In situ vibrational spectroscopy was used to reveal the microstructure evolution mechanism of iron garnet single crystals growing from multi-component oxide melts

Wang Luo^a, Han Li^a, Zhuo Li^a, Shuting Yang^a, Feng Wang^a, Lingkun Wu^b, Huaiwu Zhang^a and Qinghui Yang*^a
aState Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu, China. E-mail: yangqinghui@uestc.edu.cn
^bCollege of Chemistry, Fuzhou University, 350016 Fuzhou, China

First published on 29th July 2025

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Introduction

Ferrite single crystals, such as yttrium iron garnet Y₃Fe₅O₁₂ (YIG), spinel MnFe₂O₄, and magneto-plumbite BaFe₁₂O₁₉ (BaM), have become the core functional layers for the construction of microwave gyromagnetic resonators, magneto-optical non-reciprocal devices, and spin-wave logic platforms due to their excellent photo-electrical-magnetic multi-field coupling effects.^1–5 In particular, rare-earth iron garnets (ReIGs; such as YBiIG, YCeIG, and TbBiIG) show irreplaceable advantages in terms of regulatable magnetocrystalline anisotropy, large Faraday rotation coefficients, and ultra-low damping factors through sublattice coupling.^6–10 Many research results show that the excellent performance of ReIGs is closely related to the integrity of the lattice structure and the positioning accuracy of doped atoms.^11–13 The inherent defects of crystals (such as vacancies and composition segregation) are essentially caused by the inherent geometric shape defects of growth units in the crystalline system and the dynamic mismatch during the non-equilibrium self-assembly process.^14–17 However, there is a lack of understanding of high-temperature melt growth unit geometries and their self-assembly processes in current mainstream processes (such as the floating zone and the liquid-phase epitaxy method).^18–20 Empirical trial-and-error method is typically employed, which hinders the quality control of single crystals and increases the energy consumption.

Under the framework of the crystal growth theory, the periodic bond chain (PBC) theory,²¹ the anion coordination polyhedron model,²² and the associative complexes (ACs)²³ have established the relationship between the topological growth units of the melt and the periodic crystal network. These provide a theoretical bridge for analyzing the structural characteristics of the melt and the crystallization kinetics process. Here, the terbium iron garnet (TbIG; Tb₃Fe₅O₁₂)²⁴ lattice is taken as an example (Fig. 1a). In its cubic Ia3d lattice, Fe³⁺ occupies two sublattice positions, namely, the tetrahedral (Fe–O bond length = 1.879 Å, CN = 4) and the octahedral (Fe–O bond length = 2.014 Å, CN = 6) positions. Furthermore, the bond energy distribution of the Tb³⁺ dodecahedron shows differences, with the two types of bond lengths being 2.372 Å and 2.452 Å, respectively. The bond length gradient reveals essential differences in the chemical bonds, that is, short bonds correspond to localized covalent bonds dominated by the covalent shortening effect, while long bonds exhibit typical ionic bond characteristics.²⁵ Bond energy differentiation is a bonding process dominated by orbital hybridization and electron transfer, respectively,^26,27 which may correspond to multiple chemical dynamics processes. When only high bond-energy covalent networks are considered, the TbIG lattice presents as a three-dimensional structure formed by the co-assembly of the [–FeO₂–TbO₂–]_n²ⁿ⁻ PBC structure along the 〈100〉 crystal direction and free Fe³⁺ (Fig. 1b). Notably, this is consistent with the growth mechanisms predicted by the theories of PBC and AC, providing key structural parameters for establishing the geometry-assembly dynamics of ReIG melt cluster units.

