Origin of magnetically dead layers in spinel ferrites MFe₂O₄ grown on $\text{Al}_{2}\text{O}_{3}$: Effects of post-deposition annealing studied by XMCD

Electronics have achieved great success by controlling the charge degree of freedom of electrons in semiconductors. By adding the spin degree of freedom to the existing electronics, a new field of electronics known as spintronics is being developed. Spintronics devices have several advantages over existing electronic devices, e.g., non-volatilitiy, low energy consumption, high-speed, infinite endurance [1]. To establish next-generation electronics with semiconductor-based spintronics, injection of spin-polarized carriers into semiconductors should be realized at room temperature by utilizing a magnetic spin injector formed on the semiconductor. The spin filter is a promising technology to inject highly spin-polarized current into semiconductors. Insulating spinel-ferrite thin films are attracting high attention as a promising material for spin filters because they have the down-spin and up-spin conduction bands at different energies [the 3d-t_2g band of Fe${}^{3+}(O_{h})$ and the 3d-e band of Fe${}^{3+}(T_{d})$, as Fig. 1(a)] [2], and their Néel temperatures are much higher than room temperature (790 K for $\text{CoFe}_{2}\text{O}_{4}$ [3, 4, 5], and 850 K for $\text{NiFe}_{2}\text{O}_{4}$ [2, 6]). However, the experimentally obtained spin-filtering efficiency of ferrite-based tunnel barriers still remains considerably lower than the theoretical value of $100\%$ [7, 8, 9, 10]. In recent investigation, possible causes for this low spin-filtering efficiency have been proposed. One is that midgap impurity states are induced by structural and/or chemical defects [4, 2, 11]. For example, in $\text{CoFe}_{2}\text{O}_{4}$, the presence of Co³⁺ degrades the spin filter due to the formation of up-spin states in the middle of the band gap. Another possibility is that layers with degraded magnetic properties are formed in the interfacial region, which is often called magnetically dead layers. They are well known for epitaxial $\text{Fe}_{3}\text{O}_{4}$ thin films grown on MgO substrates, and are thought to originate from antiphase boundaries and their antiferromagnetic interdomain exchange interaction [12, 13, 14, 15, 16]. In addition, a recent study on epitaxial $\text{Fe}_{3}\text{O}_{4}$ thin films grown on MgO substrates revealed that the first $\text{Fe}_{3}\text{O}_{4}$ monolayer lacks Fe³⁺ ions at the tetrahedral sites [17], resulting in a loss of the ferrimagnetic order due to missing superexchange paths.

In recent works [18, 19, 20], the magnetic properties of $\textit{M}\text{Fe}_{2}\text{O}_{4}$(111)/$\text{Al}_{2}\text{O}_{3}$(111)/Si(111) (M=Co, Ni) structures [21] were studied using the element-specific probes of x-ray absorption spectroscopy (XAS) and x-ray magnetic circular dichroism (XMCD). The authors revealed that the decrease of the inversion parameter y , defined by $=[\textit{M}_{1-y}\text{Fe}_{y}]_{T_{d}}[\text{Fe}_{2-y}\textit{M}_{y}]_{O_{h}}\text{O}_{4}$ is correlated with the formation of magnetically dead layers. The inversion parameter y, which is equal to unity in the ideal inverse spinel, represents the regularity of the cation distribution in the spinel structure. It was found that the reduced thickness of the $\text{CoFe}_{2}\text{O}_{4}$ film leads to a significant reduction in both $y$ and ferrimagnetic ordered moment. It was also found that $\text{NiFe}_{2}\text{O}_{4}$ has a larger $y$ ($=0.79\text{--}0.91$) than $\text{CoFe}_{2}\text{O}_{4}$ ($y=0.54\text{--}0.75$), indicating that Ni has a higher $O_{h}$-site selectivity than Co. Considering that the cation distribution in $\textit{M}\text{Fe}_{2}\text{O}_{4}$ can be modified by post-deposition annealing [5, 22], it is expected that annealing recovers the ferrimagnetic behavior of the interfacial region degraded by the formation of the magnetically dead layers. In the present study, we investigate the electronic and magnetic states of as-grown and annealed $\textit{M}\text{Fe}_{2}\text{O}_{4}$(111)/$\text{Al}_{2}\text{O}_{3}$(111)/Si(111) (M=Co, Ni) thin films using XAS and XMCD. We reveal that the degraded magnetic properties of the magnetically dead layer can be partially recovered by annealing through the redistribution of the cations. Furthermore, we find that there are a significant number of vacant $T_{d}$ sites in the magnetically dead layers, and that such vacancies may degrade the ferrimagnetic order in the $\textit{M}\text{Fe}_{2}\text{O}_{4}$ thin films.

