Iron oxide magnetite (Fe₃O₄), a half-metallic ferromagnet with large spin polarization and high Curie temperature of 858 K, has attracted much attention owning to its intriguing physical properties and potential applications in spintronic devices.^[1–6] The further applications on devices closely rely on the physical properties of Fe₃O₄ films that depend on the type of substrates, thickness and deposition conditions. As we know, epitaxial Fe₃O₄ films have been grown on a variety of single crystal substrates, e.g., MgO, α-Al₂O₃, ZnO, Si, and GaAs, using different methods such as molecular beam epitaxy (MBE), sputtering, and pulse laser deposition (PLD).^[3,7–9] Among the substrates mentioned above, MgO is one of the most frequently used because it has a nearly perfect lattice match with Fe₃O₄. The lattice constant of MgO is 4.213 Å, which is nearly the half of Fe₃O₄ (8.3967 Å). Although the lattice mismatch in Fe₃O₄ films on MgO (Fe₃O₄/MgO) is only +0.3%, the prominent changes took place in the magnetic and electronic properties of Fe₃O₄/MgO films due to the tensile strain imposed by MgO substrate.^[10,11] It has been already reported that the magnetic properties of Fe₃O₄ films change significantly with the decreasing thickness, which is closely related with the existence of antiphase boundaries (APBs).^[12–14] Revealing the strain effects from substrates and the changes of microstructure with thickness would provide useful information for understanding the magnetic properties of Fe₃O₄ films.

Raman spectroscopy is a powerful tool to probe the microstructure of thin films and its relationship with other physical properties of oxides.^[15,16] In past decades, Raman spectroscopy has been widely employed to study the structure of Fe₃O₄ films.^[8,9,17] Tiwari et al. have demonstrated that Raman spectroscopy is a tool to evaluate the APBs in Fe₃O₄ films.^[9] Kumar et al. have employed Raman spectroscopy to study the spin-phonon coupling in Fe₃O₄ films at Verwey temperature.^[18] However, most researches were carried using non-polarized Raman spectroscopy, while polarized Raman study of Fe₃O₄/MgO was rarely reported. With the help of polarized Raman scattering, the symmetry of Raman peaks can be assigned, and the crystallinity and orientation of film can be identified. What is more, the overlapped Raman peaks can be isolated, promising feasible peak fitting and further analysis.

In this work, Fe₃O₄ films were studied systematically as a function of film thickness by polarized Raman spectroscopy. Discrepancy to Raman selection rules (RSRs) observed in the cross-sectional geometry was attributed to the tetragonal deformation in the growth direction due to the lattice mismatch between Fe₃O₄ and MgO. Raman peaks were fitted with different numerical functions and a deeper insight into thickness effects on the structure of Fe₃O₄ films was obtained.

Epitaxial Fe₃O₄ films were deposited on MgO single crystal substrates using reactive magnetron sputtering. The details of deposition were reported elsewhere.^[19] In this work, Fe₃O₄ films with thicknesses of 27 nm, 50 nm, 85 nm, 170 nm, 217 nm are used for the Raman study. The epitaxial properties of Fe₃O₄ films have been demonstrated using θ−2θ and Φ-scan x-ray diffraction (XRD) experiments. Raman spectra were collected under backscattering geometry using a confocal micro-Raman spectrometer (Horiba/Jobin Yvon Aramis) with a 473 nm laser source. The laser power on the film surface was less than 0.5 mW to prevent laser-induced heating effect on films. Two types of backscattering configurations, including normal and cross-sectional scattering configurations were employed in the Raman measurements. The schematic diagraphs of these two Raman measurement configurations are shown in Fig. 1, in which the X, Y and Z axes were the laboratory coordinates. The x and y axes of the Fe₃O₄ film were along the [100] and [010] directions of the MgO substrate, while the z axis was the growth direction of the film. In the normal scattering configuration as illustrated in Fig. 1(a), the x, y and z axes of films parallel respectively with the X, Y and Z axes. On the other hand, in the cross-sectional scattering configuration, the x, y and z axes of films are respectively along the Z, Y and X axes. As displayed in Fig. 1(b), the incident light propagates along the Z axis, which corresponds to the x axis of Fe₃O₄ film. Thus the incident polarization (P_i) parallel with the z axis, and the scattered polarization can be along the y (or z) axes. Cross-sectional Raman scattering can provide more information about the stress distribution, domain structure and the crystalline orientation of thin films.^[20–22]

