Introduction

Magnons, i.e., collective spin wave excitations originating from spin precession in magnetically ordered materials, have the potential to serve as a promising medium for quantum information devices. Since the propagation of magnons does not require the transport of a charge, preventing electrical losses such as Joule heating1, it gives rise to a burgeoning research field known as magnonics2,3. Antiferromagnetic insulators have garnered considerable attention in this emerging field, primarily due to their ultrafast spin dynamics compared to ferromagnetic counterparts, which are essential for device operation in the terahertz range4,5,6. Nevertheless, effectively guiding and coherently manipulating magnons using external stimuli is still a significant challenge.

Heterointerfaces between two different materials can provide model systems for investigating the relation between external stimuli and collective spin waves. Examples are the effects of lattice strain7, interfacial coupling, and charge transfer on magnons8,9 and their spin currents10,11,12. In particular, interfaces between an antiferromagnetic insulator and a metal have been considered for novel spin-charge conversion13,14. Despite some astonishing predictions from magnetic insulator/metal interfaces15, the fundamental understanding of how a metallic interface affects the spin-wave dispersion of an antiferromagnetic insulator remains elusive.

Sr2IrO4, a 5d transition-metal oxide, is a quasi-two-dimensional antiferromagnetic insulator with strong spin-orbit interaction resulting in the Jeff = 1/2 pseudospins. The distinctive canted antiferromagnetism and magnetic anisotropy in the Jeff = 1/2 state can be useful for spintronic applications16,17. Notably, Sr2IrO4 hosts spin waves at terahertz frequencies with a significant stress response mediated by strong spin-orbit interactions7. Its similarities to La2CuO4, a parent compound of high Tc superconductors, suggest a potential for superconducting antiferromagnetic magnonics18. Therefore, Sr2IrO4 presents a compelling avenue for studying the influence of metallic interfaces on spin-wave dispersion and its heterostructures offer opportunities to explore intriguing phenomena19,20.

In this article, we report a systematic investigation of the spin-wave dispersion in Sr2IrO4 thin films epitaxially interfaced with various metallic and insulating single crystals. High-resolution resonant inelastic x-ray scattering (RIXS) measurements reveal a significant softening of single-magnon peaks near the (π/2, π/2) zone boundary for Sr2IrO4 thin films interfaced with metallic crystals, without any accompanying broadening of the magnon spectrum. In contrast, the magnon spectrum of Sr2IrO4 thin films remains unaltered when interfaced with insulating crystals. Raman spectroscopy further corroborates these findings, as the two-magnon excitations—predominantly representing zone-boundary magnons—exhibit a consistent trend. We propose that electron-phonon interactions, occurring either at the heterointerface or within the metallic substrate, may modify the magnon dispersion in Sr2IrO4 thin films via long-range magnon-acoustic phonon interactions. Complementary experimental techniques, including resonant elastic x-ray scattering, optical spectroscopy, and transmission electron microscopy, indicate that conventional interfacial mechanisms such as strain, doping, and proximity effects are unlikely to account for these observations. Our findings give an insight into magnonics, leveraging metal-insulator transitions in adjacent crystals as an effective mechanism for manipulating terahertz magnon propagation.

Results

We constructed epitaxial heterostructures by depositing Sr2IrO4 epitaxial thin films on ruthenates single crystals (Fig. 1) using pulsed laser deposition21,22. To minimize the potential influence of spin-spin interactions, we selected ruthenates with paramagnetic characteristics. Sr2RuO4 single crystals exhibit a tetragonal crystal structure and metallic transport behavior, while Ca3Ru1.98Ti0.02O7 single crystals are orthorhombic and undergo a metal-insulator transition at 55 K, exhibiting metallic behavior above this temperature and insulating behavior below it23,24. This transition is accompanied by minor changes in the b- and c-lattice constants (Supplementary Fig. 1). To systematically investigate the strain effects, we also studied Sr2IrO4 thin films deposited on insulating (LaAlO3)0.3(Sr2TaAlO6)0.7 (LSAT) substrates, which has a similar lattice mismatch with Sr2IrO4 as Sr2RuO4.

