M_{s}^{2}=-1.23$ MJ/m³. Here, $M_{s}$ denotes the saturation magnetization of Fe, which are 1400 and 1700 kA/m at room temperature and 100 K, respectively as determined by VSM. We also performed the same analysis at 100 K, and obtained $K_{i}$ and $K_{v}$ are $+1.02\pm 0.07$ mJ/m² and $-1.79\pm 0.03$ MJ/m³, respectively.

We emphasize that the temperature dependence of the interfacial PMA of Fe/NiO appears to be weaker than that of CoFeB/MgOSato et al. (2018). As the PMA is dominated by magnetization at the interface of Fe layerIbrahim et al. (2020), the observed weaker temperature dependence of the PMA in Fe/NiO compared to CoFeB/MgO indicates that the magnetic exchange coupling between Fe and NiO at the interface may suppress thermal fluctuations of the Fe spins. Therefore, this system could be useful in applications owing to the greater robustness against thermal fluctuations.

Figures 5 and 6 show the Fe and Ni $L$-edge X-ray absorption spectra as well as the XMCD with angular dependence of the normal incidence (NI) and grazing incidence (60^∘) (GI) cases of Cr(2 nm)/Fe(0.6 nm)/NiO(20 nm)/MgO(001), respectively. The NiO(001) layers were grown at O₂ flow rates of 2.5 and 1.5 sccm for the perpendicular magnetization (Fig. 5) and in-plane magnetization (Fig. 6) samples, respectively. For both the samples, the clearly observed metallic line shapes of Fe suggest a lack of interfacial oxidation. In the case of the perpendicular magnetization sample, the XMCD intensity at the $L_{3}$-edge varied with the measurement geometry. The enhanced $L_{3}$-peak in the NI geometry corresponded to orbital magnetic moments ($m_{\rm orb}$). By applying the sum rule analysis, we obtained the spin magnetic moments and $m_{\rm orb}$ to be 1.32 and 0.09 $\mu_{B}$, respectively, for the NI case. Here, the 3d hole number of 3.39 was assumed, which is the same as the case for Fe/MgO Okabayashi et al. (2019). If we express the $m_{\rm orb}$ components parallel and normal to the film plane as $m_{\rm orb}^{\perp}$ and $m_{\rm orb}^{\parallel}$, respectively, the difference of $m_{\rm orb}$, defined as $\Delta m_{\rm orb}=m_{\rm orb}^{\perp}-m_{\rm orb}^{\parallel}\simeq 0.05\mu_{B}$, provides the reasonable origin of the observed PMAMiura and Okabayashi (2022).Here, we assumed that the orbital moment anisotropy originated from the second order perturbation of the spin-orbit interactionMiura and Okabayashi (2022). A magnetic dipole moment of less than 0.01 $\mu_{B}$ was also estimated, which is sufficiently smaller than $m_{\rm orb}$. This suggests that the orbital magnetic moment anisotropy is dominant at the Fe/NiO interface. In contrast, in the case of the in-plane magnetization sample, $L_{3}$-edge intensity remained unchanged for NI and GI set up, which suggests the isotropic $m_{\rm orb}$ of 0.05 $\mu_{B}$ because the shape anisotropy becomes dominant. Hysteresis loops at Fe $L_{3}$-edge photon energy shown in Figs.5(d) and 6(d) roughly reproduce the characteristic magnetization processes for the perpendicular and in-plane magnetization films, respectively. The asymmetry in XMCD spectrum reveals that the large orbital moments are induced in the perpendicular components. These features are quite similar to the case of Fe/MgOOkabayashi et al. (2014). However, the effect of Fe-O bonding to anisotropic charge distribution does not work in the in-plane magnetization sample even with 0.6 nm thickness. As shown in Figs.5 and 6, there are no XMCD signals at the Ni $L$-edge for both the NI and GI cases because antiparallel spins at the Ni sites are compensated completely, although small differential signals appeared, originating from application of the magnetic field along the perpendicular direction during the measurements.

Interestingly, there were no signs of Ni³⁺ in XAS, as shown in Figs. 5 and 6 (c). This result appears to be inconsistent with the XPS and XRD results, which indicate that the oxygen-rich NiO contains Ni³⁺ and Ni-site vacancies in addition to Ni²⁺ (Sec. III.1). The fact that no traces of iron oxide were detected (Fig. 5 (a)) implies that no significant oxidation occurred between the excess oxygen in NiO and the metallic Fe layer. Koo et al. pointed out that a variation in the interface composition due to oxygen atoms floating up from the Cr buffer layer and reaching the MgO interface is key to enhancing the PMA in MgO/Fe/Cr/MgO(001)Koo et al. (2013). Similarly, the variation or diffusion of excess oxygen in the NiO layer by annealing may play an important role in enhancing the PMA in the Fe/NiO system. Based on this, the XAS results of no signs of Ni³⁺ can be consistently explained by the migration of excess oxygen in the NiO layer to the Cr layer which works as an oxygen absorber, and the interface structure of Fe/NiO becomes optimized to exhibit PMA.

