Electronic paramagnetic resonance analysis of point defects in lithium niobate: progress and prospects

Abstract

Lithium niobate (LiNbO₃) crystals, renowned for their exceptional piezoelectric, electro-optic, and nonlinear optical properties, are indispensable in photonic applications such as optical communication, integrated optics, and laser technology. However, the performance of LiNbO₃-based devices is fundamentally limited by point defects. Consequently, elucidating the mechanisms underlying point defect formation and achieving precise control over defect engineering have emerged as critical research priorities. Although conventional characterization techniques face inherent limitations in directly resolving the microstructures of point defects, electron paramagnetic resonance (EPR) spectroscopy has proven to be a pivotal analytical tool for the non-destructive characterization of paramagnetic defects, driving significant advancements in LiNbO₃ defect research. This article summarizes the intrinsic and impurity defects that significantly affect the optoelectronic properties of LiNbO₃ crystals. Firstly, it elucidates the primary types of point defects, their microstructural characteristics, and their impacts on material properties. Subsequently, it highlights the advancements in EPR technology for studying point defects and provides an in-depth analysis of its advantages in defect analysis. Finally, it proposes the future concerns of studying point defects in LiNbO₃ crystals using EPR technology.

---

1. Introduction

Lithium niobate (LiNbO₃) crystals, as a multifunctional crystal material,¹ exhibit the piezoelectric effect, electro-optic effect, nonlinear effect, photorefractive effect, photo-elastic effect, and acousto-optic effect² (Fig. 1). Various bulk and thin film devices based on LiNbO₃ crystals are widely used in fields such as optical frequency combs,^3,4 optical communication, integrated optics,⁵ and lasers.⁶ Owing to its excellent optical-electrical properties, LiNbO₃ is regarded as “optical silicon” in the optics field. Due to the significant advantages of single-crystal thin-film LiNbO₃ in integrated optics, Professor Burrows at Harvard University proposed “Now entering, Lithium Niobate Valley”.

Fig. 1 Properties of LiNbO₃ crystals.

Single-crystal defects can be classified into four categories⁷ based on their spatial dimensions: point defects, line defects, planar defects, and bulk defects. In LiNbO₃ crystals, the main types of defects include bulk defects (e.g., inclusions), planar defects⁸ (twinning boundaries), line defects⁹ (dislocations), and point defects¹⁰ (vacancies). Notably, advancements in crystal growth techniques coupled with improved microscopic characterization methodologies have enabled substantial progress in elucidating the formation mechanisms of the first three defect categories, along with effective suppression of their occurrence density. Nevertheless, atomic-scale characterization limitations persist in obscuring the generation dynamics and microstructure of point defects, becoming a critical bottleneck in optimizing the functional performance of LiNbO₃ crystals. As is well known, the performance of LiNbO₃ crystals is closely related to point defects. However, the formation mechanisms and elimination methods of point defects in LiNbO₃ crystals have been scarcely researched.

The investigation of point defects requires the integration of multi-scale characterization techniques, primarily encompassing magnetic resonance spectroscopy (e.g., electron paramagnetic resonance¹¹ and nuclear magnetic resonance¹²), spectral analysis (photoluminescence¹³ and X-ray absorption fine structure¹⁴), atomic-level microscopy techniques (scanning transmission electron microscopy^15,16), synchrotron radiation characterization, and computational simulations (density functional theory¹⁷). Among these, electron paramagnetic resonance (EPR) spectroscopy enables non-destructive acquisition of critical defect information, including local symmetry, coordination environment and charge state through the detection of spin resonance signals from unpaired electrons.¹⁸ This technique is widely recognized as the central methodology for establishing comprehensive point defect models in materials science.¹⁹ Although significant experimental efforts have been devoted to analyzing the point defects in LiNbO₃ crystals by EPR spectroscopy, systematic reviews about point defect characterization in LiNbO₃ crystals remain strikingly limited. Notably, existing review articles^20,21 predominantly focus on the electronic structure and localized environmental analysis of extrinsic defects, while systematic investigation of the EPR spectrum signatures and defect dynamics in intrinsic defect systems remains notably scarce.

Firstly, this review reviews the pivotal advancements facilitated by EPR spectroscopy in characterizing point defects within LiNbO₃ crystals, systematically describing the analysis results of EPR spectroscopy for intrinsic and external defects. Secondly, we also noticed that EPR spectroscopy has more important analytical application in stoichiometric lithium niobate (SLN) crystals. Lastly, the future application of EPR spectroscopy in defects analysis is proposed.

2. Point defects in LiNbO₃

The ideal crystal structure of an LiNbO₃ crystal consists of oxygen octahedra stacked in coplanar arrangements, with their shared planes perpendicular to the trigonal symmetry axis (i.e., polar axis). These different stacked units interconnect through edge-sharing coordination, forming an oxygen-octahedral framework^22,23 (Fig. 2a). As a ferroelectric material with a Curie temperature of approximately 1483 K (1210 °C), it exhibits distinct paraelectric and ferroelectric phase structures. Its ferroelectric phase structure arises from the cooperative displacement of Li⁺ ions and Nb⁵⁺ ions along the crystallographic c-axis, generating spontaneous polarization through ionic rearrangement (Fig. 2b). At this point, cations in the +c direction fill the oxygen octahedron in the form of “–Li Nb–□–Li Nb–□–”, where “□” represents vacancies.²² This structure would be one of the key factors causing LiNbO₃ crystals to be plagued by defects.

Fig. 2 (a) Ideal structure of LiNbO₃, (b) ferroelectric phase (left) and paraelectric phase (right) structure of LiNbO₃.

2.1. Intrinsic defects

LiNbO₃ crystal is a typical non-stoichiometric crystal, and its high-quality single crystal is usually grown from a congruent melt (Li : Nb = 48.6 : 51.4) using the Czochralski method, which is called a congruent lithium niobate (CLN) crystal. Due to the absence of Li⁺, intrinsic defects mainly consisting of Li vacancy (V_Li) and anti-site Nb (Nb_Li) appear in the lattice. The existence of these intrinsic defects significantly affects the electro-optical and nonlinear optical properties of the crystal, thereby limiting their applications in optoelectronic modulators, surface acoustic wave devices, and related fields. Therefore, the regulation of these intrinsic defects and their effects on material performance remains a critical research focus in the field of LiNbO₃ crystals.

Over the past few decades, substantial research efforts have been devoted to developing intrinsic defect structure models in LiNbO₃ crystals. However, due to inherent theoretical limitations and inconsistencies among various defect models, many have been subsequently abandoned. This chapter focuses on four representative defect models that have demonstrated particular significance in understanding the structural properties of LiNbO₃ crystals.

