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Abstract
Bismuth-substituted lutetium iron garnets have exhibited a remarkable enhancement in Faraday rotation (FR) for films thinner than 50 nm. A sevenfold amplification in the magneto-optic gyrotropy was found to occur within 2 nm of the air-surface interface at 532 nm wavelength. The present study delves into the underlying physical mechanisms contributing to such amplification. Near-surface changes in band structure in these materials and their connection to the magneto-optic response are explored. Density functional theory is employed to investigate the changes in density of states and overall band structure reconfiguration of surface atoms. The transition dipole matrix (TDM) model is then applied to both bulk and surface states, correctly predicting a Faraday rotation enhancement at the surface as a result of overall surface band structure reconfiguration and resulting bandgap reduction. Surface versus bulk FR spectral response is extended beyond prior studies over the full visible and the near-infrared spectral ranges, predicting significant amplification across the telecom band. Experimental analysis through X-ray photoelectron spectroscopy (XPS) and UV-Vis spectroscopy reveal a reduction in bandgap as films are thinned down from 200 nm to 40 nm. By providing a deeper physical understanding of the origin of enhanced Faraday rotation at the surface, this work opens up avenues for more efficient miniaturized Faraday rotation applications. Knowledge of the band structure information thus uncovered may be used to demonstrate novel and more advanced applications.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Bismuth-substituted lutetium iron garnets ($Bi_{1}Lu_{2}Fe_{5}O_{12}$, BiLuIG) are essential ferrimagnetic insulators utilized in various applications, such as radars, attenuators, optical isolators, circulators, filters, and switches [1–12].Recent investigations on iron garnet films have revealed a substantial enhancement in their magneto-optic response near the surface compared to the bulk [13–24].Previous studies on BiLuIG have provided experimental evidence linking surface reconstruction to specific Faraday rotation changes within a few nanometers of the surface [13–19]. A prior density-functional-theory (DFT) study on the parent compound (yttrium iron garnet), conducted by the same authors, demonstrated surface reconstruction and a decrease in the optical bandgap. This led to significant near-surface modifications in magneto-optical properties in ultra-thin films [25].
In this investigation, we employ multiple techniques. X-ray photoelectron spectroscopy (XPS), a surface science technique, is used to analyze the surface sensitivity of elements constituting BiLuIG at different angles. Additionally, UV-Vis measurements with unpolarized sources are conducted to study absorption, transmission of ultra-thin samples, and changes in the near Fermi level band structure for thinner samples. With no evidence on previous first-principles studies on surface effects impacting the enhancement in magneto-optic response in these materials, we conduct first-principles calculations to examine changes in the density of states and band structure of surface atoms, utilizing the Vienna Ab-Initio Simulation Package (VASP) software. XPS valence spectra are also employed to obtain U-J parameters for various elements in first-principles calculations. Furthermore, we connect this analysis to its impact on magneto-optical properties, particularly Faraday rotation, using the transition dipole moment (TDM) model [26]. This study investigates the physical bases for these differences and explores potential areas for miniaturization of devices employing magneto-optic materials. In addition, it predicts surface-induced FR amplification in the telecommunications band, a wavelength range of significant technological importance not yet explored for surface FR enhancement.
Combining experimental and computational band structure analyses, we demonstrate a reduction in the bandgap for BiLuIG materials as they are thinned down from 200 nm (bulk). Below 50 nm, ($Fe^{T}$) bands split at the Fermi level, with occupied bands shifting to lower binding energy. The occupied states of $Fe^{T}$ also shift closer to the Fermi level, thus lowering the bandgap. This is the primary reason for Faraday rotation enhancement through the reduction of the bandgap. Additionally, the band structure from DFT results indicates a small bandgap at the surface. BiLuIGs exhibit a significant increase in Faraday rotation in the TDM model across the full range of probe energy used in our measurements. We predict a multi-fold increase in specific Faraday rotation at the surface over the bulk for probing energies (0 eV-6 eV). This outcome holds substantial implications for the technological development of BiLuIG materials in the miniaturization of devices utilizing magneto-optic materials like optical isolators.