High-temperature in situ vibrational spectroscopy and density functional theory (DFT) calculations are regarded as effective methods for revealing the microstructures of melts and the differences between crystal phase structures.^28–35 In this work, they were used to analyze the microstructure and crystallization evolution mechanism of the TbBiIG-based melts [(Fe₂O₃–Tb₄O₇–Bi₂O₃) (1) and (Fe₂O₃–Tb₄O₇–Bi₂O₃–B₂O₃) (2)]. The results show that the four-metal ion clusters [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} [A = Tb³⁺ or Bi³⁺; n (m) = 2 and 3] in 1 and 2 are regarded as ReIG growth units due to their role as the main components of the melt. Furthermore, the solidification experiment indicates that when the temperature of melt 1 decreases, the growth units restructure into periodic long chains [–AO₂–Fe(III)O₂–]_n²ⁿ⁻. The quantitative molecular surface analysis of the electrostatic potential (ESP) indicates that the growth of ReIGs may follow the electrostatic bonding self-assembly of [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} and free Fe³⁺ to form growth units with lattice structures, which are superimposed onto the growth interface to achieve the growth process. Furthermore, trace amounts of B₂O₃ enhance the freedom and stability of the system by increasing the concentration of non-bridging oxygen and the interaction between clusters. This work reveals the microscopic dynamic mechanism of ReIG crystal growth, providing a theoretical basis for optimizing the performance of single crystals through the regulation of melt structures.

Results and discussion

In our previous work, it has been demonstrated that high-quality bismuth-doped terbium iron garnet (TbBiIG) single crystal thin films can be grown in melts 1 and 2 (see the SI) through the SGGG substrate epitaxy. Compared with melt 1, adding a trace amount of a boron oxide flux to 2 can effectively lower the growth temperature (2% mol, about 10 K), which helps to reduce energy consumption. Importantly, the low absorption coefficient and great Faraday rotation (θ_F = 2812 deg cm⁻¹ at 1064 nm, θ_F = 1452 deg cm⁻¹ at 1310 nm) of the grown TbBiIG in the near-infrared band are used in the 1064- and 1310-nm band optical communication Faraday rotators.^36,37

In order to reveal the coordination structure and microscopic evolution mechanism of growth units in multi-component oxide melts, the melt rheology and in situ vibrational spectroscopy were used to analyze the structural characteristics of melts 1 and 2. The temperature-dependent changes in the viscosity curves of 1 and 2 show a similar trend (Fig. 2a), with step-type transitions at 1135 and 1124 K, respectively. This shows that boron oxide effectively reduces the solidification point temperature of the melt by about 10 K. Furthermore, the viscosity difference between the two melts is maintained on a very small magnitude (Δη is less than 0.75 mPa s) before the solidification point (Fig. 2b), indicating that B₂O₃ has little effect on the type and volume of ion clusters in the melt. Therefore, B₂O₃ mainly enhances the thermodynamic stability of the melt by enhancing the interaction between structural units. The dynamic changes in the microstructures of melts 1 and 2 were further revealed by the temperature-dependent curves of the Raman spectrum. Both melts at 1473 K show multiple characteristic envelope peaks (attributed to vibration modes such as 190–370 cm⁻¹, 420–480 cm⁻¹, 858–1073 cm⁻¹, and 1102–1169 cm⁻¹), which indicates that the ion clusters in the melt have multilevel complex characteristics (Fig. 2c). Furthermore, the high consistency of Raman bands of 1 and 2 indicates that their high-temperature melt cluster compositions are similar to those of coordination geometries. This also confirms that the boron oxide does not significantly change the molecular volume of the growing unit clusters in the melt, indicating that the ion cluster structures in 1 and 2 have good stability. Complex envelope Raman signals can be divided into a low-wavenumber band (less than 400 cm⁻¹), an intermediate-wavenumber band (400–800 cm⁻¹), and a high-wavenumber band (850–1200 cm⁻¹).³⁸ These signals represent the order of the ionic cluster orientation, symmetric bending vibration and stretching vibrations of bridged oxygen (BO; such as Fe–O–Tb/Fe–O–Bi), and non-bridged oxygen (NBO; such as Fe–O, Bi–O, and Tb–O). It can be seen that the strong Raman signals of low and high wavenumbers may mean that the microstructures in melts 1 and 2 have short-range orders and rich non-bridged oxygen coordination structures. Furthermore, the normalized intensity of the 1102–1169 cm⁻¹ Raman band of 2 is significantly higher than that of 1, which indicates that boron oxide in the system increases the concentration of non-bridging oxygen. The rapid solidification experiment shows that the characteristic Raman signals of 1 and 2 attenuate with decreasing temperature until they disappear (Fig. 2d–f). However, new Raman bands appear in the glassy state, 235–377, 394–492, and 539–690 cm⁻¹, respectively. This may be due to the consumption of cluster structures in the high-temperature melt to reconstruct a new scale coordination atomic network. In addition, the Raman shifts corresponding to the Raman signals of the glass of 1 and 2 are basically consistent, but the intensity distribution is significantly different. This is attributed to the fact that boron oxides restrict interconnections between microstructures in the melt during solidification (Fig. S3). Overall, B₂O₃ enhances the freedom of ion clusters in the melt by increasing the concentration of non-bridging oxygen, which reduces the growth temperature and solidification point of ReIGs. In addition, during the cooling process, it alters the reconstruction path of the melt atomic coordination network and the energy barrier of the orientation arrangement of structural units, ultimately affecting the solidification kinetics of the glass atomic network.