Fay et al. (1968) first proposed the oxygen vacancy model,²⁴ postulating that the absence of Li in crystals generates Li vacancies, while requiring the concomitant formation of oxygen vacancies to maintain charge neutrality. The structural formula of this model is [Li_1−2xV_2x]Nb[O_3−xV_x], where V represents a vacancy. Based on this model, a positive correlation between crystal density and Li content would be expected. However, precise experimental results demonstrate that the crystal density decreases with an increase in Li/Nb ratio.²⁵ This discrepancy between theoretical predictions and experimental observations ultimately led to the rejection of the oxygen vacancy model.

The Nb vacancy model was proposed,²⁶ wherein excess Nb occupies octahedral vacancies lacking lithium, forming Nb_Li, with charge compensation achieved by niobium vacancies (V_Nb) (Fig. 3a). At this time, the crystal chemical structure formula is [Li_1−5xNb_5x]Nb[O_1−4xV_4x]O₃. However, based on the niobium vacancy model, it was calculated that there are 5.9 mol% Nb_Li and 4.7 mol% V_Nb in the CLN crystal with Li/Nb = 0.942. From an energy perspective, these high concentrations of high valence Nb_Li is unstable. Therefore, the ilmenite structure formed by the partial exchange of Li⁺ and Nb⁵⁺ was proposed (Fig. 3b). This localized ilmenite structure can transform high-charged Nb⁴⁺_Li and V⁵⁻_Nb into simple V⁻_Li, thereby significantly improving the overall energy stability of defect structures based on the niobium vacancy model.

Fig. 3 Defect models in LiNbO₃ crystals. (a) Nb vacancy model, (b) ilmenite model, and (c) Li vacancy model.

Based on the differences in density and cell parameters of LiNbO₃ crystals with different Li/Nb ratios, the Li vacancy model was proposed in 1968. This model suggests that excess Nb in CLN crystals occupies the Li sites to form Nb_Li, with charge compensation achieved through the formation of Li vacancies (V_Li), as illustrated in Fig. 3c. The structural formula is [Li_1−5xV_4xNb_x]NbO₃. Both the lithium vacancy model and niobium vacancy model fundamentally exclude oxygen vacancies in the LiNbO₃ crystal, instead proposing the presence of Nb_Li defects. The concentration of Nb_Li in the lithium vacancy model is only around 1/5 of that in the niobium vacancy model, resulting in a more energetically favorable and stable defect configuration. In 1992, Iyi²⁷ measured the lattice parameters, density, and crystal powder diffraction data of LiNbO₃ crystals with different compositions, supporting the lithium vacancy model. Subsequent experimental studies^28–30 have consistently demonstrated that the lithium vacancy model is a more accurate defect structure model, which has gained widespread acceptance in the scientific community. Density functional theory is commonly used to determine the main intrinsic defects in crystals. According to the formation energy of different defect structures (E_VLi ∼ −0.23 eV, E_VNb ∼ −1.20 eV, E_NbLi+4VLi ∼ −0.25 eV, E_5NbLi+4VNb ∼ −1.12 eV), Xu et al. predicted that the defect cluster composed of four lithium vacancies compensating for anti-site niobium in CLN crystals is the most stable structure.³¹ Li et al. used a mixed hybrid exchange–correlation functional to improve the computational accuracy and obtained similar conclusions that for most LN crystals, their Fermi level is located in the lower half of the electronic bandgap, and anti-site niobium and Li vacancies coexist (i.e. ). Nb vacancies may only form under specific conditions.³²

Table 1 presents a comprehensive comparison of the four major defect models for the LiNbO₃ crystal. Among them, the Nb_Li defect has emerged as the most widely accepted defect in LiNbO₃ crystals, which means that analyses focusing on Nb_Li would be the key for defect analysis. Recent studies have further revealed that Nb_Li defects exert a significant influence on the physical properties of LiNbO₃ crystals, demonstrating predominantly detrimental effects across various crucial material characteristics. For example, Nb_Li defects act as photorefraction centers³³ between energy levels (Fig. 4a), greatly reducing the optical-damage resistance threshold of the crystal. The electro-optic coefficient, γ₆₁, of the LiNbO₃ crystal decreases with a decrease in Li content from a stoichiometric ratio to the congruent component, which was also assigned to the increase in Nb_Li defects³⁴ (Fig. 4b). Furthermore, the pinning effect of Nb_Li defects hinders domain inversion,³⁵ substantially increasing the domain inversion voltage in CLN crystals compared to near stoichiometry lithium niobate (NSLN) crystals (Fig. 4c). In addition, Wang et al. confirmed that the piezoelectric coefficient, , and electromechanical coupling coefficient, , of NLSN crystals are superior to that of CLN crystals at operating temperatures in the range of 0–650 °C, which is also attributed to the contents of Nb_Li defects³⁶ (Fig. 4d).

Table 1 Comparison of defect models for LiNbO₃

Model	O vacancy model	Nb vacancy model	Ilmenite model	Li vacancy model
Li vacancy	√	—	—	√
O vacancy	√	—	—	—
Nb vacancy	—	√	√	—
Anti-site Nb	—	√	√	√

---

Fig. 4 (a) Nb_Li acts as a photorefractive center in CLN crystals. (b) Dependence of the electro-optic coefficient, γ₆₁, on the crystal composition in pure LiNbO₃ crystals, where X_c represents the Li content in the LiNbO₃ crystal.³⁴ Reproduced from ref. 34 with permission from AIP Publishing, copyright 1998. (c) Ferroelectric hysteresis loop of NSLN measured at room temperature.³⁷ Reproduced from ref. 37 with permission from Elsevier, copyright 2022. (d) Variations in electromechanical coupling factors and piezoelectric coefficients as a function of temperature for NSLN (red) and CLN (green) crystals.³⁶ Reproduced from ref. 36 with permission from the American Chemical Society, copyright 2024.

2.2. Extrinsic defects

The incorporation of various doping elements significantly enriches the properties and broadens the application prospects of LiNbO₃ crystals^40–46 (Fig. 5). For instance, hydrogen atoms typically exist in oxide crystals as OH ions,^47,48 and the presence of unexpected H ions can alter the refractive index of LiNbO₃ crystals. Elements such as Mg,^49–51 Zn,⁵² In,^53,54 Sc,⁵⁵ Sn,⁵⁶ Hf^57,58 and Zr,^39,59,60 which possess stable valence states and optical inertness, are employed to enhance the optical damage resistance in LiNbO₃ crystals. Conversely, Cu,^61–63 Mn,⁶⁴ Fe,^65,66 Ni and Ce^67,68 were used to enhance the photorefractive effect by introducing the impurity defect energy levels in the crystal bandgap. Additionally, rare earth ions such as Er,^69–71 Nd,^72,73 Yb,^46,74 Tb,⁷⁵ Dy,⁷⁶ Ho^77,78 and Tm⁷⁹ serve as active ions, imparting laser properties to LiNbO₃.

