Regulation of growth temperature on structure, magnetism of epitaxial FeCo₂O₄ films

Abstract

Epitaxial FeCo₂O₄ films were grown by pulsed laser deposition on Al₂O₃ (0001) substrates at different growth temperatures in this work. The growth temperature directly affects the occupation of cations and the lattice constant, resulting in different magnetic phases and conductivity. The optimal growth temperature range was 450–550 °C. Double bandgaps were observed in the UV absorption spectra. Electrical measurements showed that the film grown at 450 °C had the lowest activation energy, and the structure of this film was more ordered. The magnetic analysis demonstrated that, in addition to the ferrimagnetic phase formed by the antiparallel arrangement of the tetrahedral and octahedral magnetic moments, there were two kinds of antiferromagnetic phases. One kind of antiferromagnetism was from the antiphase boundaries, and the other was localized antiferromagnetism at the octahedra formed by the Co²⁺ ions. The three kinds of magnetic phases showed different characteristics with changes in the growth temperature and measurement temperature.

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1. Introduction

Spinel ferrites have been extensively investigated in recent decades. In particular, cobalt-substituted magnetite (Fe_3−xCo_xO₄) is very attractive due to the typical anisotropy of the Co ions.^1–3 It is an important ferromagnetic material with excellent physical properties, such as high Curie temperature,⁴ high permeability,⁵ high resistivity⁶ and good thermal stability,⁷ and can be widely used in magnetic storage, semiconductor devices, electrode materials and other fields.^8–10 At present, investigations on FeCo₂O₄ mainly focus on its powder form,^7,9 while there are a few reports on FeCo₂O₄ films.¹¹ The calcination temperature has a great influence on the distribution of the tetrahedral and octahedral cations in the spinel structure.^12–14 Some reports show that partial cationic inversion in spinel can induce magnetic hardening.¹⁵ Our previous studies have demonstrated that pure phase FeCo₂O₄ powders can only be formed in the calcination temperature range of 950–1050 °C,¹³ which affects cation occupation and the magnetic properties. Generally, non-stoichiometric phases are ubiquitous, extensively found in the transition metal oxides, and result in the formation of intrinsic or native defects.¹⁶ Compared with the polycrystalline structure, high-quality epitaxial films are more practical in reflecting the intrinsic properties of the material. During the preparation of films, the growth temperature (T_G) is an important parameter as it provides activation energy to the atoms and directly affects atomic mobility.⁸ Our previous research has shown that the T_G of epitaxial NiCo₂O₄ films can change the valence and occupation of the cations. At higher T_G, octahedral Ni ions can replace tetrahedral Co ions more easily and change the relative Ni³⁺/Co³⁺ concentration.¹⁷ Combined with oxygen pressure, T_G can tune the metallic behavior and magnetic phases of the NiCo₂O₄ film.¹⁸ In CoFe₂O₄ films, it was found that with the increase in growth temperature, the cations migrated between the tetrahedral and octahedral sites, and the spinel structure showed a tendency to change from inverse to normal spinel.¹² The T_G is also known to have significant effects on the crystallinity,^19,20 lattice parameters and surface morphology of films.^21,22 Therefore, it is necessary to explore the effect of growth temperature on the magnetic and electrical properties of epitaxial FeCo₂O₄ films.

In this work, FeCo₂O₄ films were grown by pulsed laser deposition (PLD) on Al₂O₃ (0001) substrates at different growth temperatures. The effect of T_G on the growth mode was investigated. The magnetic properties of the films were analyzed, and it was found that with an increase in T_G, the magnetic domains became more and more pronounced. In addition to ferrimagnetism presented by the antiparallel arrangement of the tetrahedral and octahedral magnetic moments, two kinds of antiferromagnetism are thought to coexist in the films. One is due to the presence of the antiphase boundary, and the other local lattice antiferromagnetism in the octahedral sites due to the Co²⁺ ions, which increase with T_G. The electrical transport properties exhibited typical semiconductor properties. The activation energy of the film grown at 450 °C was the lowest, and the structure of the film could be considered as a standard spinel structure.