$\text{CoFe}_{2}\text{O}_{4}$(111) and $\text{NiFe}_{2}\text{O}_{4}$(111) thin films with various thicknesses were epitaxially grown on $\text{Al}_{2}\text{O}_{3}$(111) buffer layers formed on Si(111) substrates using the pulsed laser deposition (PLD) method. Schematic illustrations of the sample structures are shown in Figs. 1(b) and 1(c).

2.4 nm- and 1.4 nm-thick $\gamma$-$\text{Al}_{2}\text{O}_{3}$(111) buffer layers were adopted for $\text{CoFe}_{2}\text{O}_{4}$ and $\text{NiFe}_{2}\text{O}_{4}$ thin films, respectively. The thicknesses of the films were d = 1.4, 2.3, 4, and 11 nm for $\text{CoFe}_{2}\text{O}_{4}$, and d = 1.7, 3.5, and 5.2 nm for $\text{NiFe}_{2}\text{O}_{4}$. In order to avoid charging up of the samples during the XAS and XMCD measurements, we used highly phosphorus-doped Si(111) substrates with a low electrical resistivity 2 m$\Omega$cm. For the epitaxial growth of the $\gamma$-$\text{Al}_{2}\text{O}_{3}$ buffer layers on the Si substrates, we used solid-phase reaction of Al and $\text{SiO}_{2}$. More detailed description of sample preparation and characterization are provided in Refs. 18, 19. Some of the $\text{CoFe}_{2}\text{O}_{4}$ and $\text{NiFe}_{2}\text{O}_{4}$ thin films were annealed in order to redistribute the cations in the thin films, aiming at the recovery of the inversion parameter $y$. In order to suppress the oxidation of the Si substrate, the post-deposition annealing temperature was set to 973 K because the oxidation rate of Si rapidly increases particularly above 1073 K [23]. The films were annealed at 973 K for 48 hours in air. Since higher inversion parameters of $\text{CoFe}_{2}\text{O}_{4}$ have been reported in slowly cooled bulk crystals than in rapidly quenched ones [5], we set a slow cooling rate of 1 K/min down to 673 K and then the samples were naturally cooled down to room temperature.

XMCD measurements were performed at beamline BL-16A of Photon Factory, High Energy Accelerator Research Organization (KEK-PF). A magnetic field of 5 T was applied parallel to the incident x rays. The measurements were done at room temperature ($\sim 300$ K). The absorption signals were detected in the total-electron-yield (TEY) mode. Since the probing depth in the TEY mode is a few nm [24, 25], the XAS and XMCD spectra of a few nm-thick films reflect the electronic and magnetic properties of the entire $\textit{M}\text{Fe}_{2}\text{O}_{4}$ film including the magnetically dead layers near the spinel/$\text{Al}_{2}\text{O}_{3}$ interface. By increasing the film thickness to $\gtrsim 5\text{ nm}$, the spectra more strongly reflect the signals away from the interface. The XMCD signals were collected by switching the photon helicity at every energy point.