Fig. 5 Application of dopants in the LiNbO₃ crystal.^38,39 Reproduced from ref. 38 with permission from the Editorial Office of Opto-Electronic Journals Group, Institute of Optics and Electronics, copyright 2022. Reproduced from ref. 39 with permission from the Optical Society of America, copyright 2011.

However, doping engineering also introduced external defects due to the different radii and ionic valence of the dopants. When the doping concentration of Mg exceeds 6 mol%, the optical damage resistance threshold of the Mg:CLN crystal significantly decreases, which is caused by the Mg_Nb defect formed by Mg occupying the Nb sites. Lanthanide elements such as Nd and Yb have large ionic radii, which cause severe lattice distortion in LiNbO₃ crystals, making them prone to cracking during the growth process. In addition, the segregation effect causes a concentration gradient of doping elements along the crystal axis, which changes the thermal expansion coefficient of the crystal and may lead to cracking during cooling. Obviously, micro defects serve as critical determinants governing the physical properties of LiNbO₃ crystals. Consequently, the application of advanced characterization techniques is essential to systematically investigate the formation mechanism of defects and their influence on the physical properties of crystals.

Lithium niobate on insulator (LNOI) is completely changing the lithium niobate industry, with advantages such as higher performance and new equipment and applications.^80,81 It not only maintains the excellent optical properties of bulk crystals, but also enables photonic devices/circuits to be easily scaled down to the sub-micron scale.⁸² However, processing methods such as ion implantation, ion beam etching, and ion irradiation can cause lattice damage and introduce new defects.⁸³ Current research on LNOI primarily focuses on fabrication quality, with the use of high-resolution X-ray diffraction to verify the ordering of single crystals⁸⁴ and Raman spectroscopy to evaluate the quality of lattice arrangement.⁸⁵ There are few reports on the analysis of defects in LNOI, and aberration corrected electron microscopy can be used to directly observe the atomic occupancy. However, EPR technology has not yet been applied to the analysis of defects in LNOI. The defects or damages have a significant impact on the various physical properties of LN crystals. Post-annealing treatment is an effective method for restoring these damages and defects. Usually, H ion implantation into waveguides requires annealing at a temperature of 200–300 °C to reduce optical absorption and improve the waveguide performance. Ashley et al.⁸⁶ injected a high dose of Ti into LN to form a planar waveguide, and the ion-implanted region was completely amorphized. After annealing at 1000 °C for 1 h, its electro-optic coefficient, γ₃₃, was measured to be 29 pm V⁻¹, which is close to that of bulk crystals. High-temperature annealing helps to restore the electro-optic properties of ion-sliced LN films.^87,88 Moreover, SHG experiments showed the recovery of the nonlinear coefficient of a LN thin film after annealing at 600 °C.⁸⁹

3. Application of EPR in defect characterization

3.1. Introduction of EPR spectroscopy

EPR spectroscopy is sensitive high-resolution spectrum technology for the detection of unpaired spins, which has been widely used in fields such as physics, chemistry, biology, and materials. Briefly, when EPR spectroscopy is used to study unpaired electron spins in solid materials, Hamiltonian parameters can be used to describe various possible interactions, which generally take the following form:

H_spin = H_EZ + H_HF + H_CF + H_Q + H_NZ

where H_EZ is the electronic Zeeman interaction, representing the interaction between the effective spin, S, and the applied magnetic field, B. As long as there are unpaired electrons, there must be electron Zeeman interactions, which are an essential component of the Hamiltonian parameter. H_EZ can be represented by a g-tensor, which can reflect the local point symmetry of defects. H_HF is a hyperfine interaction, representing the interaction between the magnetic moment of unpaired electrons and the magnetic moment, I, of nearby atomic nuclei. When I > 0, hyperfine splitting occurs, dividing the spectral lines into (2I + 1) lines. Obtaining an effective spin, S, and magnetic moment, I, through EPR spectrum analysis can help us quickly determine the types and charge states of impurity elements. Due to the influence of the electrical crystal field, additional interactions called fine structure interactions (H_CF) can occur in paramagnetic defects with S > 1/2, which will result in 2S splitting of the EPR spectrum lines. H_Q and H_NZ are the nuclear quadrupole interaction and nuclear Zeeman interaction, respectively, which are small compared to the Zeeman energy and not stated here. For more details, readers can refer to textbooks on EPR spectroscopy, as well as the recent article by Rudowicz,⁹⁰ in which the current situation in this area is reviewed and discussed.

3.2. Application of EPR spectroscopy in defect analysis of LiNbO₃

The formation of defect structures in crystals is fundamentally governed by the charge states of impurity ions occupying lattice sites and their corresponding charge compensation mechanisms. Excessive Nb occupies the Li sites in CLN crystals to form Nb_Li defects, whose concentration and structure have not yet been determined. Due to the complexity of the CLN crystal structure and the limitation of experimental equipment resolution, it is usually difficult to directly observe the structural information of Nb_Li defects. Furthermore, the substitution mechanisms of doping elements in CLN crystals, particularly concerning site occupancy preferences and charge compensation, remain poorly understood and require further systematic investigation.

Fortunately, these defects in the crystal are originally paramagnetic or after specific treatment, which can be detected by EPR spectroscopy very accurately. EPR spectroscopy exhibits exceptional sensitivity, and different elements with determined nuclear spin numbers and abundances produce characteristic spectral splitting patterns, which can serve as a “fingerprint” for identifying defect identities.²⁰ Additionally, ENDOR spectroscopy can probe the surrounding environment of defects, providing crucial insights into their charge compensation mechanisms. Therefore, some progress has been made by EPR and ENDOR technology in analyzing defects in LiNbO₃ crystals over the past few decades.

