Interface-induced ferromagnetism in μ-Fe₂O₃/β-Ga₂O₃ superlattices

A new monoclinic μ-phase of Fe₂O₃, isomorphic to β-Ga₂O₃, was recently stabilized using plasma-assisted molecular beam epitaxy (PAMBE).¹ Scanning transmission electron microscopy (STEM) structural and chemical imaging showed the registry of the μ-Fe₂O₃ to the β-Ga₂O₃ lattice, indicating that high-quality epitaxial growth of these heterostructures was feasible. While bulk μ-Fe₂O₃ was predicted to be antiferromagnetic, the μ-Fe₂O₃/β-Ga₂O₃ superlattices show ferromagnetic hysteresis at room temperature.¹ 

β-Ga₂O₃ is a wide bang gap (∼4.6 eV) semiconductor with a very high breakdown voltage (E_b = 8 MV/cm) being developed for high-power devices.^2,3 The monoclinic structure of β-Ga₂O₃ results in anisotropic properties with the growth plane (010) having provided the highest growth rate compared to any other orientation, such as (⁠$2¯01$⁠) and (100).⁴ The electron spin lifetimes (on the order of 100 ns)⁵ and the high breakdown voltage² make β-Ga₂O₃ a good candidate for spin-based field effect transistors. These devices typically require a magnetic semiconductor component to provide spin-split valence and/or conduction band edges, which could be achieved by alloying or heterostructuring β-Ga₂O₃ with Fe³⁺-rich (spin-5/2) layers. β-Ga₂O₃ also has a low lattice thermal conductivity,⁶ which is actually beneficial for thermoelectric power factors. While wide bandgap semiconductors are generally bad candidates for thermoelectrics, magnon-electron drag in combination with low lattice thermal conductivity might enable large thermoelectric power factors.⁷ Previously, ferromagnetism at room temperature was reported in Mn²⁺ and Fe³⁺ doped β-Ga₂O₃.^8,9 Density functional theory (DFT) calculations have suggested that Ga cation vacancies at the tetrahedral and octahedral sites result in spin polarization due to the local moments of the O²⁻ anions.¹⁰ Gallium vacancy defects can have charge states from 0 to 3−.¹¹ They are paramagnetic in the 2−, 1−, and 0 charge states, and are diamagnetic in the 3− charge state.¹¹ However, the β-Ga₂O₃ substrates used in both this study and the study from Jamison et al.¹ were found to be purely diamagnetic.

Previous DFT calculations predicted that μ-Fe₂O₃ should exhibit antiferromagnetic order with Fe³⁺ spins on equal numbers of octahedral and tetrahedral sites coupled antiferromagnetically, presumably through the superexchange mechanism.¹¹ The theoretical lattice constants for μ-Fe₂O₃ from the DFT calculations were within 1.5% of those of β-Ga₂O₃, resulting in a strain energy of 0.03 eV per formula unit.¹ According to the DFT calculations, ferromagnetism emerges at the interface region between β-Ga₂O₃ and μ-Fe₂O₃ layers where Ga³⁺ and Fe³⁺ occupy alternating tetrahedral and octahedral sites.¹ 

Here, we test the interfacial magnetism hypothesis from Jamison et al. by investigating how variations in the roughness of the interface layer between β-Ga₂O₃ and μ-Fe₂O₃ layers affect the observed magnetic response. Rougher epilayers exhibit higher saturation magnetizations consistent with higher fraction of Fe³⁺ in the ferromagnetic state.

μ-Fe₂O₃/β-Ga₂O₃ superlattices are grown via PAMBE in a Riber/MBE Control M7 system equipped with Ga and Fe effusion cells and a Veeco oxygen plasma source with a forward power of 300 W (with ≤1 W reflected). The flow of O₂ is continuously monitored and maintained at a growth chamber pressure of 1.5 × 10⁻⁵ Torr. The flux of Fe is held constant between samples with a beam equivalent pressure of 3.4 × 10⁻⁸ Torr. Each μ-Fe₂O₃ layer is deposited for 30 s by cycling the Fe-shutter. The substrate temperature T_sub (as measured through the thermocouple) is varied between 500 and 700 °C. β-Ga₂O₃ spacers are grown by varying the Ga flux (Φ_Ga) between 2.5 and 6 × 10⁻⁸ Torr with a constant deposition time at 400 s.