In order to analyze the XAS and XMCD spectra quantitatively, we performed configuration-interaction (CI) cluster-model calculation [26]. The model is a good approximation for localized electron systems like the insulating spinel ferrites. In the present calculation, we used an Xtls version 8.5 program [27]. In choosing parameter values for the calculation, we adopted the following empirical rules : (1) The ratio between the on-site Coulomb energy between 3d electrons U_dd and the attractive 2p core hole-3d electron Coulomb energy U_dc was fixed to $U_{dc}/U_{dd}\sim 1.3$ [28, 29]. (2) The ratio between Slater-Koster parameters $(pd\sigma)$ and $(pd\pi)$ was fixed to $(pd\sigma)/(pd\pi)=-2.17$ [30]. The hybridization strength between O 2p orbitals $T_{pp}$ was fixed to 0.7 eV for the $O_{h}$ site and 0 eV for the $T_{d}$ site [27, 28]. The Slater integrals were set to be 80% of the Hartree-Fock values. Thus, the crystal-field splitting 10Dq, the charge-transfer energy $\Delta$, $U_{dd}$, and $(pd\sigma)$ were treated as adjustable parameters. As for the Fe cations, the parameters were adjusted to reproduce all the measured Fe $L_{2,3}$-edge spectra by the weighted sum of the calculated spectra for the Fe${}^{2+}(O_{h})$, Fe${}^{3+}(T_{d})$, and Fe${}^{3+}(O_{h})$ ions. Here, parameters for Fe${}^{2+}(O_{h})$ were adopted from the previous report on $\text{NiFe}_{2}\text{O}_{4}$ [19]. The adjusted parameter values are listed in Table 1.

As in our previous works [18, 19], we fitted the weighted sum of the calculated XAS and XMCD spectra for the Fe${}^{2+}(O_{h})$, Fe${}^{3+}(T_{d})$, and Fe${}^{3+}(O_{h})$ ions to the experimental ones. From this analysis, we obtained the relative amount of the three Fe components and thereby the inversion parameter y.

We discuss the role of the cation vacant sites in the magnetically dead layers. As introduced above, based on the studies on Fe₃O₄ [12, 13, 16], it is believed that the magnetically dead layers in the spinel ferrites are caused by antiphase boundaries. However, as shown above, we find that there are a significant number of vacant $T_{d}$ sites near the interface, and the transfer of the cations from the $O_{h}$ to $T_{d}$ sites caused by annealing significantly recovers the ferrimagnetic order. The antiferromagnetic superexchange interaction between the $T_{d}$-site and $O_{h}$-site cations is the origin of the ferrimagnetic order in the spinel ferrites. Therefore, the lack of superexchange interaction due to the vacancies should significantly suppress the ferrimagnetism of magnetically dead layers. Here, we focus on how the vacant $T_{d}$ sites affect the spin structures in the magnetically dead layers.