Bulk Fe₃O₄ has a cubic inverse spinel structure with space group Oh7 (Fd3m), which gives rise to five Raman-active modes, Γ_R = A_1g + E_g + 3T_2g. Normally, only four peaks are observed in the Raman spectra of Fe₃O₄, as revealed in the previous studies.^[8,9,17] Figure 2 displays the polarized Raman spectra of the 217-nm-thick Fe₃O₄ film collected in different scattering configurations. According to the RSRs,^[23]A_1g and E_g modes only appear in the VV scattering geometry under the normal scattering configuration, in which P_i is along the X axis as shown in Fig. 1(a), while the T_2g modes show up in the VH scattering geometry. In Fig. 2(a), the Raman modes comply with the RSRs in the normal backscattering configuration. The peaks around 307 cm⁻¹ and 665 cm⁻¹ are assigned as the E_g and A_1g modes, respectively, while the peaks at 193 cm⁻¹ and 535 cm⁻¹ are attributed to the T_2g modes.^[17,18,22] The Raman spectra of other thinner films share the similar polarization dependences. The good agreement between our results and RSRs suggests the highly epitaxial characteristics of Fe₃O₄ films. A very weak peak can be seen at the A_1g position in the VH geometry, which can be attributed to the lattice defects in the Fe₃O₄ film. Although Fe₃O₄ films were epitaxially grown, small amount of defects, such as dislocations and vacancies, cannot be excluded. It has been demonstrated by many researchers that the antiphase boundaries (APBs) is the main lattice defects that play a key role in the anomaly properties of epitaxial Fe₃O₄ films.^[11,24,25] APBs are related to the lattice relaxation, formed at the junction of neighboring grains.^[13,26]

In order to further study the microstructure in Fe₃O₄ films, the cross-sectional Raman scattering was carried out. In Fig. 2(c), the remarkable spectral features are observed when P_i parallels with the z axis. The T2g(3) mode appears in the VV geometry which is in contract with the results obtained in the normal Raman scattering configuration. Furthermore, the polarized spectra resemble the features of the normal scattering configuration as the incident polarization is along the y axis (not shown here). The A_1g and E_g modes appear in the VV geometry, while the T_2g modes are observed in the VH geometry. Such spectral divergence between Figs. 2(a) and 2(c) cannot be attributed to the lattice defects in the films. If the leakage of T2g(3) mode comes from lattice defects, T2g(3) mode should be seen in the VV geometry all the time when the incident polarization parallels with the three axes of the film. However, it only turns out when the incident polarization parallels with z axis. As discussed previously, the crystalline axis a = b > c in Fe₃O₄ films on MgO substrates. The in-plane axes are equal, so the polarized Raman spectra in the normal scattering configuration are identical while rotating the incident polarization from the x axis to the y axis. In contrast, the out-of-plane axis is compressed and shorter than the in-plane axes, giving rise to a tetragonal deformation in Fe₃O₄ films. As the lattice constant of Fe₃O₄ is slightly smaller than the double of the MgO lattice constant, the in-plane axes of Fe₃O₄ films are elongated in two directions due to the tensile stress in the film. The tetragonal deformation not only leads to the elongated in-plane axes, but also can induce the lattice dislocations in the out-of-plane axis in order to release internal stress in the film. The orientation of the crystalline axis for the Fe₃O₄ film is not strictly along the 〈100〉 directions of the MgO substrate due to the existence of APBs.^[13] Luysberg et al. have demonstrated that the presence of APBs are associated with the formation of misfit dislocations with partial Burgers vectors.^[27] As demonstrated by the selected-area electron diffraction (SAED) patterns, the charge ordering of B-site Fe atoms exists in the epitaxial Fe₃O₄ films.^[19] The T2g(3) mode originates from the asymmetric bends of oxygen ions with respect to Fe ions, so that it is sensitive to the strain deformation along the crystalline axes.^[28] The tetragonal deformation in the film would contribute to the conflicts to RSRs for the T2g(3) mode.^[29] As presented in Fig. 2(b), the T2g(3) mode arises in the VV geometry after rotating the polarization by 45° under the normal incident configuration. According to the RSRs, the T2g(3) mode is not zero when the incident and scattered polarizations are parallel to the [110] direction. The VV spectra in the cross-sectional configuration (Fig. 2(c)) exhibits the obvious similarity to the VV spectra under 45° polarization geometry in Fig. 2(b), suggesting the existence of nano-sized areas in which the lattice dislocations are along the 〈110〉 directions. Therefore, the presence of T2g(3) mode in the VV spectra in the cross-sectional configuration undoubtedly demonstrated the existence of APBs.

In order to get a clear insight into the evolution of Raman peaks as a function of film thickness, the Raman spectra were deconvoluted using the Lorentz/Gaussian mixed function. Figures 3(a)–3(c) show the thickness-dependent peak positions of E_g, T2g(3) and A_1g modes. Taking the A_1g mode as an example, it shifts from 671.7 cm⁻¹ to 668 cm⁻¹ quickly when the film thickness increases from 27 nm to 85 nm (6.4 × 10⁻² cm⁻¹/nm). The similar phenomenon was observed by Tiwari et al. in the Fe₃O₄ films thinner than 150 nm.^[9] Then, the peak position of A_1g mode varies slowly, with a rate of 5.8 × 10⁻³ cm⁻¹/nm, for a thicker film, as exhibited in Fig. 3(c). The other two peaks shift following the same trace as that of the A_1g mode. As presented in Figs. 3(d)–3(f), similar to the peak position, bandwidth decreases while film thickness increases from 27 nm to 85 nm, then keeps at a constant for thicker films. As we know, bandwidth is the reciprocal of phonon lifetime, which decreases while lattice defects increase, so that the broadening of Raman peaks is associated with the increasing defects in the lattice.^[30,31] More lattice defects emerge as a result of the increasing density of APBs while the film thickness is decreasing.^[27,29,32] Thus, the broadening of Raman peaks of Fe₃O₄ films can be attributed to the increasing APBs when the film thickness decreases. It is accepted that the lattice relaxation takes place to release internal stress while the film thickness increases.^[27,29] At the same time, the grain size in the film becomes larger as a result of decreasing APBs.^[13] From the Raman spectra, one can see the improvement of Raman signal, such as bandwidth shrinking and frequency softening, as presented in Fig. 3.