2. Experimental details

2.1. Film preparation

The Al₂O₃ (0001) substrate was first ultrasonically cleaned in acetone and ethanol, then with deionized water and finally dried with nitrogen. The substrate was placed in a vacuum chamber. The base pressure was 1.5 × 10⁻⁵ mTorr. Prior to film deposition, the substrate was heat-treated at 700 °C for 2 h under the oxygen pressure of 75 mTorr to remove the damages on the crystal surface caused by machine polishing. Then, the epitaxial FeCo₂O₄ films were grown on Al₂O₃ (0001) single-crystal substrates at different temperatures between 250–650 °C by using the pulsed laser deposition technique with a KrF excimer laser (λ = 248 nm) of energy 3.94 J cm⁻². During deposition, the oxygen pressure was maintained at 75 mTorr. All the films were deposited at a frequency of 8 Hz for 20 000 shots.

2.2. Structural characterization and property measurement

The structures of the films were investigated by X-ray diffraction (X'pert PRO, XRD, Cu-Kα radiation, λ = 1.54 Å) and high-resolution transmission electron microscopy (HR-TEM, FEI Tecnai F20). The cross-sectional TEM samples were prepared by mechanical thinning and ion milling with Ar⁺ ions at 3.2–4.8 keV for a few hours. The thickness of the film was determined by X-ray reflection (XRR). The surface morphologies of the FeCo₂O₄ films were scanned using an atomic force microscope (AFM, Nanoscope IV). The magnetic domains of the films were characterized by magnetic force microscopy (MFM, Nanoscope IV). Raman measurements were conducted at room temperature using a Renishaw's InVia Raman microscope with an excitation wavelength of 532 nm. The bond structure and chemical state of the atoms in the films were characterized by Fourier transform infrared spectroscopy (FTIR, Nicolet 380). The bandgap of the films was measured by an ultraviolet-visible spectrophotometer (UV-3600), and the optical bandgap was analyzed from the measured reflection spectrum. The magnetic properties were measured by a superconducting quantum interference device (Quantum Design, SQUID-VSM) magnetometer. The SQUID measurements recorded the hysteresis loop (M–H) of the films in the temperature range of 2–400 K. The zero-field cooled (ZFC) and field cooled (FC) curves were measured at a magnetic field of 500 Oe. The electronic conductivity of the film was measured by the standard four-probe method.

3. Results and discussion

3.1. Structure and morphology

Fig. 1(a) shows the crystal structure of FeCo₂O₄, which is cubic in the space group Fd3̄m, while Al₂O₃ is hexagonal in the space group R3̄C (Fig. 1(b)). FeCo₂O₄ can be epitaxially grown on Al₂O₃ (0001) in principle, and FeCo₂O₄ (111) films are grown in a triangular lattice. Fig. 1(c) shows the atomic model of the FeCo₂O₄ (111)/Al₂O₃ (0001) epitaxial relationship. The solid hexagonal shape with blue atoms represents the FeCo₂O₄ lattice, and the gray atoms in the dashed hexagon show the Al₂O₃ lattice. According to the lattice mismatch formula¹⁷

ε = (d_film − d_sub)/d_sub (1)

where d_film and d_sub represent the atomic spacings of the FeCo₂O₄ film and Al₂O₃ (0001) substrate, respectively. The lattice mismatch between FeCo₂O₄ (111) and Al₂O₃ (0001) was 21.7%, and the films suffered compressive stress.

Fig. 1 Schematic diagrams of the (a) FeCo₂O₄ crystal structure and (b) Al₂O₃ crystal structure; (c) the FeCo₂O₄ (111)/Al₂O₃ (0001) epitaxial relationship atomic model.

Fig. 2(a) shows the XRD patterns of the FeCo₂O₄ epitaxial films grown at different T_G. It can be observed that, with the increase in T_G, the crystallization quality of the film improved. When the growth temperature was in the range of 450–550 °C, the epitaxial films showed only one orientation with good crystal quality. For clarity, the (222) diffraction peaks of the FeCo₂O₄ film are enlarged in Fig. 2(b), and it was found that, with increasing T_G, the diffraction peak first moved to a lower angle and then to a higher angle, indicating that the out-of-plane lattice constant increased first and then decreased. On increasing the growth temperature further to 650 °C, the diffraction peak returned back to a lower angle, and the out-of-plane lattice constant increased again. Fig. 2(d) gives the thickness of films grown at different T_G, as measured by XRR, and the inset is the film thickness curve of the FeCo₂O₄ film grown at 350 °C. Differences in T_G change the atomic mobility and the adhesion of atoms on the substrate. Therefore, the epitaxial films still showed different thicknesses due to the different growth temperatures, even if the same oxygen pressure, shots and power were maintained in the process of film growth.