Fig. 1: Sr2IrO4 thin-film heterostructure systems.
figure 1

Schematic representation of Sr2IrO4 thin films interfaced with various substrates, including ruthenates single crystals and reference LSAT substrates. Sr2RuO4 and LSAT single crystals have comparable in-plane lattice constants but exhibit distinct electronic properties, with Sr2RuO4 being metallic and LSAT insulating. The Ca3Ru1.98Ti0.02O7 single crystal has a temperature-dependent metal-insulator transition, exhibiting metallic behavior above 55 K and becoming insulating below this temperature.

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High-resolution Z-contrast scanning transmission electron microscopy of the Sr2IrO4/Sr2RuO4 heterostructure (Supplementary Fig. 2) reveals an atomically sharp heterointerface with minimal interfacial diffusion, similar to the sharp Sr2IrO4/Ca3Ru2O7 (ref. 25) and Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterointerfaces (Supplementary Fig. 3). Distinct x-ray (0 0 l)-diffraction peaks are observed for the Sr2IrO4 thin films as well as the Sr2RuO4, Ca3Ru1.98Ti0.02O7, and LSAT substrates, accompanied by interference fringes near the (0 0 12) peak (Supplementary Fig. 4a).

X-ray reciprocal space mapping confirms that the in-plane lattice of Sr2IrO4 thin films is strained to all three substrates without relaxation (Supplementary Fig. 4b, c). Notably, the Sr2IrO4 thin films on both Sr2RuO4 and LSAT experience the same amount of compressive strain of −0.51% (Supplementary Table 1). In contrast, the Sr2IrO4 thin film on Ca3Ru1.98Ti0.02O7 undergoes a more complex strain profile: −2.22% compressive strain along the a-axis and 0.33% tensile strain along the b-axis above 55 K, which increases to 2% tensile strain along the b-axis below 55 K (Supplementary Table 2).

In recent years, RIXS has emerged as a powerful tool for collecting momentum-resolved and element-specific insights into collective magnetic excitations, such as magnons and spin-orbit excitons, in transition metal oxides26,27,28,29. Figure 2a presents representative energy loss spectra of our Sr2IrO4/Sr2RuO4 heterostructure, measured with different momentum transfers in the magnetic Brillouin zone. Figure 2b provides an intensity map derived from the energy loss spectra in Fig. 2a, highlighting the key spectral features. The low-energy range (0–0.25 eV) shows a dispersive magnetic excitation (magnon), while the higher-energy range (0.30–0.90 eV) reveals a dispersive orbital excitation (spin-orbit exciton), both of which reflect the intrinsic properties of the system18,27. The presence of well-defined dispersive magnons and spin-orbit excitons underscores the high crystallinity of the Sr2IrO4/Sr2RuO4 heterostructure, further validating the quality of the epitaxial thin films used in this study.

Fig. 2: RIXS spectra of the Sr2IrO4/Sr2RuO4 heterostructure.
figure 2

a Energy loss spectra of the Sr2IrO4/Sr2RuO4 heterostructure at 20 K with different momenta in the Brillouin zone. The inset illustrates high symmetry points of both the undistorted tetragonal unit cell and the magnetic unit cell. b Image plot of the energy loss spectra shown in (a), highlighting the dispersive magnon and spin-orbit exciton modes. The detection of well-defined dispersive features confirms the high crystalline quality of the Sr2IrO4 thin film. The orange dashed line in (a, b) serves as a guide to the magnon dispersion. The intensity scale bar is in arbitrary units. c Schematic of the horizontal scattering geometry used during the RIXS measurements.

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The noteworthy feature observed in the RIXS experiments is the pronounced softening of the low-energy magnon dispersion in Sr2IrO4 films, specifically near the (π/2, π/2) zone boundary, when their interfaced single-crystal substrates transition from insulating to metallic states. This softening, by ~20 meV, is a striking contrast to the consistent magnon energies observed in other regions of the Brillouin zone. Figure 3a illustrates the low-energy magnon spectra of all Sr2IrO4 thin films along the high-symmetry directions (π, 0) and (π/2, π/2). At (π, 0), the magnon peak energy remains nearly identical, around 200 meV, across all systems studied: Sr2IrO4/Sr2RuO4, Sr2IrO4/Ca3Ru1.98Ti0.02O7 (both above and below 55 K), Sr2IrO4 /LSAT, and the Sr2IrO4 single crystal. However, at (π/2, π/2), a notable difference emerges. Thin films interfaced with metallic substrates—Sr2IrO4/Sr2RuO4 (orange) and Sr2IrO4/Ca3Ru1.98Ti0.02O7 above 55 K (red)—exhibit a significant softening of the magnon peak energy, with a reduction of approximately 20 meV. In contrast, thin films on insulating substrates, such as Sr2IrO4/Ca3Ru1.98Ti0.02O7 below 55 K (blue) and Sr2IrO4/LSAT (cyan), show magnon peak energies at (π/2, π/2) that are indistinguishable from that of the Sr2IrO4 single crystal. This shift in magnon energy exceeds the experimental error bar, underscoring the significance of this observation28.