Taking a close look at the fitting curves of Raman peaks, it is interesting to find that the lineshapes of Raman peaks are different. One can see that the T2g(1) mode exhibits an asymmetric lineshape with a tail at low frequency, as presented in Fig. 4(a). In sharp contrast, as shown in Figs. 4(b)–4(d), the E_g, T2g(3) and A_1g modes show the symmetric lineshape, which can be well fitted by the Lorentz function, implying the good crystalline quality of Fe₃O₄ films. The asymmetric lineshape comes from the lattice disorder effects, which has been observed in some oxides and semiconductor films.^[33–35] In the ideal single crystal, only phonons near the center of Brillouin zone (q ∼ 0) contributed to the Raman spectrum. On the other hand, the disorders in the film result in the breaking of the translational symmetry, leading to the contribution of q ≠ 0 phonons to Raman lineshape, which is the so-called finite-size effect. Since the Fe₃O₄ films in our hand are highly oriented, the lattice defects are low. As we know, the defects in Fe₃O₄ films mainly from the location shift of Fe ions.^[36] This kind of defects mainly affects the low frequency Raman peaks, so that the T2g(1) mode exhibits an asymmetric lineshape. Furthermore, these high-frequency E_g, T2g(2) and A_1g modes originating from Fe–O vibrations keep the symmetric Lorentz lineshape. The asymmetric lineshape of Raman modes can be described by a spatial correlation model. The assumption of a Gaussian factor exp(−q²L²), where L is the diameter of the correlation region, is employed in the spectra fitting of mode T2g(1).^[33–35]

The Raman intensity I(ω) at a frequency ω can be written as

$$ \begin{eqnarray}I(\omega )\sim \displaystyle {\int }_{0}^{1}\exp \left(-\displaystyle \frac{{q}^{2}{L}^{2}}{4}\right)\displaystyle \frac{4\pi {q}^{2}{{\rm{d}}}^{3}q}{{[\omega -\omega (q)]}^{2}+{\left(\displaystyle \frac{\gamma (q)}{2}\right)}^{2}},\end{eqnarray}$$ ()

As shown in Fig. 5(a), the bandwidth increases while film thickness is decreasing, especially for the films thinner than 100 nm. The broadened bandwidth clearly evidences more lattice defects in thinner Fe₃O₄ films. Interestingly, one can see from Fig. 5(b) that L increases with decreasing thickness, following the same trace of bandwidth. As we know, L is the correlation length, which can be used to represent the grain size in the film.^[33–35] The results shown in Fig. 5(b) suggest that the correlation length (or grain size) increases with the decreasing film thickness. It has been reported that the asymmetry feature becomes smaller with the increasing correlation length. The asymmetry of T2g(1) is calculated using the ratio of half-widths at half maximum on low- and high-frequency sides (Γ_l/Γ_h). As shown in the inset of Fig. 5(b), the asymmetric ratio of T2g(1) becomes smaller in a thinner film, which agrees well with the prediction from the variation of L. It has been demonstrated that the density of APBs in a thin Fe₃O₄ film is higher than that in a thick Fe₃O₄ film. Consequently, the grain size in a thinner Fe₃O₄ film is thought to be smaller. However, as shown in Fig. 5(b), grain size increases in the thin Fe₃O₄ film. As we know, L is physically the correlation length for Raman phonons, in which phonons can propagate freely. Our results suggest that APBs are just a kind of lattice defects rather than crystalline boundaries, at least phonons take the adjacent antiphase areas as a whole for propagation.

In this work, polarized Raman spectroscopy has been employed to investigate the microstructure of Fe₃O₄ films as a function of film thickness. The Raman spectra in the cross-sectional configuration clearly imply the tetragonal deformation in the growth direction due to the lattice mismatch between Fe₃O₄ films and MgO substrates. The Raman peaks shifting to a higher frequency indicates the decrease of tensile strain with decreasing film thickness, while the broadened peaks imply the increasing lattice defects due to the increasing density of APBs. Moreover, the lowest T_2g mode exhibits an asymmetric lineshape, which can be used to monitor the grain size in the Fe₃O₄ film. Our results provide a deeper insight into the lattice structure of Fe₃O₄ films on MgO substrates, which are expected to be helpful for preparation of Fe₃O₄ films and further applications in spintronic devices.