The substrates used for these growths are 5 × 5 × 0.5 mm³ unintentionally doped (010) β-Ga₂O₃ single crystals (Tamura Corporation). The substrates are cleaned by sonication for 5 min in acetone followed by the same sonication procedure in methanol and isopropanol. Cleaned substrates are indium-bonded to the unpolished side of a 3 in. silicon wafer. A final cleaning is performed in the growth chamber by heating the substrates to 800 °C for 10 min while being exposed to the O₂ plasma. Following the pregrowth cleaning procedure, the substrates are cooled to their final growth temperatures.

The layer structure is designed to investigate how variations in the interface quality between μ-Fe₂O₃ and β-Ga₂O₃ affect the ferromagnetic response. First, a 100-nm-thick buffer layer of β-Ga₂O₃ is grown followed by a superlattice with a constant thickness of μ-Fe₂O₃ (∼3 ml) with ∼8–16 nm-thick β-Ga₂O₃ spacers, depending on the Ga flux. A total of 10 periods are grown with the final layer being a capping layer of β-Ga₂O₃.

Figure 1(a) shows a cross-sectional STEM high-angle annular dark field (HAADF) image of a superlattice grown at T_sub = 700 °C and Φ_Ga = 6 × 10⁻⁸ Torr. STEM data are recorded using a probe corrected Themis-Z S/TEM instrument operated at 200 kV for the HAADF image and an FEI Titan 60/300 STEM instrument operated at 300 kV with a beam current of 60–90 pA for the energy dispersive x-ray (EDX) elemental map. Contrast in the HAADF image is related to the atomic number; thus, the Fe oxide layer exhibits dark contrast relative to the β-Ga₂O₃ spacers. The EDX elemental map in Fig. 1(b) confirms the identification of the layers in the superlattice and Au on the top protective layer. The HAADF-STEM image at higher magnification [Fig. 1(c)] shows the μ-Fe₂O₃/β-Ga₂O₃ interfaces along the [001] direction. While the epitaxial relationship is well defined and there are no detectable defects at the interfaces, the interfaces between μ-Fe₂O₃ and β-Ga₂O₃ are undulating [Fig. 1(c)]. This may be associated with roughness due to the island-layer-by-layer growth mode or elemental diffusion between Fe and Ga around their interfaces.

The entire growth (i.e., during both Ga and Fe deposition) is observed by in situ reflection high energy electron diffraction (RHEED), representative patterns shown in Figs. 1(d) and 1(e) indicative of 2D growth without an identifiable change in lattice parameters or surface structure.

To investigate the epilayer morphology of the superlattices, atomic force microscopy (AFM) is performed using the Bruker AXS Dimension Icon. Figure 2 shows 1 × 1 μm² scans of the starting β-Ga₂O₃ substrate and different superlattices grown at various substrate temperatures. The bare (010) β-Ga₂O₃ substrate has a surface roughness of 0.205 nm [∼1 monolayer (ML) roughness].

The AFM surface morphologies of the superlattices appear similar to previously reported β-Ga₂O₃ (010) PAMBE growths at these temperatures.¹² Islandlike plateaus are clearly seen in the AFM data for all the samples, regardless of the growth conditions. This is indicative of island-layer-by-layer growth or the Frank–van der Merwe (FM) growth mode and is consistent with the observed 2D RHEED patterns. The FM growth mode is only stabilized for the so-called “strong” substrates whose lattice constant is imposed on to the film atoms,¹³ which implies near-perfect lattice matching between the substrate and the growth layers. Because the theoretical lattice constants of μ-Fe₂O₃ are within ∼1.5% β-Ga₂O₃,¹ the observations of the FM growth mode seen in the AFM data confirm that the μ-Fe₂O₃ layers are lattice-matched to β-Ga₂O₃ across the 10 period superlattice structure.