Fig. 3: Magnon softening in Sr2IrO4 thin films interfaced with metallic substrates at the (π/2, π/2) zone boundary.
figure 3

a RIXS spectra of Sr2IrO4 thin films on various substrates, compared to single-crystal Sr2IrO4 (light green) at (π, 0) and (π/2, π/2). Substrates include metallic (Sr2IrO4/Sr2RuO4 (orange) and Sr2IrO4/Ca3Ru1.98Ti0.02O7 at T > 55 K (red)) and insulating (Sr2IrO4/LSAT (cyan) and Sr2IrO4/Ca3Ru1.98Ti0.02O7 at T < 55 K (blue)) crystals. Thin films interfaced with metallic substrates show pronounced softening of the single magnon mode at the (π/2, π/2) zone boundary. b Magnon dispersion extracted from the RIXS spectra and compared with single-crystal Sr2IrO4 data. The solid orange and cyan lines represent theoretical fits using the model Hamiltonian for Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT, respectively.

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Essentially, the results can be categorized into two groups (Fig. 3b): Sr2IrO4 heterostructures with insulating substrates retain higher magnon energy near (π/2, π/2), comparable to single-crystal Sr2IrO4, while those interfaced with metallic substrates exhibit a pronounced magnon energy softening, reduced by approximately 20 meV. This behavior highlights the critical role of substrate properties—particularly metallicity—in tuning the magnon dispersion of Sr2IrO4 thin films. The softened magnon energy at (π/2, π/2) is a highly unusual phenomenon, as it increases the magnon dispersion between the (π, 0) and (π/2, π/2) zone boundaries.

In typical antiferromagnetic S = 1/2 systems like La2CuO4, the magnon energy difference between these zone boundaries is relatively small, as observed in inelastic neutron scattering experiments30. However, in Sr2IrO4 single crystals (a Jeff = 1/2 pseudospin system), this energy difference is significantly larger, and it increases further in Sr2IrO4 thin films interfaced with metallic substrates. According to linear spin-wave theory18,31, the magnon energy dispersion (\({\omega }_{{{\bf{q}}}}\)) is described as: \({\omega }_{{{\bf{q}}}}=\sqrt{{A}_{{{\bf{q}}}}^{2}-{B}_{{{\bf{q}}}}^{2}}\), where: \({A}_{{{\bf{q}}}}=2({J}_{1}-{J}_{2}-{J}_{3}+{J}_{2}\cos {q}_{x}\cos {q}_{y})+ {J}_{3}(\cos {2q}_{x}+\cos 2{q}_{y})\), \({B}_{{{\bf{q}}}}={J}_{1}(\cos {q}_{x}+\cos {q}_{y})\). Here, J1, J2, and J3 represent the in-plane exchange interactions between the nearest, next-nearest, and third-nearest neighbors, respectively. The magnon energies at the (π, 0) and (π/2, π/2) zone boundaries are expressed as: \({\omega }_{\left(\pi,0\right)}\) = \(2({J}_{1}-{2J}_{2})\), \({\omega }_{\left(\frac{\pi }{2},\frac{{{\boldsymbol{\pi }}}}{{{\boldsymbol{2}}}}\right)}\) = \(2({J}_{1}-{J}_{2}-2{J}_{3})\). Thus, the experimentally observed magnon softening near the (π/2, π/2) zone boundary can be attributed to changes in J2 and J3, specifically \({2}({-}{J}_{2}+2{J}_{3})\).