3.2.1. EPR spectrum analysis of intrinsic defect. In LiNbO₃ crystals, the Nb_Li defect has been widely recognized as the most critical intrinsic defect. It was believed that due to the lower content of Li in the CLN crystal, the higher strength of Nb–O bonds compared to Li–O bonds, the small difference in ionic radius between Li⁺ (r = 0.76 Å) and Nb⁵⁺ (r = 0.69 Å) and their similar spatial environment, Nb tends to occupy the Li sites to form Nb_Li.¹⁰ Peterson discovered two types of lattice environments for Nb⁵⁺ in the CLN crystal lattice through ⁹³Nb nuclear magnetic resonance experiments, which implied the existence of Nb_Li.²⁶ Therefore, extensive research has been conducted using EPR spectroscopy to analyze the structural information of Nb_Li.

Schinner⁹¹ firstly obtained a nearly equidistant 10-line EPR spectrum in CLN crystals after laser irradiation (Fig. 6a). This was attributed to the hyperfine interaction between unpaired electrons and ⁹³Nb nuclei (I = 9/2). The relevant Hamiltonian parameters were calculated to be g_‖ = 1.90, g_⊥ = 1.72, A_‖ = 0.011 cm⁻¹ and A_⊥ = 0.023 cm⁻¹. Its hyperfine splitting and g-shift are typical features of Nb⁴⁺ in a distorted oxygen octahedral environment.^92,93 Based on the axial symmetry of the spectrum, they attributed this signal for the first time to the electron self-trapping of the Nb lattice, i.e. Nb⁵⁺_Nb + e⁻ → Nb⁴⁺_Nb. However, Müller et al. proposed an alternative interpretation by analyzing the angular dependence of the Nb⁴⁺ signals. Their fitting of the anisotropic g-tensor and A-tensor (Fig. 6b) suggested a reduction in local symmetry around the Nb⁴⁺ center.⁹⁴ The observed symmetry reduction arises from the formation of a charge compensation structure induced by the excess positive charge of Nb_Li. This distortion of the local coordination environment provides compelling evidence that the EPR signals originate from the Nb ions occupying the Li sites. Faust⁹⁵ noticed that the intensity of EPR spectrum of Nb⁴⁺_Nb is lower in thermally reduced CLN crystals doped with 6 mol% MgO (Fig. 6c). The reason for this may be that high concentration Mg doping eliminates the Nb_Li defects in CLN crystals, resulting in the disappearance of the EPR spectrum belonging to Nb⁴⁺_Li. Zheng et al.⁹⁶ provided the calculated Hamiltonian parameters for Nb_Li defects, demonstrating excellent agreement with experimental data. Their analysis further revealed the structural configuration of the defect center, showing that Nb_Li is displaced from the ideal Li site by Δz ≈ 0.19 Å along the polar axis, while the coordinating oxygen ions in the plane between Nb⁴⁺_Li and Nb⁵⁺_Nb exhibit a lateral displacement of Δx ≈ 0.30 Å away from the C₃ axis. The reason for the offset is that when Nb⁵⁺_Li captures electrons to form Nb⁴⁺_Li, the decrease in electrostatic repulsion causes Nb⁴⁺_Li to shift towards the center of the oxygen octahedron. Meanwhile, due to the overlap of electron clouds, the oxygen ions between Nb⁴⁺_Li and Nb⁵⁺_Nb are far away from the oxygen triangle center. Regrettably, the underlying mechanisms responsible for the enhanced Nb⁴⁺_Li signal in annealed CLN crystals following Xe lamp irradiation remain unclear. In particular, the local charge compensation structure associated with Nb_Li defects has not been fully elucidated.

Fig. 6 (a) Two-photon-induced ESR at higher microwave power.⁹¹ Reproduced from ref. 91 with permission from AIP Publishing, copyright 1978. (b) Angular dependence of experimental resonance fields with fitted positions for metastable Nb⁴⁺, T ≈ 20 K, v ≈ 9 GHz.⁹⁴ Reproduced from ref. 94 with permission from Taylor & Francis, copyright 2011. (c) EPR spectrum of Nb⁴⁺-type centers in undoped (black) and 6 mol% Mg-doped (red) congruent LiNbO₃ crystals after vacuum reduction for the magnetic field parallel to the crystal c axis. (d) Defect structure of Nb⁴⁺_Li center in LiNbO₃.⁹⁶ Reproduced from ref. 96 with permission from Elsevier, copyright 2008.

LiNbO₃ crystals exhibit darkening when heated to 500 °C under a vacuum, hydrogen, or argon atmosphere, with progressively intensified coloration as the temperature increases.⁹⁷ UV-vis absorption spectroscopy shows that annealed samples generate a broad absorption band centered at approximately 500 nm, which shifts to 760 nm after xenon lamp irradiation (optical bleaching).^98,99 The proposed mechanism^98,100 is that the oxygen vacancy introduced during reduction initially traps two electrons to form neutral F-centers, which are responsible for the 500 nm absorption peak. Upon optical bleaching, the F-centers release one electron to become F⁺-centers. The unpaired electron in the F⁺-centers interacts through hyperfine coupling with adjacent Nb ions neighboring the oxygen vacancy, manifesting as a 10-line EPR spectrum. Although other intrinsic defects such as lithium and niobium vacancies may exist, they have not yet been experimentally confirmed through spectroscopic characterization.

3.2.2. EPR spectrum analysis of extrinsic defects. The deliberate introduction of extrinsic defects by dopants during crystal growth serves as a crucial strategy for tailoring the properties of materials. Thus, to elucidate the impact of doping elements on the physical properties of crystalline materials, a comprehensive understanding of their lattice occupancy behavior and chemical states is essential. The paramagnetic nature of most dopant species in the LiNbO₃ crystal makes EPR spectroscopy particularly advantageous for analyzing these extrinsic defects. Among the various dopants, transition metal ions and rare earth ions represent the primary extrinsic species in LiNbO₃ crystals, consequently receiving the most extensive attention in EPR-based defect studies.

(1) Transition metal ions

Transition metal ions are widely used to enhance the photorefractive ability of LiNbO₃ crystals. Because their unstable valence states can form defect energy levels in the energy band of LiNbO₃ crystals, they serve as photorefractive centers. The typical transition metal ions used are Fe, Cu, and Mn, with Fe being the most extensively studied due to its superior ability to improve the photorefractive performance.

For example, five different lattice sites of Fe have been identified in LiNbO₃ crystals, namely Fe₁, Fe₂, Fe₃, Fe₄, and Fe₅, respectively. The Fe₁ center with C₃ symmetry in Fe-doped CLN crystals has been found, and several studies^103–106 have consistently reported a zero-field splitting (ZFS) parameter of b⁰₂ ≈ 0.1680 cm⁻¹ (Fig. 7a). Zhao¹⁰⁷ calculated the ZFS parameters D and a_F of Fe³⁺ at the Li (D = 0.860 cm⁻¹, a_F = 0.03 cm⁻¹) and Nb (D = 1.054 cm⁻¹, a_F = 0.114 cm⁻¹) sites in Fe³⁺: LiNbO₃. The ZFS parameters for Fe³⁺ at Nb sites closely match experimental results¹⁰⁸ (D = 1.106 cm⁻¹, a_F = 0.128 cm⁻¹), indicating that the impurity ion Fe³⁺ substitutes Nb⁵⁺, rather than Li⁺ in the LiNbO₃ lattice.