To investigate the dependence of the NiO layer thickness on the magnetization process, we conducted AHE measurements on the stacking of Cr/Fe(0.6 nm)/NiO($t_{\mathrm{NiO}}$)/MgO(001) with a wedge-shaped NiO layer ($t_{\mathrm{NiO}}=$ 0 - 30 nm) (Fig. 1(b)). As shown in Fig. 7, the films with thicker NiO layers have a higher coercive force $H_{c}$ at all temperatures and a greater temperature dependence of $H_{c}$. Generally, magnetic anisotropy is among the dominant parameters determining $H_{c}$; However, as mentioned in Sec. III.2, the PMA exhibited little temperature change. The fact that the temperature dependence of $H_{c}$ is more significant than that of PMA means that $H_{c}$ is dominated by the bulky features of the NiO layer rather than the interfacial effect. The difference between the two samples with different NiO thicknesses could be explained by considering the blocking temperature ($T_{B}$) of antiferromagnetsMeiklejohn and Bean (1957); Ambrose and Chien (1998); Devasahayam and Kryder (1999). According to the previous study of $T_{B}$ in antiferromagnets by Devasahayam et al.Devasahayam and Kryder (1999), the thickness dependence of $T_{B}$ can be expressed by the power law owing to the finite-size effect. The estimated correlation length was $\approx 2$ nm for NiO films and therefore, $T_{B}$ approaches or becomes less than the room temperature if $t_{\mathrm{NiO}}\lesssim 2$ nm. Thus, our sample with $t_{\mathrm{NiO}}=15$ nm has $T_{B}$ above 300 K, while in the case of the sample with $t_{\mathrm{NiO}}=0.8$ nm, the $T_{B}$ is well below room temperature. As $t_{\mathrm{NiO}}$ of the latter sample is sufficiently thinner than the correlation length of NiO, the role of the exchange coupling between NiO and Fe at the interface or magnetic effect of antiferromagnetism of the NiO layer must be negligibly small. In contrast, the magnetization process of Fe layer in the the sample with $t_{\mathrm{NiO}}=15$ nm is strongly affected by the antiferromagnetic nature of NiO through the interfacial exchange coupling.

We also examined whether exchange bias emerges at the interface between the ferromagnetic Fe(001) layer and the antiferromagnetic NiO(001) layer for samples with an additional field annealing process. The details of the annealing process are as follows. Three films of Cr/Fe(0.6 nm)/NiO(20 nm) were simultaneously grown on MgO(001) substrates with dimensions of 10 mm $\times$ 10 mm $\times$ 0.5 mm. Two of the three films were annealed at 250^∘C in vacuum with a magnetic field of $\mu_{0}H=$1 T for 1 h. They were placed parallel and perpendicular to the magnetic field, respectively. Subsequently, the samples were spontaneously cooled to room temperature under the magnetic field. The third sample was annealed in zero magnetic field as a control sample.

Hysteresis loop shifts, which are characteristic of the exchange bias effect, have often been reported in Fe/NiO(001), which exhibits in-plane preferential magnetizationLuches et al. (2010, 2012); Młyńczak et al. (2013); Li et al. (2019); Kozioł-Rachwał et al. (2020) rather than perpendicular magnetization. Even at an interface between a ferromagnet and a compensated antiferromagnet layers, a finite exchange bias could be realized if the spins of both the ferromagnet and antiferromagnet lie in-plane because of the frustration of the first antiferromagetic layerKiwi et al. (1999). In our case, no clear shift in the magnetization curve or a clear change in $H_{c}$ was observed in all three samples, regardless of the presence of the applied field during the annealing process or the direction of the applied field. This means that the antiferromagnetic spin configuration near the interface cannot be controlled by an external field, although the origin of $H_{c}$ could be dominated by interfacial spin frustrationNogués and Schuller (1999); Leighton et al. (2000). We would like to emphasize that the difference between whether Fe is a perpendicularly magnetized film or an in-plane magnetized film appears to govern the absence or presence of an exchange bias in the Fe/NiO(001) system. Moreover, the relationship between the Néel vector of NiO(001) and the preferential magnetization direction of the ferromagnetic layer is important for understanding the exchange bias mechanism in such bilayer systems.