Quantum chemistry simulations based on DFT were used to determine the microstructure corresponding to the Raman signals of the melt and glass.^32,38,40 A series of possible ion cluster structures was constructed and optimized, and vibration mode calculations were performed. Fig. S1 shows the basic ion cluster species existing in the melt. Among them, the characteristic vibration modes of [FeO₄]⁵⁻, [BiO₄]⁵⁻, [BiO₅]⁷⁻, and [TbO₄]⁵⁻ mainly contribute in the range of 190–370 cm⁻¹, which are 285, 197, 342, and 353 cm⁻¹, respectively. In addition, the characteristic vibrations of [FeO₅]⁷⁻ (879 cm⁻¹) and [FeO₆]⁹⁻ (532 cm⁻¹) contribute to the 858–1073 cm⁻¹ and 408–537 cm⁻¹ Raman ranges, respectively. This is mainly due to the different changes in polarizability caused by the characteristic vibration of bond energy differences. These basic structural units in high-temperature melts can coordinate with each other to form clusters of different dimensions. Fig. S2 shows the ionic structures of chains constructed by dual-metals and tri-metals. However, the characteristic peaks of these clusters all appear within the weak-intensity range of the Raman spectrum. Therefore, these cluster contents may be considered to be weak or exist in the melt as transition states. Impressively, the Raman vibration mode of the constructed four-metal chain-like ion structure corresponds to the Raman band of the melt, and its diffuse Raman displacements almost all belong to the melt Raman band (Fig. 3a–h). These chain-like ionic clusters can be recorded with the general formula [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} [A = Tb³⁺ or Bi³⁺; n (m) = 2 and 3], and the main difference is the occupancy site of Tb³⁺ and Bi³⁺ ions and the amount of oxygen (NBO) at the terminal metal. In addition, the Raman bands of [Tb₂Fe₂O₉]⁶⁻ and [TbBiFe₂O₉]⁶⁻ contribute to all the Raman peaks, except for 1130–1165 cm⁻¹, indicating that they may be the main components in [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−}. In fact, these four-metal ion clusters can form more complex ionic clusters through non-bridged or bridged oxygen coordination. Fig. 3i shows a possible two-dimensional topological ion cluster with characteristic Raman shifts (385 and 872 cm⁻¹) distributed in the melt, with weak Raman bands suggesting their low contents. For the Raman peak in the highest frequency segment (1102–1165 cm⁻¹) in the melt, we tried to construct a larger anion cluster^38,39 but did not get suitable results (Fig. S4). In fact, positive ionic structures have been shown to exist in silicate melts, and the vibration mode contributes to high-wavenumber Raman bands such as [Si₂F₇]⁺ (1095 cm⁻¹) and [SiF₃]⁺ (1175 cm⁻¹).⁴⁰ In addition, when heavy metal ions stretch the Fe–O bonds in the O–Fe–O geometry, they induce the transformation of Fe³⁺ to Fe⁴⁺, such as Fe–O–Mo.⁴¹ Therefore, four positive ion structures composed of Fe⁴⁺ were constructed, namely, Fe(IV)O₂, [BiFe(IV)O₂]³⁺, [TbFe(IV)O₂]³⁺, and [Fe(IV)₂O₃]²⁺ (Fig. 3j–m). Fortunately, their characteristic Raman band shifts coincide with the high-wavenumber Raman peaks of the melt (Fig. 3r), so it can be considered that these positively charged cation clusters exist in melts 1 and 2. More importantly, the one-dimensional long-chain structure forms ([Tb₄Fe₄O₁₆]⁸⁻, [Tb₂Bi₂Fe₄O₁₆]⁸⁻, [Tb₄Fe₄O₁₇]¹⁰⁻ and [Tb₂Bi₂Fe₄O₁₇]¹⁰⁻) reconstituted by [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} exhibit diffuse Raman bands, which are consistent with the significant Raman peak heights in the glass of 1 (Fig. 3n–q and r). It can be seen from this that [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} and its recombinant long chain (for example, [Tb₄Fe₄O₁₆]⁸⁻ and [Tb₄Fe₄O₁₇]¹⁰⁻) are the main components of the melt neutralization glass salt, respectively.