Fig. 2 (a) XRD patterns of the FeCo₂O₄ films grown at different T_G; (b) the enlarged view of the (222) peaks; (c) out-of-plane lattice constants of the FeCo₂O₄ films grown at different T_G; (d) change in film thickness with T_G, as measured by XRR. The inset shows the XRR curve of the FeCo₂O₄ film grown at 350 °C.

The out-of-plane lattice constants calculated by the Bragg diffraction equation are shown in Fig. 2(c). When the T_G was low (250 °C), a cation deficient spinel with cation vacancies and a small lattice constant was obtained.²³ The out-of-plane lattice constant of the FeCo₂O₄ film grown at 350 °C was larger than that of bulk FeCo₂O₄ (8.244 Å). We noted that the thickness of the film grown at 350 °C had a large lattice constant and was the thinnest (Fig. 2(d)), making the film more susceptible to compressive stress from the substrate. When the T_G was increased to 450–650 °C, the film (∼130 nm) was thick enough, and the stress was released. More octahedral Co²⁺ had formed in the films, and the lattice constant was mainly affected by cation occupation, which was confirmed by the FTIR results presented below. Considering the fact that the radius of Co²⁺ is greater than those of Fe³⁺ and Co³⁺, and the lattice constants of the FeCo₂O₄ films grown at 450–650 °C increased with the increase in Co²⁺ content. In our previous studies on FeCo₂O₄ powders, it has also been found that different calcination temperatures had a great effect on cation occupancy.¹³ When the temperature was 250 °C, the film presented low crystal quality, and the full width at half-maximum (FWHM) was wide. For the film grown at 350 °C, the compressive stress was larger, and the FWHM further increased. With increasing growth temperature, the intensity of the diffraction peaks gradually enhanced, the peak width decreased, and the crystallization quality of the film improved. For the film grown at 650 °C, the (222) peak became asymmetric, which indicated that the FeCo₂O₄ film was partially decomposed at 650 °C. A similar report has been made on the NiCo₂O₄ epitaxial film.²⁴ From the above analysis, it is evident that low growth temperatures mainly affect the migration of atoms, while high growth temperatures play an important role in regulating the occupation of cations.

In order to observe the surface morphology and domain structure of the films, AFM (left) and MFM (right) measurements were performed. Fig. 3(a–e) shows the morphology and domain images of the FeCo₂O₄ epitaxial films grown at different T_G. We could find that the surface roughness of the films grown at lower and very high T_G was elevated. At lower growth temperatures, the adsorbed atoms on the substrates would not have enough energy to cross the energy barrier to reach an equilibrium position.¹⁸ Therefore, there was great agglomeration in the film grown at 250 °C. With an increase in T_G, the mobility of the atoms on the surface of the films would increase gradually. As a result, the agglomeration phenomenon would decrease gradually, with the atomic deposition mode gradually changing to layered growth.¹⁹ Therefore, agglomeration in the film grown at 350 °C was decreased, and the film had become thinner. At 450 °C and 550 °C, the growth temperature was high enough for the surface particles of the films to be uniform, rendering the surface smooth. When the T_G was higher than 650 °C, the agglomeration of the particles appeared again due to large grain sizes. Considering the large mismatch between the substrate and the FeCo₂O₄ lattice, some defects may have formed during the growth of the film, such as lattice defects and stacking faults in the lattice. These defects can lead to antiphase boundaries (APBs). As the T_G increased, the APBs in the film decreased. The films grown at 450–550 °C demonstrated good epitaxial quality. Magnetic domains appeared in the films when the T_G was above 450 °C. With a further increase in T_G, the magnetic domains gradually became obvious, indicating an enhancement in the magnetic moment with increasing T_G. To further verify the existence of different domains in the film, we performed micromagnetic simulations based on the idea of finite segmentation.²⁵ The models were set to have a length of 500 nm and a thickness of 130 nm, and the grids were divided into 5 nm × 5 nm × 1 nm. The simulation parameters, namely saturated magnetization, exchange integral constant, and magnetocrystalline anisotropy, were M_S = 0.5 × 10⁶ A m⁻¹, A = 1.2 × 10⁻¹¹ J m⁻¹, and K = 0.7 × 10⁶ J m⁻³, respectively.²⁶ The magnetic moment distribution of FeCo₂O₄ was obtained (Fig. 3(f)), and different ferromagnetic regions were observed in the films, and spin inversion could be found at the interface.