Prior work has shown that the Faraday rotation (FR) enhancement in these iron garnets originates from within a few nm of the top surface. Reference 18 data explicitly disengages surface and film from the GGG interface contribution by probing surface and bulk contributions in thick films that do not probe the GGG interface. Electromagnetic field theoretical analysis on FR data versus film thickness shows that the GGG interface does not explain the observed FR enhancement. The work presented below describes surface-sensitive XPS measurements with a profiling depth of 2-4 nm. For the UV-VIS measurements presented here, the GGG absorption data was subtracted out, and the DFT calculations were only performed for the top surface. [13,17,18]
2. Results
2.1 Sample preparation for XPS and UV-Vis
The BiLuIG utilized in our experiments was grown on a [100]-oriented gadolinium gallium garnet (GGG) substrate with a thickness of 2 $\mu$m, employing liquid-phase epitaxy at II-VI, Inc./Coherent Corp. The chemical composition, expressed per formula unit (pfu), is $Bi_{1}Lu_{2}Fe_{4.3}Ga_{0.7}O_{12}$. To ensure consistency in elemental constituents and reliable outcomes, all samples used in our measurements were sourced from the same wafer. The lattice parameters for BiLuIG and GGG are 12.377 Å and 12.382 Å, respectively, resulting in a 0.006 Å to 0.01 Å lattice mismatch. Strain cannot explain the observed FR surface enhancement, as shown in [13,17,18].
The material underwent wet etching and thinning in gyrating phosphoric acid, heated above 100 $^{\circ }$C, tailored to the specific constituents and thickness of each sample. Thinning was carried out at the microfabrication facility at Michigan Technological University, reducing the sample thickness to 40 nm. This approach preserves the surface quality of our samples [17]. Following thinning, the samples were meticulously cleaned with acetone and isopropyl alcohol, and then rinsed with de-ionized water. No surface sputtering was conducted before the XPS studies, as this step is known to alter the oxidation state of Fe [27].
The experiments were performed only on films grown via liquid-phase-epitaxy in well-lattice-matched samples with the substrate. These are high-quality mono-crystal films. Different growth conditions such as those caused by rf sputter-deposition or pulsed-laser-deposition were not tested and may affect the FR enhancement effect reported here.
XPS was employed for the detailed investigation of the chemical species of elements in the BiLuIG sample, focusing on the near-surface regions. This non-destructive technique provided valuable insights into the surface composition.
The bandgap of BiLuIG materials decreases with a decrease in the thickness of the material. We study the change in band energy of the occupied states using XPS and the unoccupied states using UV-Vis spectroscopy. Further, we conduct a first-principles analysis to examine the surface bandgap and density of states and compare them with those of the bulk using VASP.
2.2 High-resolution XPS
Clean surface samples of BiLuIG were used for the XPS measurements. The angle of incidence varied from 90$^{\circ }$ (bulk sensitive - 7nm) to 25$^{\circ }$ (surface sensitive - 2nm) measurements, as shown in Fig. 1. CASA-XPS software was used to further analyze the plots. The spectra was charge corrected to the dominant O1s energy peak at 530.1 eV.
Fig. 1. (top) Presents HD-XPS data for Fe at three incident angles: 25$^{\circ }$, 45$^{\circ }$, and 90$^{\circ }$. (left) Illustrates a shift in the binding energy of iron 2p towards lower values. (right) Depicts the deconvolution of the XPS $^{2}p_{3/2}$ plot, distinguishing iron-octahedral and tetrahedral bonding.
The deconvolutions at $^{2}p_{3/2}$ indicate the presence of two Fe species in the garnet. The peak positions (Fig. 1) are on average at 713 eV for the higher intensity and at 710 eV for the lower intensity peak. From the deconvolution process, we find two dominant types of Fe binding energies. The peak at 713 eV corresponds to octahedrally coordinated Fe ions ($Fe^{O}$), and the peak at 710 eV corresponds to tetrahedrally coordinated Fe ions ($Fe^{T}$). The peak distance between octahedral and tetrahedral gradually increases from 2.54 eV to 3.16 eV for our scans from 90$^{\circ }$ (bulk) to 25$^{\circ }$ (surface) angle. In the deconvolution, the octahedrally-coordinated peak position stays almost unaffected, whereas the tetrahedral Fe bond moves towards the lower binding energy. This signifies that tetrahedrally-bonded Fe ions are more susceptible to adopt a more stable state compared to the octahedrally-bonded Fe ions. Thus playing an important role in lowering the bandgap for the BiLuIG material at the surface through surface reconstruction. We find similar evidence in our previous DFT analysis on the parent compound yttrium iron garnet (YIG) [25].