The significant Raman shifts of all species structures are recorded in Table S1 and are used as the basis for deconvolving the Raman peaks of melt 1 and its glass using a Lorentz function. When different species have Raman bonds of similar wavenumbers, multiple types of species are attributed to one Raman shift.⁴⁰ For melt 1, a series of characteristic Raman peaks are fitted to convergence within the Raman band coverage (Fig. 4a). The results show that the Raman peaks, except for the last peak (1130–1165 cm⁻¹), are all related to the [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−}-type ionic structures (Table 1), which means that the main proportion of the four-metal short-chain clusters exists stably in the melt. The difference in the amount of oxygen on the metals at their terminal may be attributed to the fact that these chain ion clusters are in a chemical equilibrium state of mutual conversion (Reactions 1 and 2). In addition, the envelope peaks of glass 1 are deconvolved by the Raman bands contributed by the eight-metal chain structures ([Tb₄Fe₄O₁₆]⁸⁻, [Tb₂Bi₂Fe₄O₁₆]⁸⁻, [Tb₄Fe₄O₁₇]¹⁰⁻, and [Tb₂Bi₂Fe₄O₁₇]¹⁰⁻) (Fig. 4b). This indicates that during the cooling process, the four-metal chains in the melt tend to extend axially into long chain structures, such as [A₂Fe₂O₈]⁴⁻ and [A₂Fe₂O₈]⁶⁻, recombining [A₄Fe₄O₁₆]⁸⁻ and [A₄Fe₄O₁₇]¹⁰⁻ eight-metal ion clusters (Reactions 3 and 4). In general, the compositions of melts 1 and 2 also contain multiple geometric characteristics and anion and cation cluster structures in addition to free metal ions (Fe³⁺, Tb³⁺, and Bi³⁺). Among them, the four-metal chain structures, as the main negative electrical ion clusters, have the tendency to recombine the axial PBC structure [–AO₂–Fe(III)O₂–]_n²ⁿ⁻ during the energy disturbance process.

[A2Fe(III)2O8]4− + O2− ⇌ [A2Fe(III)2O9]6−	(1)

[A2Fe(III)2O9]6− + O2− ⇌ [A2Fe(III)2O10]8−	(2)

[A2Fe(III)2O8]4− + [A2Fe(III)2O8]4− → [A4Fe(III)4O16]8−	(3)

[A2Fe(III)2O9]6− + [A2Fe(III)2O8]4− → [A4Fe(III)4O17]10−	(4)

Here, A is either Tb³⁺ or Bi³⁺.