Fig. 3 (a–e) AFM (left) and MFM (right) images and (f) magnetic moment distribution of the FeCo₂O₄ films obtained by micromagnetic simulation.

To determine the crystal structure of the FeCo₂O₄ thin films, the HR-TEM observations of the FeCo₂O₄ film on the Al₂O₃ substrate (T_G = 550 °C) were recorded. Fig. 4(a) shows a cross-sectional HR-TEM image of the FeCo₂O₄ film on Al₂O₃ along the (111) direction. It was found that there were different crystal plane spacings. The standard FeCo₂O₄ (111) crystal plane spacing was 4.759 Å. More octahedral Co²⁺ ions and the partial decomposition of the sample would lead to an increase in crystal plane spacing. Furthermore, it was found from the enlarged image (the inset of Fig. 4(a)) that APBs were formed by the stacking faults of the lattice. Therefore, we believed that there might be different regions in the film. The selected area electron diffraction (SAED) patterns of the film and partial substrate showed spots arranged in hexagons (Fig. 4(b)). The crystal plane corresponding to the diffraction spots was calibrated according to the distance and angle between the diffraction spots. The lattice mismatch between FeCo₂O₄ (111) and Al₂O₃ (0001) was observed in the enlarged view. However, the mismatch was not as large as that obtained from the theoretical calculation. It is thought that the observation direction is not exactly perpendicular to the diffraction plane.

Fig. 4 (a) Cross-sectional HR-TEM image of FeCo₂O₄ (111)/Al₂O₃ (0001); (b) selected area electron diffraction patterns of FeCo₂O₄ (111)/Al₂O₃ (0001) along the (111) zone axis.

Fig. 5(a) shows the Raman spectra of the FeCo₂O₄ films grown at different T_G. The A₁ (670 cm⁻¹) mode is related to the stretching of the metal–oxygen bond in the tetrahedral sites, and other low-frequency modes, including E_g (486 cm⁻¹) and F_2g (590 cm⁻¹), correspond to the octahedral sites.^10,27 It can be noted that with an increase in growth temperature, the peak patterns of the A_lg and E_g vibration modes became symmetrical and narrower. We believe that the thin films would have metal cation defects at low temperatures, and the crystalline quality of the films gradually would increase with growth temperature. A new vibration mode F_2g appeared when the temperature rose to 450 °C, probably due to the entry of Co²⁺ ions into the octahedra. Fig. 5(b) shows the infrared spectra of the FeCo₂O₄ epitaxial films grown at different T_G. We found that the vibration modes of the films grown at 250 and 350 °C were similar. However, the larger epitaxial stress on the film grown at 350 °C had a more obvious effect on the octahedron than the tetrahedron. When the T_G was increased from 250 °C to 350 °C, it was noted that the ν₁ peak shifted to a higher wavenumber, and the intensity of the ν₂ vibration increased, while the ν₃ peak did not move. With increasing growth temperature, the occupation of ions will change. When the T_G was further increased to 450–550 °C, the intensity of the ν₃ vibration decreased, and the ν₂ vibration broadened. The infrared spectrum of the film grown at 350 °C was deconvoluted into three peaks. The peak at 482 cm⁻¹ (ν₁) was from the vibration of octahedral Fe³⁺–O,^28,29 and the vibration of the octahedral Co³⁺–O bond was located at 529 cm⁻¹ (ν₂).³⁰ The signal at 630 cm⁻¹ (ν₃) is considered to arise from tetrahedral Co²⁺–O.^31,32 When the growth temperature was increased to 450 °C, two other peaks and appeared (Fig. 5(c)). The peak was caused by the vibrations of octahedral Co²⁺–O. The octahedral Co²⁺ ions have two possible sources: one is the tetrahedral Co²⁺ ions entering the octahedral sites, and the other is from the reduction of some octahedral Co³⁺ ions to Co²⁺ due to partially released oxygen. As more Co²⁺ enter the octahedral sites, more octahedral Fe³⁺ ions will migrate into the tetrahedral sites. The vibration represented the vibration of tetrahedral Fe³⁺–O.^28,29 Due to the fact that the films were partially decomposed at 650 °C,³³ an increase in the intensity of the octahedral Co²⁺–O vibrations could be observed. More Co²⁺ at the octahedral sites would cause local antiferromagnetic interactions.^34–36 The magnetic moments of the tetrahedral and octahedral cations were antiparallel, showing long-range ferrimagnetism. The coexistence of ferrimagnetism (FIM) and antiferromagnetism (AF) was confirmed by the following magnetic measurements.