The binding energy of the $^{2}p_{1/2}$ peak in Fig. 1 is near 724 eV with hardly any distinguishable features to be considered for further analysis. The small satellite peaks formed between the $^{2}p_{3/2}$ peak and the $^{2}p_{1/2}$ peak are difficult to resolve in the garnet structure for analysis.
Additionally, we observe a peak in the survey analysis for Bi-4s bond at energy 935 eV. From our previous paper [13], we conclude that the peak is the result of change in vibrational mode as predicted in our earlier Raman Spectroscopy measurements. The change in bond length plays an important role in Faraday rotation [28]. The survey spectra for the three angles of incidence and the elemental concentration analysis can be found in the Supplement 1.
The XPS data corroborates our UV-Vis analysis that the thinning of the sample affects the Faraday rotation after it is thinned down enough to affect the tetrahedral bonds. We also see the tetrahedral and octahedral absorption peaks separating for UV-Vis absorption per unit length. The Tauc UV-Vis absorption plot for various thicknesses is used to determine the optical bandgap of these materials for their respective thickness [29]. It shows a decrease in bandgap with decrease in thickness. Details of the UV-Vis absorption settings, spectroscopy, and analysis can be found in the Supplement 1.
2.3 Density of states and band structure analysis from DFT calculation
The density functional theory (DFT) analysis was conducted on the bulk in comparison to the surface model for BiLuIG materials. Both bulk and slab models were created, replacing bismuth with lutetium in a 1:2 ratio in bismuth-substituted iron garnets. The composition gives a stable [100] surface for surface studies and is also in alignment with our experimental sample stoichiometry.
Fig. 2. (top) Density of states for bulk configuration for BiLuIG materials and (bottom) density of states for surface [100] configuration for BiLuIG materials.
The computational model considered a ferrimagnetic arrangement with substantial spin-orbit coupling on iron atoms from bismuth atoms. XPS valence spectra were utilized to study the density of state plots via first-principles calculations for the surface model. Detailed XPS plots, including the U-J parameter analysis from them, are available in the Supplement 1. Further details, including the density of states (DOS) profiles, are illustrated in Fig. 2.
An intriguing observation lies in the degeneracy lifting at the surface, attributable to symmetry breaking. Examining the surface DOS (Fig. 2 (bottom)), it is observed that above the Fermi level, the states of tetrahedrally bonded iron (Fe) ions are predominantly unoccupied, offering available states for Faraday rotation transitions. Notably, the degeneracy of the density of states for tetrahedral Fe ions experiences a more pronounced impact compared to their octahedral counterparts above the Fermi level. This finding, in addition to the decrease in bandgap, aligns seamlessly with our analysis using UV-Vis double derivative spectroscopy analysis.
3. Discussion
3.1 Faraday rotation analysis
The Faraday rotation in both bulk and thin film BiLuIG materials is predicted by leveraging the band structures obtained from first-principles models for both bulk and surface configurations. The transition dipole matrix (TDM) model, detailed in the GitHub repository [26], was employed for calculations. Noteworthy agreement between modeled predictions and experimental data for bulk Faraday rotation in the parent compound yttrium iron garnet (YIG) was previously established [25]. The TDM model utilizes Vaspkit [30] to derive the transition dipole matrix associated with electronic transitions responsible for Faraday rotation in the material. Respective bandstructures for these models can be found in the Supplement 1. The first principles calculations using VASP predict a bandgap slightly lower than the experimentally observed bandgap. Consequently, the TDM model forecasts a marginally red-shifted Faraday rotation compared to the values obtained in experiments. However, our primary focus was to assess the distinctions between the bulk and surface models in our studies. As such, the systematic bandgap error does not significantly impact our conclusions.
In Fig. 3, the calculated Faraday rotation for BiLuIG materials is presented. The blue plot illustrates the predicted bulk Faraday rotation, while the red plot showcases the predicted surface [100] Faraday rotation. Our model’s predictions align closely with our earlier experimental findings [13]. Notably, a substantial enhancement in Faraday rotation is observed across the entire probing spectrum (0 eV to 6 eV). Our calculations utilized the band structure with the maximum bandgap, ensuring that our results fall within a margin below the calculated error.
Fig. 3. Expected Faraday rotation based on first-principles calculations for various probing energies (left) and probing wavelengths (right). Here, blue represents the bulk model and red represents the surface [100] model.