Fig. 7 EPR Fe³⁺ spectra of (a) 0.02% Fe-doped LN crystal.¹⁰¹ Reproduced from ref. 101 with permission from Taylor & Francis, copyright 2011. (b) 6 mol% Mg, Fe-doped CLN crystal.¹⁰² Reproduced from ref. 102 with permission from IOP Publishing, copyright 1990. (c and e) 0.45% Mg and 0.01% Fe co-doped LN-K crystal.¹⁰¹ Reproduced from ref. 101 with permission from Taylor & Francis, copyright 2011. (d) 0.001% Fe-doped LN-K crystal.¹⁰¹ Reproduced from ref. 101 with permission from Taylor & Francis, copyright 2011.

When the doping concentration of Mg exceeds the threshold, the Fe₂ center¹⁰² emerges in Fe, Mg co-doped CLN crystals (Fig. 7b). The angle dependence of the EPR spectra indicates that this center exhibits low symmetry.¹⁰⁹ Boker¹⁰² proposed that Fe³⁺ preferentially occupies the Nb⁵⁺ sites, forming stable charge compensation structures (Mg⁺_Li − Fe²⁻_Nb). The reason for this is that the smaller ZFS parameter D corresponds to the geometric position of Fe³⁺ occupying the Nb sites, making this configuration energetically favorable in heavily doped CLN crystals. The Fe₃ (Fig. 7c) and Fe₅ (Fig. 7e) centers are distinguished in stoichiometric lithium niobate crystals (grown with K₂O as the flux, denoted as SLN-K) doped with 0.45 mol% Mg and 0.01 mol% Fe.^101,110 The Fe₄ center is observed in the SLN-K crystal with 0.001% Fe (Fig. 7d). Due to the smaller crystal field parameter b⁰₂, Fe₃, Fe₄, and Fe₅ are attributed to Fe occupying the Nb sites. The variation in EPR spectra for Fe centers at Nb sites is closely linked to the concentration of intrinsic and extrinsic defects in the crystal lattice. In Mg:CLN crystals, their charge compensation structure is completed by 2Mg⁺_Li − Fe²⁻_Nb, while in SLN-K crystals, charge compensation is achieved through protons or additional Li⁺.

Mn:Fe:LN crystals with deep and shallow energy levels can utilize dual color storage to exhibit non-volatile storage properties. Understanding the substitution mechanism of Mn²⁺ in LiNbO₃ crystals is essential for optimizing their performance. The larger hyperfine splitting constant of Mn²⁺ suggests that the Mn–O bond tends to be highly ionic.¹¹¹ Peterson¹¹² proposed that doped ions that do not exhibit a tendency to form covalent bonds, but preferentially substitute at the Li⁺ sites. This conclusion is further supported by ENDOR studies,¹¹³ confirming the Li site as the dominant occupancy site for Mn. However, the zero-field splitting parameter b⁰₂ of Mn²⁺ decreases with an increase in temperature.^114–116 This trend suggests a reduction in octahedral distortion, consistent with Mn²⁺ shifting toward the center of the Nb–O₆ octahedron. This behavior suggests that Mn²⁺ substitutes at the Nb⁵⁺ site rather than the Li⁺ site, contradicting earlier interpretations based on hyperfine splitting and ENDOR studies.

The above-mentioned results indicate that there is still controversy over the occupancy of Mn in LiNbO₃ crystals. To resolve this inconsistency, more comprehensive EPR experiments should be designed and performed to unambiguously determine the position of Mn²⁺ in the lattice. Some other transition metal ions, such as Cr³⁺, Ti³⁺, Ni²⁺, and Co²⁺, in LiNbO₃ crystals have also been studied using EPR spectroscopy technology.^117–120

(2) Rare earth ions

Rare earth (RE) ions are incorporated into LiNbO₃ crystals as optically active centers, enabling their widespread use in solid-state lasers,¹²¹ optical amplifiers, and wavelength converters. The spectral properties of these dopants are critically dependent on their local crystal field environment, which is closely related to the site location of the doped ions. RE ions in LiNbO₃ crystals can locate at four cation sites, i.e., three octahedral sites (Li⁺ site, Nb⁵⁺ site and a vacant octahedron) or an interstitial tetrahedral site. However, the actual occupancy situation is much more complex. Spectroscopic studies have shown that even if rare earth ions occupy the same lattice sites in LiNbO₃ crystals, they exhibit different spectral properties due to being surrounded by different lattice environments. The lanthanide ions with unpaired electrons located in their 4f orbital are usually used in LiNbO₃ crystals. Emission spectroscopy²¹ and EPR spectroscopy¹²² have identified multiple non-equivalent centers with different symmetries for these ions, suggesting that the actual incorporation mechanism involves a dynamic interplay between dopant ions and the defect structure of the host lattice.

Nd³⁺ defect centers (g_‖ = 1.42 and g_⊥ = 2.94) with C₃ symmetry in CLN crystals have been found.^125,126 However, the EPR spectrum of Nd³⁺ in CLN crystals displays exceptionally broad lines, making it difficult to resolve contributions from different defect centers or isotopic effects. This explains that why the hyperfine structure was not studied in ref. 110 and 111. The EPR spectrum lines of Nd in NSLN crystals have higher spectral resolution (Fig. 8a). Therefore, eight non-equivalent Nd³⁺ centers were identified in NSLN crystals and the g-tensor values of all the centers were determined. Although all eight centers are the Nd-occupying Li sites,¹²³ they exhibit different symmetries. Nd₁ and Nd₈ exhibit C₃ symmetry, as evidenced by their angle-independent EPR spectra in the xy-plane (Fig. 8b and c), respectively. The symmetry of the other six defect centers is relatively low, and the reason for the different symmetries is that the defect positions used for charge compensation are different (Table 2).