By fitting the magnon dispersion data (Fig. 3b) using the Heisenberg spin model, we extracted the in-plane exchange interactions up to the fourth-nearest neighbor (J4) for the Jeff = 1/2 pseudospins in Sr2IrO4. The best-fit parameters are summarized in Supplementary Table 3: For the Sr2IrO4 thin films contacted with insulating substrates: J1 = 55 meV, J2 = −17 meV, J3 = 16 meV, and J4 = 7.3 meV. For thin films interfaced with metallic substrates: J1 = 55 meV, J2 = −21 meV, J3 = 20 meV, and J4 = 4.6 meV. Notably, while J1 remains unchanged, the magnitudes of J2 and J3 increase in Sr2IrO4 interfaced with metallic substrates, consistent with the predictions of linear spin-wave theory discussed above.

The two-magnon peak energies observed in high-resolution Raman spectra corroborate the RIXS results. Figure 4a illustrates the B2g two-magnon modes in Sr2IrO4/Sr2RuO4 and Sr2IrO4/LSAT at 10 K, while Fig. 4b presents the temperature-dependent Raman spectra of B2g two-magnon modes in Sr2IrO4/Ca3Ru1.98Ti0.02O7. The two-magnon peak energies (ω2M) were determined by fitting the data to a model function comprising two Lorentz oscillators. Notably, the two-magnon energies of thin films on metallic substrates (Sr2RuO4 and Ca3Ru1.98Ti0.02O7 above 55 K) are lower than those of thin films on insulating substrates (Ca3Ru1.98Ti0.02O7 below 55 K and LSAT). Given that the two-magnon mode primarily reflects zone boundary excitations32, this observation is consistent with the softening of the (π/2, π/2) zone boundary magnon. These results establish a strong agreement between the Raman and RIXS measurements, further confirming the substrate-dependent modification of magnon dynamics in Sr2IrO4 thin films.

Fig. 4: Softening of two-magnon modes in Sr2IrO4 thin films interfaced with metallic substrates.
figure 4

a Raman spectra of B2g two-magnon modes in Sr2IrO4/Sr2RuO4 (orange) and Sr2IrO4/LSAT (cyan) heterostructures measured at 10 K. b Temperature-dependent Raman spectra of B2g two-magnon modes in the Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure. The two-magnon peak energy is lower in Sr2IrO4 thin films interfaced with metallic substrates (Sr2RuO4 and Ca3Ru1.98Ti0.02O7 at T > 55 K) compared to those interfaced with insulating substrates (LSAT and Ca3Ru1.98Ti0.02O7 at T < 55 K). Two-magnon peak positions in both figures were determined using fits to a model comprising two Lorentz oscillators, represented by smooth solid curves for each component. The total fit is shown by the black solid line.

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Raman spectroscopy reveals a noticeable hardening of the phonon modes in Sr2IrO4 thin films by ~8–11 cm−1 (1–1.4 meV) when the contacted substrate transitions from insulating to metallic, likely indicating electron-phonon interactions. Figure 5a shows the A1g and B2g phonon modes of the Sr2IrO4 thin film in the Sr2IrO4/LSAT and Sr2IrO4/Sr2RuO4 heterostructures. While the phonon modes in Sr2IrO4/LSAT closely resemble those of Sr2IrO4 single crystals, the Sr2IrO4/Sr2RuO4 heterostructure exhibits a significant upward energy shift of approximately 1.4 meV for the A1g mode and 1 meV for the B2g mode. Similarly, an upward shift of up to 0.7 meV in phonon energy is observed in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures when the substrate transitions from an insulating to a metallic state at 55 K (Fig. 5b).

Fig. 5: Hardening of phonons in Sr2IrO4 interfaced with metallic substrates.
figure 5

a A1g and B2g phonon modes of Sr2IrO4/Sr2RuO4 (orange) and Sr2IrO4/LSAT (cyan) heterostructures. The solid black lines represent Lorentzian fits to the data. b Temperature-dependent evolution of the B2g phonon modes in the Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructure. Inset: Temperature-dependent peak position of the B2g phonon modes in the same heterostructure, illustrating the phonon hardening behavior as the substrate transitions from an insulating to a metallic state. Error bars represent uncertainties estimated from the peak widths and curve-fits.