The surface roughness of the superlattices is strongly correlated with the substrate temperature T_sub [Fig. 2(e)]. Samples grown at T_sub = 700 °C have surface roughness measurements close to ∼0.5 nm (2 ML), whereas those grown at T_sub = 500 °C have large surface roughness close to ∼1.1 nm (4 ML). This suggests that the SL interface quality deteriorates at low T_sub perhaps due to statistical roughening caused by a reduced adatom diffusion length. The surface roughness measurements are also correlated with Φ_Ga. Superlattices grown at Φ_Ga = 6 × 10⁻⁸ Torr have smoother surfaces (RMS ∼ 0.54 nm), and thus have better interface quality than those grown at Φ_Ga = 2.5 × 10⁻⁸ Torr (RMS ∼0.70 nm). The smoothest surfaces are observed at high Φ_Ga and high T_sub.

X-ray diffraction (XRD) is performed using a Bede diffractometer in the triple axis mode and a 4-bounce (220) Ge monochromator. High-resolution XRD in Fig. 3 shows the presence of superlattice peaks (SL₀, SL_n+1) alongside the substrate peak for all the samples in this study. Jamison et al. determined the b lattice parameter for μ-Fe₂O₃ through CADEM (Ref. 14) XRD fitting of the superlattice XRD data as 3.12 ± 0.4 Å, consistent with DFT calculations.¹ The average b lattice parameter for the superlattices is calculated from the interplanar spacing (d₀₂₀) of the (020) 0th order SL₀ diffraction peak assuming a monoclinic structure for the superlattices and ranges from 3.046 to 3.055 Å. The individual Fe₂O₃ layer thicknesses range from 2.86 to 4.11 ml. The average Ga₂O₃ spacer thickness is ∼29 ml at Φ_Ga = 2.5 × 10⁻⁸ Torr and ∼53 ml at Φ_Ga = 6.0 × 10⁻⁸ Torr. Laue oscillations are noted in the XRD data but disappear at low T_sub and low Φ_Ga, indicative of higher interface roughness. The SL₋₁ peaks in the XRD data are narrower at high T_sub and high Φ_Ga (large spacer thickness) (Fig. 3). The full width at half maximum (FWHM) of the SL₋₁ peak is strongly anti-correlated with Φ_Ga [Fig. 3(b)]. The FWHM at Φ_Ga = 6 × 10⁻⁸ Torr is ∼ 2 × smaller than at Φ_Ga = 2.5 × 10⁻⁸ Torr. The FWHM of the XRD satellite peaks are indicative of the coherency of the SL structure and are sensitive not just to interface roughness but also to strain inhomogeneity, which can arise due to composition fluctuations or partial strain relaxation.

Superconducting quantum interference device (SQUID) magnetometry is performed on the SL structures to investigate their magnetic properties. The applied field (H) is scanned in a hysteretic fashion between ±80 kOe along the [102] direction (in plane) and the induced moment is measured. The diamagnetic background is removed by measuring magnetization versus H of a bare β-Ga₂O₃ substrate, which exhibits a purely diamagnetic response. The magnetization (M) of the μ-Fe₂O₃ layers is obtained by normalizing the magnetic moment of each sample by the volume of μ-Fe₂O₃ within each sample as determined by the XRD measurements. Ferromagnetic hysteresis (non-zero coercivity and remanence) is observed across the measured temperature range (5–300 K) as shown in Fig. 4(a). A paramagnetic component emerges at low temperature.