Fig. 8 (a) EPR spectra of Nd³⁺ at B‖z in congruent and nearly stoichiometric LiNbO₃ crystals doped with 0.06 wt% Nd₂O₃ in the melt (thick red line: ν = 9.5 GHz and T = 10 K and thin blue line: ν = 9.8 GHz and T = 19 K), as well as in a congruent crystal doped with 1% of Nd (medium green line: X-band, T = 20 K).¹²³ Reproduced from ref. 123 with permission from AIP Publishing, copyright 2015. (b) Angular dependence of the EPR spectra in nearly stoichiometric LN:Nd³⁺. T = 19 K, ν = 9.813 GHz.¹²⁴ Reproduced from ref. 124 with permission from John Wiley and Sons, copyright 2006. (c) Angular dependence of the EPR spectra in NSLN:Nd³⁺. T = 19 K, ν = 9.813 GHz.¹²⁴ Reproduced from ref. 124 with permission from John Wiley and Sons, copyright 2006.

Table 2 Cartesian components of g-tensors for Nd³⁺ centers in crystallographic axes of LiNbO₃.¹²³ Reproduced from ref. 123 with permission from AIP Publishing, copyright 2015

Center	gxx	gyy	gzz	gzy	±gzx	±gxy
Nd1	2.995	2.995	1.448	0	0	0
Nd2	3.090	2.920	1.345	−0.040	0.015	0.240
Nd3	3.277	2.750	1.419	0.024	0.109	0.030
Nd4	3.430	2.700	1.421	0.035	0.100	0.220
Nd5	3.43	2.60	1.43	−0.13	0.18	0.20
Nd6	2.915	3.06	1.454	0.008	0.043	0.025
Nd7	3.14	3.04	1.488	0.044	0.062	0.030
Nd8	2.970	2.970	1.563	0	0	0

---

Earlier studies¹²⁶ suggest that the Er³⁺ centers with g_‖ = 15.1–15.4 and g_⊥ = 2.1 in the CLN crystal have C₃ symmetry (Fig. 9a). However, the angular dependence of the EPR spectrum in the xy-plane (Fig. 9b) confirms that the Er³⁺ center (g_xx = 0.546 ± 0.110, g_yy = 1.356 ± 0.024, and g_zz = 15.093 ± 0.074) in the CLN crystal has C₁ symmetry.^127–129 The relatively large anisotropy of the g-factor indicates that the Er³⁺ defect center may be located in the distorted Li–O octahedron, i.e. Er³⁺ occupies the Li site. Th. Nolte¹³⁰ proposed that this symmetry reduction (C₃ → C₁) arises from the random distributions of the charge compensation structure Er³⁺–V⁻_Li, as illustrated in Fig. 9c. A new Er³⁺ defect center with g_‖ = 4.26 ± 0.05 and g_⊥ = 7.8 ± 0.1 was identified in Mg, Er:CLN crystals. The mean g value, (g_‖ + 2g_⊥)/3 = 6.6, is characteristic of the Er³⁺ center and closely matches that of the previously reported center.¹²⁶ The relatively small g-tensor anisotropy in this case suggests that the Er³⁺ ions are located at the Nb site compare to the previous one.

Fig. 9 (a) EPR spectrum of Er³⁺ in LiNbO₃, measured at T = 5 K and v_EPR = 25 GHz.¹³⁰ Reproduced from ref. 130 with permission from Elsevier, copyright 1997. (b) Angular dependence of the EPR spectra of the LN:Er³⁺ crystal measured at 8 K in all three perpendicular planes.¹²⁸ Reproduced from ref. 128 with permission from John Wiley and Sons, copyright 2008. (c) Possible models of low-symmetry Er³⁺ centers.¹³¹ Reproduced from ref. 131 with permission from Materials Research Society, copyright 2009.

The tremendous narrowing of EPR spectrum in Yb (0.04 wt%):NSLN crystal (Fig. 10a) compared to Yb:CLN crystal, enabled the resolution of nine non-equivalent Yb³⁺ centers.¹³² Among them, the spectral features of the Yb₁, Yb₆, and Yb₉ centers remained invariant under rotation of the magnetic field within the xy-plane, confirming their C₃ symmetry, while the other centers exhibited lower C₁ symmetry. The Yb₁ center with g_⊥ = 2.706 ± 0.005 and g_‖ = 4.46 ± 0.01 closely resembles the previously reported Yb³⁺ center in CLN crystals.¹³³ The ENDOR experimental spectrum¹³² (Fig. 10b) reveals the hyperfine interaction between the unpaired electrons of Yb₁ and Nb nuclei, directly indicating that Nb is the nearest neighbor nuclei (Fig. 10c). Therefore, it is reasonable to conclude that Yb₁ is the Yb³⁺ ion substituting for Li⁺. Due to the similarity between the characteristics of the Yb₂, Yb₃, Yb₄, Yb₇, and Yb₈ centers (Table 3) and the Yb₁ center, Malovichko⁹⁰ proposed that all these defect centers can be attributed to the substitution of Li⁺ by Yb³⁺. This change in symmetry may be caused by the different configurations of Li vacancies around Yb³⁺ or the different positions of Yb³⁺ in the lattice.

Fig. 10 (a) Assignment of lines of different nonequivalent centers and hyperfine structures of Yb³⁺.¹³¹ Reproduced from ref. 131 with permission from Materials Research Society, copyright 2009. (b) ENDOR spectrum for the Yb₁ center in SLN:Yb³⁺ at B||z.¹³² Reproduced from ref. 132 with permission from John Wiley and Sons, copyright 2008. (c) Model of the Yb₁ center.¹³² Reproduced from ref. 132 with permission from John Wiley and Sons, copyright 2008.

Table 3 Cartesian components of g-tensors for centers in LiNbO₃:Yb³⁺. The sign ± reflects the presence of mirror conjugated centers with g_xy (L) = −g_xy (R), g_zx (L) = −g_zx (R).¹³² Reproduced from ref. 132 with permission from John Wiley and Sons, copyright 2008

Center	gxx	gyy	gzz	gzy	±gzx	±gxy
Yb1	2.706	2.706	4.46	—	—	—
Yb2	2.84	2.48	4.56	0.22	0.45	0.02
Yb3	2.63	2.67	4.35	−0.15	0.10	0.17
Yb4	2.65	2.44	4.56	0.21	0.38	0.08
Yb6	2.68	2.68	4.44	—	—	—
Yb7	2.64	2.44	4.56	0.21	0.39	0.024
Yb8	2.71	2.765	4.36	0.11	0.14	−0.07

---

4. Summary and prospective

In summary, EPR spectroscopy stands out as a powerful tool for the characterization of defects in LiNbO₃ crystals, providing unique insights into the formation and local structure of point defects. Through the comprehensive analysis of EPR spectra and determination of Hamiltonian parameters, this technology enables the precise identification of defect types, quantification of defect concentrations, localization of defect sites, and characterization of structural modifications in the surrounding environment. The structural information derived from Zeeman interactions and zero-field splitting parameters, combined with the analysis of quadrupole interactions and hyperfine couplings between impurity electrons and their host/nuclear environments, provides a robust foundation for structural modeling. These critical insights are crucial to explore the impact of defects on the properties of crystals and how to precisely control defects to improve the performance of crystal devices.