Fig. 5 (a) Raman spectra of the FeCo₂O₄ films grown at different T_G; (b) FTIR spectra of the FeCo₂O₄ films grown at different T_G; (c) FTIR decomposition spectra of the FeCo₂O₄ films grown at 350–450 °C; (d) (αhν)²–E_g plots from the absorption spectra of the films grown at different T_G. The inset shows the UV-vis absorption spectra of the FeCo₂O₄ films grown at different T_G; (e) the two optical bandgaps of the film obtained by extrapolating (αhν)² = 0; (f) band structure of FeCo₂O₄.

Fig. 5(d) shows the UV absorption spectra of the FeCo₂O₄ epitaxial films grown at different T_G at room temperature. The inset shows the reflection spectra. The absorption bandgap energy, E_g, can be determined from the UV absorption spectra using the following equation:¹⁷

(αhν)ⁿ = A(hν − E_g) (2)

where hν is the photon energy, α is the absorption coefficient, A is a constant for a given material, and n = 1/2 for an indirect transition, while n = 2 for an allowed directed transition.³⁷ In our case, the best fit indicated n = 2. Similar to the report on NiCo₂O₄,³⁸ we also observed a double bandgap structure in the films at about 3.43 eV and 4.51 eV, as shown in Fig. 5(e). We found that the film grown at 350 °C had the smallest bandgap. Fig. 5(f) shows the three possible electronic transitions. I represents the transition from O 2p to Co 3d-t_2g (or Fe 3d-t_2g), II shows the transition from O 2p to Co 3d-e_g (or Fe 3d-e_g) and III represents the transition from Co 3d-t_2g to Co 3d-e_g (or Fe 3d-t_2g to Fe 3d-e_g). The electron transitions I and II correspond to the two direct bandgaps of the FeCo₂O₄ epitaxial films, respectively.

3.2. Magnetic properties

Fig. 6(a–e) shows the FC-ZFC curves of the FeCo₂O₄ films grown at different T_G under a magnetic field of 500 Oe. It was observed that the magnetic moment in the ZFC curves gradually reached the maximum with an increase in the measurement temperature, and the temperature at which the maximum magnetization is reached in the ZFC curve is defined as T_P. When we continued to increase the measurement temperature, the FC and ZFC curves coincided. With increasing T_G, the magnetic moment gradually increased due to the decrease in APBs,³⁹ and the T_P first decreased and then increases (Fig. 6(f)). The T_P moved to a lower temperature due to the partial decomposition of the film at 650 °C. The APBs in the film resulted in the local antiferromagnetism of spins,⁴⁰ and a decrease in the saturation magnetization.^41,42 It is worth noting that the ZFC curves of the films grown at 450–650 °C reached the maximum magnetization with two exceptional slopes, as shown by the arrows in Fig. 6(c–e). The temperatures at the inflection points of the two exceptional slopes are defined as T₁ (∼100 K) and T₂ (∼250 K), respectively. Below T₁, the change in the magnetic moment with temperature could be ignored. When the measurement temperature was higher than T₁, the magnetic moment increased gradually with increasing measurement temperature. However, when the measurement temperature was above T₂, the magnetic moment increased rapidly. In the FeCo₂O₄ film, the tetrahedral and octahedral magnetic moments are thought to be antiparallel, forming a ferrimagnetic phase. There would also be two kinds of antiferromagnetic phases: one kind of antiferromagnetism is localized in the octahedra formed by the Co²⁺ ions (defined as α-AF),^35,36 and the other is from the APBs (defined as β-AF). The antiferromagnetism between octahedral Co²⁺ is within the lattice, while the antiferromagnetism from the APBs is caused by the interactions between crystalline grains. In contrast, α-AF is more susceptible to temperature. In a small field of 500 Oe, the magnetic moment of the film would be in a chaotic frozen state at low temperatures. When the measurement temperature rises to T₁, due to the thermal disturbance, α-AF becomes weak, and the magnetic moment of the film gradually increases. When the measurement temperature is higher than T₂, β-AF decreases with an increase in the measurement temperature, and the magnetic moment increases rapidly. Of the two antiferromagnetisms with different origins in these films, we believe that there is more β-AF in the films grown at lower T_G and more α-AF in those grown at higher T_G. When the T_G is low (250–350 °C), the film has poor crystalline quality, and many APBs exist in the film. The magnetism in the films is mainly dominated by β-AF and FIM. In addition, lattice distortion weakens the effective magnetocrystalline anisotropy, which lowers the T_P. In order to confirm the existence of two antiferromagnetisms in the films, we further measured the hysteresis loops of the films.