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In melts, the orientation and distribution of ions and ion clusters are closely related to the temperature and electrostatic potential (ESP). In particular, the ESP plays a key role in stabilizing static structures and mediating dynamic processes.^42–44 Therefore, we analyzed the ESP quantitative molecular surfaces of free Fe³⁺, [Tb₂Fe₂O₉]⁶⁻, and [Tb₄Fe₄O₁₇]¹⁰⁻. For Fe³⁺, the value distribution of the positive ESP ranges from 637 to 859 kcal mol⁻¹ (Fig. 5a). This means that Fe³⁺ has an electron-deficient character, and the maximum point indicates that it is the optimal electron-acceptor site. In addition, the negative ESP values of [Tb₂Fe₂O₈]⁴⁻ range from −360 to 250 kcal mol⁻¹ (Fig. 5b). Its rich electron density is alternately distributed along the ion cluster axis, with equal amounts of extreme points appearing around [–TbO₄–]^5– and [–FeO₄–]⁵⁻ fragments, respectively. This periodic characteristic is observed more intuitively in the long ion-chain [Tb₄Fe₄O₁₇]¹⁰⁻ (Fig. 5c), with a negative ESP range from −446 to −292 kcal mol⁻¹. It can be seen from this that within the short range dominated by the electrostatic potential, attractive non-covalent interactions may be established between the electrostatic potential extreme points of Fe³⁺ and [Tb₂Fe₂O₈]^4-. This also induces an interaction between O²⁻ and Tb³⁺ in the [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} chains on a three-dimensional scale (Fig. 5d). In fact, the orientation of structural units in a high-temperature melt depends on the competition between the internal energy (mainly the kinetic energy of ion clusters) and the ESP energy between neighboring ions and ion clusters. That is, when the temperature is above the saturation point, the molecular kinetic energy dominates (the ion cluster structures are disorderedly distributed), while when it is below the saturation point, the electrostatic potential dominates (the ion cluster structures are orderly oriented), and the equilibrium state is reached at the saturation point. This is consistent with the experimental phenomenon that the crystal growth rate is positively correlated with the degree of subcooling within a certain temperature range. In brief, the growth of rare-earth iron garnets may follow the electrostatic bonding self-assembly of [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} and free Fe³⁺ to form growth units with lattice structures, which are superimposed onto the growth interface to achieve the growth process (Fig. 5d).^45,46

Conclusions

In summary, the microstructure and self-assembly mechanism of the (TbBi)₃Fe₅O₁₂-based melts [(Fe₂O₃–Tb₄O₇–Bi₂O₃), 1; (Fe₂O₃–Tb₄O₇–Bi₂O₃–B₂O₃), 2] were revealed by using DFT simulations and in situ vibrational spectroscopy. The results indicated that ion clusters with multilevel size distributions were presented in both 1 and 2, in which the chain-like [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} [A = Tb³⁺ or Bi³⁺; n (m) = 2 and 3] was identified as the growth unit of ReIGs. Notably, the growth of ReIG crystals may follow the electrostatic bonding self-assembly of [Fe(III)O_n–AO₂–Fe(III)O₂–AO_m]^{[4−2(m+n)]−} and free Fe³⁺, forming growth units with a lattice structure and superimposing them on the growth interface to achieve the growth process. Furthermore, trace amounts of B₂O₃ enhanced the freedom and stability of the system by increasing the concentration of non-bridging oxygen and the interaction between clusters. This work reveals the growth mechanism of iron garnets at the ion cluster level, which helps regulate the crystal quality and performance through the melt structure.

Author contributions

Wang Luo: writing – original draft, methodology, formal analysis, data curation, and conceptualization. Han Li: methodology and formal analysis. Zhuo Li: formal analysis. Shuting Yang: methodology. Feng Wang: formal analysis. Lingkun Wu: software and formal analysis. Huaiwu Zhang: writing – review & editing, conceptualization. Qinghui Yang: writing – review & editing, supervision, funding acquisition, conceptualization.

Conflicts of interest

There are no conflicts to declare.

Data availability

All data supporting the findings of this study are available within the article and its SI.

Experimental procedures, rheological and in situ high-temperature Raman measurement details, computational simulation methods, ion cluster structure refinement and Raman simulation results, statistical results of strong Raman bands of all ion clusters and glass 1 deconvolution. See DOI: https://doi.org/10.1039/d5ta03473f.

Acknowledgements

The experiments were supported by the National Natural Science Foundation of China (U2341286, 52072062), the National Key Research and Development Program, China (SQ2018YFE0205600), and Sichuan Science and Technology Support Program, China (2023YFG0072).

Notes and references

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