This investigation into the surface band structure and DOS reconfiguration of bismuth-substituted lutetium iron garnet aimed to unravel the quantum origins and the underlying physical mechanisms responsible for the enhanced Faraday rotations observed in our previous studies. Through a comprehensive analysis involving XPS, UV-Vis, first principles DFT calculations, and the TDM model, critical insights into the phenomenon have emerged. Notably, we observe a reduction in the bandgap at the surface of these samples. The Fe tetrahedrally-coordinated atoms were particularly influenced by the surface reconstruction in the top 1 nm at the surface. In the initial thinning down of samples, first the octahedrally-coordinated Fe atoms were affected. With further thin down, due to their less rigid configuration compared to octahedrally-coordinated ions, the tetrahedrally-coordinated Fe ions exhibited a stronger structural deformation at the surface. This deformation leads to a further lifting of degeneracy at the surface, in contrast to the case of the bulk structure DOS. The diminished bandgap and increased energy available for transitions are pivotal factors contributing to the enhanced Faraday rotation. The predictions from the TDM model (Fig. 3) indicate an overall rise in available transitions within the energy range of 0 eV to 6 eV. This expansion in the range of transition possibilities holds promise for the miniaturization of devices utilizing magneto-optic materials across a broad spectrum.
The surface enhancement in FR in question is not a resonance phenomenon. It is not the result of an increase in path length due to multiple reflections. It is rather the result of surface reconstruction and symmetry-breaking at the surface in these iron garnets, leading to the kind of band-structure-reconfiguration analyzed in this paper. Prior work by some of us and co-workers has provided evidence for surface reconstruction in BiLuIG via scanning-transmission-electron microscopy, and of significant differences in the magnitude of $L_2$ edge x-ray magnetic circular dichroism, as well as differences in $L_3$ edge dichroism between surface and bulk [17,18].
Prior work by Levy et.al. in ultra-thin films shows an increased absorption correlating with enhanced FR just below the bandgap. However, the figure of merit, Faraday rotation/absorption, remains approximately the same [13,17,18].
The generation of thin-film multilayer structures to magnify the FR enhancement is an interesting idea, subject to future developmental work. The key to successful multilayer structures will be to engineer the band structure found near the BiLuIG surface. Whether this can be done by growing buffer layers between ultrathin iron garnet films, or developing materials engineering to generate band structures mimicking those of the BiLuIG surface in other materials, is an open question at this time.
4. Methods
4.1 XPS settings
XPS measurements were meticulously conducted at the Applied Chemical and Morphological Analysis Laboratory (ACMAL) at Michigan Technological University to investigate the chemical composition and surface-related binding energies at the surface/air interface. The XPS instrument employed was a Physical Electronics 15-255G AR double-pass cylindrical-mirror electron energy analyzer, featuring a double anode XR3 x-ray source (VG Microtech) operating at 15 kV and 18 mA for MgK$\alpha$ photons.The ultra-thin BiLuIG sample was mounted on a sample holder using carbon tape and subsequently loaded into a vacuum chamber, which was then transferred to the analysis chamber.
Survey Measurements: The survey was performed with a Pass Energy of 93.9 eV, 0.8 eV/step, and 20 ms/step in a single sweep. High-resolution scans for Bi used a Pass Energy of 23.5 eV, 0.1 eV/step, and 100 ms/step for 15 sweeps. O 1s spectra were acquired at 11.75 eV Pass Energy, 0.1 eV/step, and 100 ms/step for 30 sweeps. Fe 2p spectra were recorded at 11.75 eV Pass Energy, 0.05 eV/step, and 100 ms/step for 60 sweeps. Measurements were taken at 90$^{\circ }$, 45$^{\circ }$, and 25$^{\circ }$ from the plane of the surface.
High-Definition Scans: Hi-def scans were conducted at 58.7 eV, 0.125 eV/step, and 50 ms/step. A second scan at 23.5 eV, 0.1 eV/step, and 100 ms/step was performed. Fe and Bi high-resolution scans followed different parameters: 11.75 eV, 0.1 eV/step, and 100 ms/step for Fe; and 23.5 eV, 0.1 eV/step, and 100 ms/step for Bi. The high-resolution spectra obtained were analyzed for chemical species composition using CASAXPS software. The fitting involved applying the Shirley background and Gaussian line shape.