Fig. 6 (a–e) FC-ZFC curves measured at a magnetic field of 500 Oe, and (f) changes in the T_P of the FeCo₂O₄ films grown at different T_G.

Fig. 7(a–e) shows the M–H curves of the films grown at different T_G in the measurement temperature range of 2–400 K. It was found that the saturation magnetization (M_S) increased with T_G, which indicated that the magnetic moments in the films were enhanced, consistent with the results obtained from the MFM observation and FC-ZFC curves. Similar to our previous results for powder samples, Barkhausen jumps were observed in the hysteresis loops below 100 K,^43,44 as shown in the inset of Fig. 7(c). The jump phenomenon disappeared with an increase in the measurement temperature. Barkhausen jumps commonly occur due to the irreversible motion of the domain walls between two regions of opposite magnetic moments.^45,46 In our films, the Barkhausen jumps are considered to arise from the pinning of the AF to FIM. To confirm the existence of different magnetic phases in the films,⁴⁷ we took the film grown at 450 °C as an example. With the increase in T_G, the APBs gradually decrease, while β-AF reduces, and the hysteresis loops of the films, therefore, tended to be saturated. The saturation magnetization and coercivity (H_C) obtained from Fig. 7(a–e) are given in Fig. 7(f). Two extreme values of M_S were observed at about 100 K and 250 K for all the films, which further proved the existence of two kinds of antiferromagnetism in the films. The coercivity decreased gradually with on increasing the measurement temperature, and reduced to 0 Oe at about 250 K. With the measurement temperature, the magnetic phase change in the films is consistent with that in the FC-ZFC test. The coercivity of the film grown at 650 °C was smaller than those of the films grown at 450 and 550 °C, indicating that the film was partially decomposed into soft magnetic materials at high T_G.⁴⁸ Based on the above analysis, we think that there could be one kind of ferrimagnetic phase and two kinds of antiferromagnetic phases in the FeCo₂O₄ films.

Fig. 7 (a–e) Hysteresis loops in the temperature range of 2–400 K corresponding to the FeCo₂O₄ films grown at different T_G. The inset in (c) is the enlarged view of the low field; (f) M_S and H_C values of the films grown at 450 °C, 550 °C and 650 °C in a range of measurement temperatures.

3.3. Electrical transport properties

Fig. 8(a–e) shows the resistivities and conductivities of the FeCo₂O₄ films grown at different T_G. It was found that the resistivity of the FeCo₂O₄ film increased with a decrease in the measurement temperature, showing characteristic semiconductor behavior. A significant similarity could also be found in the T_G dependency of the room-temperature resistivities (= 300 K) and the out-of-plane lattice constants (Fig. 2(c) and 8(f), respectively). Similar findings were reported by Silwal et al.⁴⁹ The electron transport process mainly occurs in the plane of the film, and the in-plane interatomic spacing determines the number of times an electron is scattered. If the in-plane interatomic spacing is small, the electron suffers more scatterings and the resistivity increases. Assuming that the out-of-plane is large when the unit cell volume is unchanged, then the in-plane lattice constant is small, resulting in large resistivity.

Fig. 8 (a–e) Temperature dependence of the conductivities and resistivities of the FeCo₂O₄ films grown at different T_G and the NNH fitting results; (f) activation energies obtained from the NNH fitting results, and the room-temperature resistivities of the FeCo₂O₄ films grown at different T_G.