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It is important to note that the structural change occurring in the Ca3Ru1.98Ti0.02O7 substrate at 55 K may also contribute to the observed phonon mode shift in Sr2IrO4/Ca3Ru1.98Ti0.02O7 heterostructures. Additionally, we investigated other heterostructures, including Sr2IrO4/Ca2Ru0.91Mn0.09O4 (insulator), Sr2IrO4/Sr2RhO4 (metal), and Sr2IrO4/Ca3Ru2O7 (metal) at 10 K. These heterostructures exhibited a similar trend: the metallic substrates induced hardening of the B2g phonons in the Sr2IrO4 thin films by about 8 cm−1 (1 meV) compared to insulating substrates (Supplementary Fig. 5). Overall, a common factor across all results is the metallic state of the substrate, which strongly correlates with the observed phonon mode stiffening in Sr2IrO4 thin films.

Discussion

Our observations of significant magnon softening and phonon mode hardening in Sr2IrO4 thin films interfaced with metallic substrates, compared to insulating substrates, offer valuable insights into the underlying coupling mechanisms. However, the change in phonon energies (∆ωphonon) is an order of magnitude smaller than the change in magnon energies (∆ωmagnon). Reconciling the relatively small (~1 meV) phonon shifts with the much larger (~20 meV) magnon energy changes is challenging. Instead, these phonon shifts likely originate from structural distortions associated with the metal-insulator transition, as their magnitudes are comparable to shifts induced by thermal effects.

Developing a microscopic, quantitative theory for electron-phonon-magnon couplings in such complex heterostructures is beyond the scope of this work. The form of the magnon-phonon (or spin-phonon) Hamiltonian is inherently complex, as lattice vibrations break lattice symmetries, introducing anisotropic magnetic interaction terms even in two-dimensional systems. Consequently, first-principle calculations of all magnon-phonon coupling parameters are practically infeasible.

Nevertheless, to explain the observed modifications in magnetic interactions across the tens-of-nanometer-thick Sr2IrO4 thin film, we propose a mechanism involving propagating longitudinal acoustic phonons. These phonons, sensitive to substrate charge carriers due to metallic screening effects, mediate long-range spin interactions through magnetoelastic coupling. This coupling, particularly pronounced in spin-orbit entangled magnets like Sr2IrO4, arises from the direct interaction of lattice vibrations with the unquenched orbital components of the magnetic moments. Magnetoelastic interactions effectively generate spin-spin couplings mediated by dispersive phonon modes, extending beyond nearest neighbors. As metallic screening softens the acoustic phonons, the resulting enhancement in phonon-mediated spin interactions aligns with the increased J2 and J3 values—while J1 remains constant—as deduced from our phenomenological fits (Fig. 3b) and linear spin-wave theory.

Similar effects have been observed in lightly doped Sr2IrO4, where magnon softening and anisotropic momentum-space behavior were attributed to enhanced longer-range spin couplings mediated by softened phonons33. However, unlike the doped case, our heterostructures exhibit no broadening of magnon peaks or collapse of long-range magnetic order, suggesting that the observed changes are driven by indirect acoustic phonon-mediated interactions rather than direct coupling between Ir magnetic moments and substrate conduction electrons.

Alternative mechanisms, such as lattice strain, interfacial proximity effects, or charge transfer, are insufficient to explain the observed phenomena. The strain effect, for example, fails to account for magnon softening in Sr2IrO4/Sr2RuO4 heterostructures, as similar strain states in Sr2IrO4/LSAT heterostructures do not show comparable effects. Proximity effects at the interface are also unlikely, as our observations are made through bulk-sensitive techniques26. These experimental techniques probe the entire volume of the 20–50 nm (30-80 IrO2 layers) thin films, rather than being confined to the interface region. Moreover, Sr2IrO4/Sr2RuO4 heterostructures of varying thicknesses (12, 30, and 50 nm) show consistent magnon softening without a noticeable thickness dependence (Supplementary Fig. 6), indicating that the observed behavior is a long-range effect throughout the thin film.

Charge transfer as a mechanism also fails to explain the results. If charge transfer at the interface involved hole doping, it would typically harden the magnon peak energy at the zone boundary34,35, contrary to our observations. On the other hand, electron doping is known to soften the magnon peak energy but often results in significant broadening of the magnon spectrum and a collapse of long-range magnetic order in Sr2IrO4 (refs. 33,36.). In both Sr2IrO4/Ca3Ru1.98Ti0.02O7 and Sr2IrO4/Sr2RuO4 heterostructures, however, no broadening of magnon peaks (Fig. 3a) or collapse of long-range magnetic order was observed (Supplementary Fig. 7).