Figure 10(a) shows the exchange interaction between the cations at the $O_{h}$ and $T_{d}$ sites of the spinel structure. The values of the exchange interaction in $\textit{M}\text{Fe}_{2}\text{O}_{4}$ (M=Co, Ni) deduced from magnetization measurements [33], which are denoted as $J_{AB}$ and $J_{BB}$ in Fig. 10, are listed in Table 2 in units of K. We note that suffix $A$ ($B$) denotes the $T_{d}$ ($O_{h}$) sites, and the ratio between $M^{2+}(O_{h})$, Fe${}^{3+}(T_{d})$, and Fe${}^{3+}(O_{h})$ is $1:1:1$ in an ideal inverse spinel structure. The large negative values of $J_{AB}$ demonstrate the strong contributions of the $T_{d}$ site to the ferrimagnetic order. As for the $O_{h}$-$O_{h}$ interaction, $J_{BB}$, one can see large positive values for $M^{2+}$-$M^{2+}$ interaction, and negative ones for $\text{Fe}^{3+}$-$\text{Fe}^{3+}$ and $\text{Fe}^{3+}$-$M^{2+}$ interactions. On average, $O_{h}$-$O_{h}$ interactions are weakly ferromagnetic ($+0.6$ K for $\text{CoFe}_{2}\text{O}_{4}$ and $+4.8$ K for $\text{NiFe}_{2}\text{O}_{4}$) ¹¹1 The number of $\text{Fe}^{3+}$-$M^{2+}$ exchange pairs is twice as much as that of $M^{2+}$-$M^{2+}$ and $\text{Fe}^{3+}$-$\text{Fe}^{3+}$ exchange pairs. Therefore, the weighted average value is $\frac{1}{4}(J_{BB}^{M^{2+}-M^{2+}}+2J_{BB}^{\text{Fe}^{3+}-M^{2+}}+J_{BB}^{\text{Fe}^{3+}-\text{Fe}^{3+}})$.. We note that the number of the $O_{h}$-$T_{d}$ exchange pairs in an ideal spinel structure are 2.3 times larger than that of the $O_{h}$-$O_{h}$ ones [13]. If $\frac{1}{3}$ of the $T_{d}$ site is vacant as shown in Fig. 10(b), $J_{AB}$ is weaken to $\frac{2}{3}$ of the ideal value, degrading the ferrimagnetic order. After annealing, some $O_{h}$-site ions move to $T_{d}$ sites. For simplicity, assuming that the vacancies at the $T_{d}$ sites are equally redistributed to all the $T_{d}$ and $O_{h}$ sites, as shown in Fig. 10(c), antiferromagnetic $J_{AB}$ is recovered to $\frac{8}{9}$ of ideal value. Since the value and number of exchange interactions of $J_{AB}$ are larger than that of $J_{BB}$, ferrimagnetic order should be stabilized. Although the actual numbers of the vacancies are still unclear, it can be concluded that vacancies at the $O_{h}$ sites still preserve the ferrimagnetic order, whereas vacancies at the $T_{d}$ sites significantly degrade the ferrimagnetic order. We should note that the above discussion ignores the effects of charge unbalance caused by the cation vacancies, that is, the effects of cation valence changes and possible oxygen vacancies. We speculate that there are oxygen vacancies [35] and/or that extra $O_{h}$ sites [17] near the interface.

We have studied the electronic and magnetic states of the as-grown and annealed $\text{CoFe}_{2}\text{O}_{4}$(111) and $\text{NiFe}_{2}\text{O}_{4}$(111) thin films with various thicknesses grown on Si substrates with the $\gamma$-$\text{Al}_{2}\text{O}_{3}$ buffer layers. By analyzing the spectral line shapes using the CI cluster-model calculation, we have estimated the valences and site occupancies of Fe ions. We confirmed through the significant reduction of the XMCD intensities with decreasing film thickness that there are magnetically dead layers near the interface with $\gamma$-Al₂O₃. As reported in the previous works [18, 19], the reduction of the inversion parameters was observed in the magnetically dead layers. By annealing the films for 48 hours in air to redistribute the cations, the XMCD intensity and inversion parameters significantly increase particularly in the thinner films. Furthermore, from comparison between the results on the as-grown and annealed films, it is suggested that there are a significant number of vacant $T_{d}$ sites in the magnetically dead layers. After the post-deposition annealing, the vacancies at the $T_{d}$ sites are partially occupied by ions diffused from the $O_{h}$ sites. Thus, we conclude that vacant $T_{d}$ sites play an important role in the formation of the magnetically dead layers in spinel ferrites.

We would like to thank Ryosho Nakane for valuable advice and enlightening discussion throughout the present work, Kenta Amemiya and Masako Suzuki-Sakamaki for valuable technical support at KEK-PF BL-16A. This work was supported by KAKENHI grants from JSPS (JP15H02109, JP26289086, JP15K17696, JP19K03741, JP20K14416, JP20H02199, and JP22K03535). The experiment was done under the approval of the Photon Factory Program Advisory Committee (Proposal No. 2016S2-005). Y. K. W. and Z. C. acknowledges financial support from Materials Education Program for the Futures leaders in Research, Industry and Technology (MERIT). Y. W. acknowledges financial support from Advanced Leading Graduate Course for Photon Science (ALPS). Y. K. W. also acknowledge support from the JSPS Research Fellowship Program for Young Scientists.