In order to explore the conductive mechanism of the films, we used the nearest-neighbor hopping mechanism (NNH) to fit the conductivity values:⁵⁰

σ = a × e^{[−ΔE/(kT)]} (3)

where σ is the measured conductivity, a is a constant, k is the Boltzmann constant, and ΔE is the activation energy. The fitting curves of the films were in good agreement with the raw data (Fig. 8(a–e)). The changes in activation energy with the measurement temperature were obtained, as shown in Fig. 8(f). The film grown at 450 °C had the lowest activation energy at 184.5 meV. The structure of the film grown at 450 °C was more ordered. The proposed conduction process is the charge transfer between neighboring octahedral Co²⁺ and Co³⁺.

Fig. 9(a–e) shows the schematic of the growth mode and microstructures of the FeCo₂O₄ films grown on the Al₂O₃ substrate under T_G. Four regions have been defined to explain the changes in the microstructure of the FeCo₂O₄ films with growth temperature. Region-A is the normal FeCo₂O₄ structure, Region-B shows the FeCo₂O₄ structure containing more APBs, Region-C represents the FeCo₂O₄ structure with the octahedra occupied by more Co²⁺, and “Region-D” is the FeCo₂O₄ structure with the decomposition phase. Under low T_G, particle aggregation is observed in the film, and the film contains more APBs (Region-B). With the increase in T_G, the atomic deposition mode gradually changes to layered growth. Due to the effect of substrate stress, the APBs dominate in the structure (Region-B). At 450–550 °C T_G, the growth temperature is high enough, and the APBs decrease. More Co²⁺ ions enter the octahedral sites (Region-C). When the T_G is higher than 650 °C, the FeCo₂O₄ film is partially decomposed (Region-D).

Fig. 9 (a–e) Schematic diagram of the growth mode and microstructures of the FeCo₂O₄ films on the Al₂O₃ substrate; the green areas denote the substrate, Region-A is the normal FeCo₂O₄ structure, Region-B is the FeCo₂O₄ structure containing more APBs, Region-C is the FeCo₂O₄ structure with the octahedra occupied by more Co²⁺, and Region-D is the FeCo₂O₄ structure with the decomposition phase.

4. Conclusions

We have grown a series of FeCo₂O₄ films at different T_G (250–650 °C) on Al₂O₃ (0001) substrates by PLD. The results show that with increasing T_G, due to the difference in ionic mobility, the atomic growth mode changed from the island and layered growth to layered growth. The growth temperature directly affected cation occupation, resulting in different magnetic phases. It was found that with an increase in growth temperature, the magnetic domains of the films became more obvious, and the magnetic moment became stronger. In addition to one ferrimagnetic phase, two kinds of antiferromagnetic phases coexisted in the films: one kind from the antiphase boundary and the localized antiferromagnetism contributed by the octahedral Co²⁺ ions. With rising growth temperature, the antiferromagnetism from the antiphase boundaries decreased, while the antiferromagnetism formed by octahedral Co²⁺ gradually increased. With the increase in measurement temperature, the antiferromagnetism formed by the antiphase boundary first decreased, and then the antiferromagnetism formed by Co²⁺ decreased, and the magnetic moment increased. It was observed by UV absorption that there were double direct bandgaps in the FeCo₂O₄ epitaxial films. Electrical measurements showed that the film grown at 450 °C had the lowest activation energy, and the structure of this film was more ordered. The room temperature resistivity of the films was closely related to the out-of-plane lattice constants.

Author contributions

Jingtong Xie: conceptualization, methodology, data curation, formal analysis, investigation, visualization, writing-original draft. Congmian Zhen: funding acquisition, project administration, resources, supervision, validation, writing-review & editing. Lei Xu: methodology, formal analysis, investigation, visualization, writing-review & editing. Mengyao Su: methodology, formal analysis, investigation, visualization, writing-review & editing. Chengfu Pan: funding acquisition, investigation. Li Ma: funding acquisition, resources, investigation. Dewei Zhao: funding acquisition, resources, investigation. Denglu Hou: funding acquisition, project administration, resources, supervision, validation, writing-review & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was supported by the Key Project of Natural Science of Hebei Higher Education (grant numbers ZD2017045 and QN2019154), the National Natural Science Foundation of China (grant numbers 51971087 and 51901067), and the Natural Science Foundation of Hebei Province (grant numbers A2018205144, A2017210070, and E2019205234).

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