Over recent decades, EPR spectroscopy has undergone remarkable progress in characterizing point defects in LiNbO₃ crystals. The evolution of high-sensitivity EPR systems, combined with improved control over crystal stoichiometry and the integration of advanced characterization tools, is expected to provide unprecedented new insights into defect structures and their interactions with the host lattice. These developments are paving the way for the establishment of more sophisticated defect models, thereby establishing a robust foundation for the growth of high-quality crystals and the fabrication of high-performance devices. Looking ahead, future research may focus on the following aspects.

4.1. Anti-site defects need to be clarified

As the most important intrinsic defects in LiNbO₃ crystals, there are still doubts about the concentration, structure, and charge compensation mechanism of Nb_Li defects. Although some studies suggest that the 10-line EPR characteristic spectrum produced by xenon lamp irradiation of annealed CLN crystals originate from Nb_Li, there is still a lack of direct experimental evidence. Meanwhile, due to the lack of detailed information about the anti-site defect structure, it is impossible to construct an appropriate intrinsic defect model; therefore, it is essential to conduct more systematic and in-depth research. Firstly, anti-site Nb exhibits a positive charge state due to charge imbalance and has a stronger attraction to free electrons compared to Nb in the normal lattice position. It is necessary to find a suitable testing temperature that allows electrons at the Nb_Nb site to escape, while electrons at the Nb_Li site remain bound. At this point, Nb⁵⁺_Nb exhibits an EPR-silent state, and the characteristic spectrum of Nb⁴⁺ belongs to Nb⁴⁺_Li. Secondly, LiNbO₃ crystals with different compositions were subjected to the same treatment and their EPR spectra were detected. It can be expected that with an increase in Li/Nb, the characteristic spectral intensity of Nb⁴⁺_Li decreases and that of Nb⁵⁺_Nb increases, which will become favorable evidence for the existence of Nb_Li defects.

In addition, the thermal stability and dynamic evolution of defects were studied by first-principal theory calculation. However, the theoretical analysis could not draw a clear map of the defect evolution. The thermal activation energy of different defects varies, and at a specific annealing temperature, defects undergo migration-recombination-annihilation, resulting in a decrease in EPR intensity. By drawing the curve of EPR signal intensity and annealing temperature change through an isothermal annealing experiment, different types of point defects can be identified, their migration energy can be measured, and their interactions and evolution paths can be studied.

4.2. In depth analysis of high-resolution EPR spectrum-assisted point defects in NSLN crystals

Although the EPR signals of Nb⁴⁺ have been detected in CLN crystals, there is currently a lack of sufficient evidence to determine whether the signals originate from Nb_Li or Nb_Nb. Moreover, there are differences in the Hamiltonian parameters due to spectral broadening and insufficient resolution. When the angle between the microwave direction and the crystallographic c-axis is too large, the intensity of the split signal will decrease, thus being masked by noise. As a result, clear spectral signals can only be observed on the axis. The same problem also arises in the analysis process of doped ion defect centers. It is difficult to comprehensively detect multiple non-equivalent defect centers of doped ions in the crystal and construct suitable defect models. EPR spectrum simulations have indicated that the linewidth, asymmetry, and intensity of forbidden transitions in the spectrum are closely associated with inherent defects in non-stoichiometric crystals. This is confirmed by the EPR spectrum of SLN-K crystals, which exhibits narrower and more symmetrical features compared to that of CLN crystals.

Moreover, many new EPR signals have been reported in NSLN crystals doped with lanthanide ions. The results are consistent with multiple non-equivalent defect centers shown in the emission spectra, providing theoretical guidance for the occupancy mechanism of doped ions. Doping a small amount of elements in NSLN crystals can significantly improve certain physical properties, such as the improvement of the optical damage resistance of 1 mol% Mg-doped NSLN crystals,¹³⁴ which is similar to that of 4.6 mol% Mg-doped CLN crystals. This low concentration doping helps to explore the mechanism of ion doping and achieve precise control of functional crystals. In addition, NSLN crystals may serve as an ideal system for verifying first principles calculations due to their low defect density and perfect lattice structure. Therefore, using EPR spectrum to analyze the defect structure of NSLN crystals has important research value.

4.3. Advancing high-temperature and time-resolved EPR with AI integration

At present, most EPR spectroscopy research is focused on low-temperature conditions, and future research can be devoted to developing high-temperature EPR spectroscopy for defect analysis under conditions closer to practical applications. This technique will help to understand the defect behavior and corresponding physical property changes in materials at high temperatures, providing guidance for the preparation of high-temperature piezoelectric/electro-optic devices using LN crystals. Time-resolved EPR combined with photoexcitation can directly track the carrier trapping dynamics (hole/electron capture rates of defects), photoinduced defect kinetics (formation/annihilation paths of oxygen vacancies under UV irradiation) and spin-dependent charge transfer (inter-defect interactions governing photorefractive response). These results will provide important information for understanding how materials respond to environmental changes in practical applications. These insights are vital for optimizing the carrier lifetimes in electro-optic modulators and suppressing optical damage in high-power lasers. The significant advancement of AI spectroscopy can help researchers process large amounts of complex data more quickly and efficiently, combining machine learning and data science technology to automatically identify and classify defect features using EPR experimental data. This will improve the efficiency and accuracy of data analysis and promote the intelligent development of defect research.

Author contributions

Liu H and Sang Y provided the overall concept for this review and designed the review framework; Qin H wrote the original draft and revised and edited the manuscript; all authors contributed to the general discussion.

Conflicts of interest

There are no conflicts to declare.

Data availability

No primary research results, software or code has been included and no new data were generated or analyzed as part of this review.

Acknowledgements

We gratefully acknowledge the financial support from the National Natural Science Foundation of China (Grant No. U24A2045, 52402009), the Key R&D Plan of Shandong Province (2023CXGC010110, 2025CXGC010103), the Innovation Program for Quantum Science and Technology (2021ZD0300800), the Natural Science Foundation of Shandong Province (ZR2023LLZ001, ZR2024QE455), the Open Topic of State Key Laboratory of Crystal Materials of Shandong University (KF2306).