Resonant x-ray scattering near the Ru L2 edge further confirms the absence of Ru ions in the Sr2IrO4 thin film (Supplementary Fig. 8), ruling out intermixing between Ir and Ru ions. Additionally, optical spectroscopy reveals a clear insulating gap of approximately 0.3 eV in the Sr2IrO4/Sr2RuO4 heterostructure (Supplementary Fig. 9), similar to that of Sr2IrO4 single crystals, further eliminating charge transfer as a plausible explanation for the observed phenomena.

In summary, we have observed a pronounced softening of the zone boundary magnon energy when Sr2IrO4 thin films are epitaxially interfaced with metallic 4d TMO single crystals. We propose that electron-phonon coupling, occurring either at the interface or within the metallic substrate, influences the magnon dispersion in Sr2IrO4 via a long-range magnon-acoustic phonon interaction. This mechanism enhances second- and third-nearest-neighbor interactions, while its impact on the nearest-neighbor exchange remains minimal. Our findings underscore the need for further theoretical studies and calculations to develop a deeper understanding of the microscopic interactions between magnons and phonons in such complex systems.

In addition to the well-established role of acoustic waves in mediating magnon-phonon coupling37, we propose that metal-insulator transitions at heterointerfaces represent an effective mechanism for tuning magnons—an essential requirement for advancing magnonics. Our study also raises several compelling questions and broader perspectives. For instance, is this phenomenon unique to 5d/4d TMO heterostructures, or could it be extended to other magnetic systems, such as Yttrium iron garnets38 or van der Waals heterostructures incorporating two-dimensional magnets like Fe3GeTe2, NiPS3, CrSBr, where strong magnon-exciton coupling39 has already been observed? Future investigations across a broader range of heterostructures, featuring diverse materials and magnetic systems, will be essential for addressing these questions and further unraveling the fundamental interactions governing spin excitations in complex quantum systems.

Methods

Sample synthesis

The 5d/4d epitaxial heterostructures were fabricated by depositing Sr2IrO4 epitaxial thin films on ruthenates single crystals using a custom-built pulsed laser deposition system40. The growth conditions are a laser fluence of 1.2 J/cm2, a substrate temperature of 700 °C, and an oxygen partial pressure of 10 mTorr. The thicknesses of the Sr2IrO4 thin films were determined to be ~12 nm, 30 nm, 50 nm (Sr2IrO4/Sr2RuO4), 50 nm (Sr2IrO4/LSAT), and 20 nm (Sr2IrO4/Ca3Ru1.98Ti0.02O7).

X-ray scattering experiments

High-resolution x-ray diffraction and RIXS experiments were conducted at the 6-ID-B beamline and the 27-ID beamline of the Advanced Photon Source, Argonne National Laboratory, respectively. For RIXS spectra, a horizontal scattering geometry was employed with incident x-ray photons tuned to the Ir L3 edge (ћω = 11217 eV) and polarized in the π-direction, as illustrated in Fig. 2c.

Scanning transmission electron microscopy

Cross-sectional specimens for high-resolution scanning transmission electron microscopy were prepared using a Thermofisher Helios focused ion beam with a gallium ion source. These specimens underwent additional cleaning via argon ion milling (Fichicone Nanomill) at a beam energy of 500 eV to eliminate amorphous layers. Transmission electron microscopy images were captured with a Thermofisher Titan operating at 300 kV and employing a collection angle range of 80–300 milliradians.

Raman spectroscopy

Temperature-dependent Raman spectra were obtained in back-scattering geometry using a Jobin Yvon LabRAM HR800 spectrometer equipped with a confocal microscope. A 1.96 eV excitation line from a helium-neon laser was used, producing a focused beam spot with a diameter of ~5 μm.

Optical spectroscopy

The optical conductivity spectrum was measured using a home-built ellipsometer attached to a Bruker 66 V FT-IR spectrometer and an M2000 ellipsometer (Woollam) for the spectral ranges of 0.05–1.0 eV and 1.2–6 eV, respectively.