Angle-resolved XPS was employed to determine depth using the equation:
where $\lambda e$ is the inelastic mean free path of electrons in the material, and $\theta$ is the angle from the surface. Depth probing during XPS measurements covered angles of 90$^{\circ }$, 45$^{\circ }$, and 25$^{\circ }$, corresponding to a depth range from 7 nm to 2 nm. XPS, being a surface-sensitive measurement [31], enables precise depth profiling.4.2 DFT calculations
All Density Functional Theory (DFT) calculations were conducted using the Vienna Ab-Initio Simulation Package (VASP). The bulk BiLuIG adopts a Ia3d cubic structure [32], illustrated in Fig. 4. In this structure, iron ions occupy both tetrahedrally- and octahedrally-oxygen-coordinated sub-lattices, while bismuth atoms are positioned in a dodecahedrally-oxygen-coordinated sub-lattice.
Fig. 4. (a) $\frac {1}{4}$ of a BiLuIG conventional unit cell. The O atoms are shown as red, Bi atoms are shown as magenta spheres, Fe are shown as brown spheres and Lu are shown as cyan spheres. (b) Slab model of BiLuIG for [100] conventional unit cells with 20 Åvacuum top and bottom.
Each unit cell comprises 16 Fe atoms in the octahedral positions (16a), 24 Fe atoms in the tetrahedral positions (24d), 96 oxygen atoms at 96h positions, and 24 bismuth atoms in 24c positions within the conventional unit cell. Notably, there are two octahedrally-coordinated $Fe^{3+}$ ions and three tetrahedrally-coordinated $Fe^{3+}$ ions per formula unit (f.u). The experimental lattice constant a is determined to be 12.38 Å [32,33]. In our study, $\frac {2}{3}$ of the Bi ions are substituted with Lu ions for the bulk and surface calculations.
For surface slab modeling, we construct a [100] surface with 20 Å of vacuum between the layers, as depicted in Fig. 4. To achieve this, we leverage the Wyckoff atomic positions and the experimental lattice parameter for BiLuIG, as detailed in Table 2 in in the Supplement 1, for all bulk and surface slab BiLuIG calculations. Initial ionic relaxations are performed on both bulk and slab models, subsequent to the substitution of $\frac {2}{3}$ of Bi ions with Lu ions.
In the Surface DFT model, our focus centers on the [100] surface, mirroring the experimental set-up where the enhanced Faraday rotation was observed. In this model, the U-J parameters are set to Fe(U-J) = 5eV for d electrons and Bi(U-J) = 3eV for p electrons. These specific parameters are meticulously chosen to achieve a maximum bandgap at the Fermi level. This deliberate selection aims to also align the density of states of valence electrons with the distinct features observed in the XPS valence spectra data.
From the 10 surface layers, 4 layers were relaxed asymmetrically. The cut-off for the number of surface layers was decided for the calculation and change of surface energy with the number of relaxed layers and the atomic positions of the relaxed layers. The displacement of the first displaced layer with respect to the pristine structure was about 3.25%, 4.2%, 1.12% for $Fe^{T}$, $Fe^{O}$, and Bi atoms. The displacements are in close agreement with the STEM results done in our previous study [18]. More details about the DFT model can be found in the Supplement 1.
Funding
Photonica, Inc; Michigan Technological University (Applied Chemical and Morphological Analysis Laboratory); Electron Microscopy facility (NSF MRI 1429232).
Acknowledgments
- • The samples for the experiments were provided by II-VI, Inc.
- • The authors would like to thank Dr. T. Leftwich for XPS measurements and Dr. K Perrine for XPS analysis.
- • The VASP calculations were performed on the Superior HPC at Michigan Technological University and on the HPCs made available from the Extreme Science and Engineering Discovery Environment (XSEDE, now ACCESS), which is supported by National Science Foundation grant number ACI-1053575.
- • Parts of this study were completed using Michigan Technological University’s Microfabrication Facility.
- • The authors would like to thank Seth Nelson, and Jesse Nordeng of the Physics Department machine shop for making the sample holder for the UV-Vis measurements.
- • The authors thank R. Pandey,and R. Pati for valuable discussions and comments on the manuscript.
- • S.S. Dash, M. Levy, and G. Odegard thankfully acknowledge support from Photonica, Inc.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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