Isolated (dilute) Fe³⁺ ions should exhibit a paramagnetic response; thus, the diffusion of Fe³⁺ into the β-Ga₂O₃ spacers is likely the reason for the paramagnetic component. Assuming that at high-field the ferromagnetic component is saturated, and the antiferromagnetic component has negligible magnetization, we fit the high-field (|H| > 10 kOe) magnetization data to the Brillouin function [Eqs. (1) and (2)],

where $θ$ is the paramagnetic Curie temperature, $Np$ is the density (cm⁻³) of paramagnetic moments, g = 2.02 is the g-factor, J = 5/2 for Fe³⁺, T is the measurement temperature, and $Msat$ is the saturation magnetization of the ferromagnetic component. Examples of M versus T data at $T<40K$ are shown in Fig. 5(a), which are fit to the temperature dependent Brillouin function using just two free parameters, $θ$ and $Np$⁠. Next, the M versus H data for this sample, taken at T = 300 K [Fig. 5(b)], are fit to the field-dependent Brillouin function using a single parameter $(Msat)$ assuming that the previously acquired values of $θ$ and $Np$ do not vary with the temperature. Following this procedure, the paramagnetic component at all temperatures and fields is described by Eq. (2) and is subtracted from the data to isolate the purely ferromagnetic response [Fig. 4(c)]. The median paramagnetic Curie temperature for these superlattices is $θ=−3.55±1.03K$⁠, which indicates an antiferromagnetic coupling between dilute Fe³⁺ ions. Similar behavior was previously studied in II–VI dilute magnetic semiconductors in the low alloying regime and arises from small clusters of antiferromagnetically coupled spins via short-range superexchange.¹⁵ The magnetic properties of the superlattices, including the Brillouin parameters, are summarized in Table I.

The M versus T behavior is obtained in the standard zero-field-cooled (ZFC) and field-cooled (FC) conditions using a SQUID magnetometer with an applied field of 500 Oe. Figure 6(a) shows ZFC and FC curves for a superlattice grown at T_sub = 700 °C and Φ_Ga = 6 × 10⁻⁸ Torr. The discrepancy between the ZFC and FC data is indicative of superparamagnetic clusters (SCs), i.e., a distribution of single-domain ferromagnetic clusters, whose spontaneous magnetization averages to zero over time due to thermal fluctuations.¹⁶ As described by Bruvera et al., the peak at T ∼ 20.5 K in the ZFC curve does not correspond with a representative blocking temperature (T_B) for the SCs, but rather is governed by the details of the cluster size distribution.¹⁷ A more reliable method involves taking the derivative with respect to the temperature of the difference between the ZFC-FC data, d(ZFC-FC)/dT [Fig. 6(b)], which represents the distribution of T_B¹⁸ associated with the size distribution of SCs. The average T_B is estimated by fitting a Gaussian to the d(ZFC-FC)/dT data (T_B = 10.1 K for the sample in Fig. 6). Superparamagnetic response is observed in samples grown at T_sub = 700 °C with T_B ranging from 9.8 to 10.7 K. At T_sub = 600 °C, this behavior is less evident with T_B = 13.1 K. For superlattices grown at T_sub = 500 °C, there is no ZFC/FC discrepancy of superparamagnetism.

The saturation magnetization varies with substrate temperature, shown in Fig. 4(b). As is illustrated in Fig. 7(a), M_sat is larger for samples grown at low T_sub. The ferromagnetic hysteresis loops saturate at M_sat∼ 0.1 μ_b/Fe³⁺ at T_sub = 700 °C, ∼0.2 μ_b/Fe³⁺ at T_sub = 600 °C, and ∼0.4 μ_b/Fe³⁺ at T_sub = 500 °C [Fig. 4(c)]. The squareness of the ferromagnetic hysteresis also increases at low T_sub. The coercive field (H_c) at 300 K varies between ∼54 and 196 Oe and increases with T_sub, from ∼54 Oe at T_sub = 500 °C to ∼196 Oe at T_sub = 700 °C. The saturation magnetization is also correlated with the RMS surface roughness measurements [Fig. 7(b)]. Superlattices with rougher interfaces have larger values of M_sat. Evidently, the ferromagnetic phase increases as the interfaces get rougher. This correlation supports the interfacial magnetism hypothesis for the ferromagnetic response of these superlattices. As the growth surface becomes rougher, and the interface ferromagnetic region increases, the saturation magnetization increases with a larger fraction of Fe in a ferromagnetic state. Conversely, at higher substrate temperatures where the interfaces are smoother, the saturation magnetization decreases.

Additionally, these trends in the ferromagnetic response are consistent with the observations of superparamagnetism as evidenced by the ZFC/FC data described above. Samples with smoother interfaces grown at high temperature exhibit a clear superparamagnetic component (ZFC/FC divergence), which is consistent with a reduction in thickness of the interface ferromagnetic phase. As the thickness of the phase reduces below the stable domain size, superparamagnetic behavior is expected. Conversely, samples with rougher interfaces that exhibit the strongest ferromagnetic response exhibit no clear superparamagnetic behavior. The overall density of paramagnetic moments, as obtained through the Brillouin fits, exhibits a very small decrease with roughness, considering the error bars [Fig. 7(c)]. Although this trend is very weak, it does correlate well with the trends in the superparamagnetic response and the ferromagnetic response, such that rougher interfaces appear to lead not only to a smaller superparamagnetic component but also to a smaller number of paramagnetic moments and a larger ferromagnetic component (high M_sat).

The combined structural and magnetic characterization study described above is consistent with the ferromagnetic component in the magnetization of these superlattices emerging from the interface layer between μ-Fe₂O₃ and β-Ga₂O₃ and rules out the presence of secondary phases such as Fe clusters. This supports the previous DFT calculations, where ferromagnetism emerges at the interface region of the Ga and Fe phases of the monoclinic μ-Fe₂O₃/β-Ga₂O₃ superlattice structures.¹ However, in addition to experimentally validating the interface ferromagnetism prediction, we observe the emergence of superparamagnetism in samples with the smoothest interfaces. This suggests that as the ferromagnetic interface layer becomes too thin (as expected for smooth interfaces), the zero-field magnetization becomes unstable against rotations, i.e., superparamagnetism. Further work is needed to examine the size and geometry of these superparamagnetic clusters.

Superlattices composed of ferromagnetic μ-Fe₂O₃ and diamagnetic β-Ga₂O₃ on (010) oriented β-Ga₂O₃ substrates were grown using PAMBE. The interface quality was varied by forming identical superlattice structures at various growth conditions (T_sub = 500–700 °C, Φ_Ga = 2.5–6 × 10⁻⁸ Torr). STEM showed that the μ-Fe₂O₃ and β-Ga₂O₃ layers are lattice matched across the entirety of the superlattice. AFM imaging shows that the growth morphology becomes rougher as the substrate temperature and Ga fluxes are decreased. The AFM surface roughness is ∼2.1× larger for the superlattices grown at T_sub = 500 °C than at T_sub = 700 °C. The XRD linewidths are similarly ∼2× larger for the superlattices grown at Φ_Ga = 2.5 × 10⁻⁸ Torr than at Φ_Ga = 6 × 10⁻⁸ Torr. Magnetization data also confirm that the ferromagnetic response changes with the properties of the interfaces. The ferromagnetic component of the magnetization increases with interface roughness in agreement with the interface origin of the ferromagnetic phase in μ-Fe₂O₃/β-Ga₂O₃ superlattices. Additionally, samples with a smoother interface exhibiting a smaller ferromagnetic component show a superparamagnetic response and a higher density of paramagnetic moments.

This work was supported by the Center for Emergent Materials at The Ohio State University, an NSF MRSEC (No. DMR-1420451), and by the Army Research Office MURI (No. W911NF-14-1-0016). Electron microscopy was performed at the Center for Electron Microscopy and Analysis (CEMAS) at The Ohio State University.