References

1. H. Liu, Y. Sang, D. Sun, D. Wang and J. Wang, Lithium niobate crystals in the information age: progress and prospects, J. Synth. Cryst., 2021, 50, 708–715.
2. A. Boes, L. Chang, C. Langrock, M. Yu, M. Zhang, Q. Lin, M. Lončar, M. Fejer, J. Bowers and A. Mitchell, Lithium niobate photonics: Unlocking the electromagnetic spectrum, Science, 2023, 379, eabj4396.
3. Y. He, Q.-F. Yang, J. Ling, R. Luo, H. Liang, M. Li, B. Shen, H. Wang, K. Vahala and Q. Lin, Self-starting bi-chromatic LiNbO₃ soliton microcomb, Optica, 2019, 6, 1138–1144.
4. B. Fu, R. Gao, N. Yao, H. Zhang, C. Li, J. Lin, M. Wang, L. Qiao and Y. Cheng, Soliton microcomb generation by cavity polygon modes, Opto-Electron. Adv., 2024, 7, 240061.
5. M. Wang, Z. Fang, J. Lin, R. Wu, J. Chen, Z. Liu, H. Zhang, L. Qiao and Y. Cheng, Integrated active lithium niobate photonic devices, Jpn. J. Appl. Phys., 2023, 62, SC0801.
6. D. Sun, Y. Zhang, D. Wang, W. Song, X. Liu, J. Pang, D. Geng, Y. Sang and H. Liu, Microstructure and domain engineering of lithium niobate crystal films for integrated photonic applications, Light: Sci. Appl., 2020, 9, 197.
7. K. W. Böer and U. W. Pohl, Semiconductor Physics, Springer International Publishing, Cham, 2023, pp. 595–648.
8. A. W. Vere, Mechanical twinning and crack nucleation in lithium niobate, J. Mater. Sci., 1968, 3, 617–621.
9. S. Basu, A. Zhou and M. W. Barsoum, Reversible dislocation motion under contact loading in LiNbO₃ single crystal, J. Mater. Res., 2008, 23, 1334–1338.
10. O. F. Schirmer, O. Thiemann and M. Wöhlecke, Defects in LiNbO₃-I. Experimental aspects, J. Phys. Chem. Solids, 1992, 52, 185–200.
11. I. Stefaniuk, Electron paramagnetic resonance study of impurities and point defects in oxide crystals, Opto-Electron. Rev., 2018, 26, 81–91.
12. A. V. Yatsenko, E. N. Ivanova and N. A. Sergeev, NMR study of intrinsic defects in congruent LiNbO₃. 1. “Unoverlapping” defects, Phys. B, 1997, 240, 254–262.
13. T. Kämpfe, A. Haußmann, L. M. Eng, P. Reichenbach, A. Thiessen, T. Woike and R. Steudtner, Time-resolved photoluminescence spectroscopy of Nb_Nb⁴⁺ and O⁻ polarons in LiNbO₃ single crystals, Phys. Rev. B, 2016, 93, 174116.
14. C. Prieto and C. Zaldo, Evidence of the lattice site change of Hf impurity from Hf-doped to Hf:Mg-codoped LiNbO₃ single crystals by extended X-ray absorption fine-structure spectroscopy, J. Phys.: Condens. Matter, 1994, 6, L677.
15. J. M. Johnson, S. Im, W. Windl and J. Hwang, Three-dimensional imaging of individual point defects using selective detection angles in annular dark field scanning transmission electron microscopy, Ultramicroscopy, 2017, 172, 17–29.
16. C. Sun, E. Müller, M. Meffert and D. Gerthsen, Analysis of crystal defects by scanning transmission electron microscopy (STEM) in a modern scanning electron microscope, Adv. Struct. Chem. Imaging, 2019, 5, 1.
17. F. Schmidt, A. L. Kozub, U. Gerstmann, W. G. Schmidt and A. Schindlmayr, A density-functional theory study of hole and defect-bound exciton polarons in lithium niobate, Crystals, 2022, 12, 1586.
18. J. Su and J. Du, Electron paramagnetic resonance spectroscopy: principles and applications, Science Press, Beijing, 2022.
19. M. A. H. McCausland, Electron paramagnetic resonance: Techniques and applications, Phys. Bull., 1969, 20, 237.
20. V. G. Grachev and G. I. Malovichko, Structures of impurity defects in lithium niobate and tantalate derived from electron paramagnetic and electron nuclear double resonance data, Crystals, 2021, 11, 339.
21. G. Malovichko, V. Bratus, M. Munro, E. Kokanyan, S. Okulov and V. Grachev, Multifrequency spectroscopy of laser active centers Nd³⁺ and Yb³⁺ in nearly stoichiometric LiNbO₃, Phys. Status Solidi C, 2007, 4, 1346–1351.
22. Y. Kong, J. Xu, G. Zhang and S. Liu, Multi-functional optoelectronic material: lithium niobate crystal, Science Press, Beijing, 2005.
23. Madhu, M. Jain and P. P. Dwivedi, in Advances in Materials Processing and Manufacturing Applications, ed. A. Patnaik, E. Kozeschnik and V. Kukshal, Springer Singapore, Singapore, 2021, pp. 345–352.
24. H. Fay, W. J. Alford and H. M. Dess, Dependence of second-harmonic phase-matching temperature in LiNbO₃ crystals on melt composition, Appl. Phys. Lett., 1968, 12, 89–92.
25. S. C. Abrahams and P. Marsh, Defect structure dependence on composition in lithium niobate, Acta Crystallogr., Sect. B: Struct. Sci., 1986, 42, 61–68.
26. G. E. Peterson and A. Carnevale, ⁹³Nb NMR linewidths in nonstoichiometric lithium niobate, J. Chem. Phys., 1972, 56, 4848–4851.
27. N. Iyi, K. Kitamura, F. Izumi, J. K. Yamamoto, T. Hayashi, H. Asano and S. Kimura, Comparative study of defect structures in lithium niobate with different compositions, J. Solid State Chem., 1992, 101, 340–352.
28. A. P. Wilkinson, A. K. Cheetham and R. H. Jarman, The defect structure of congruently melting lithium niobate, J. Appl. Phys., 1993, 74, 3080–3083.
29. S. Kojima, Composition variation of optical phonon damping in lithium niobate crystals, Jpn. J. Appl. Phys., 1993, 32, 4373–4376.
30. J. Blümel, E. Born and T. Metzger, Solid state NMR study supporting the lithium vacancy defect model in congruent lithium niobate, J. Phys. Chem. Solids, 1994, 55, 589–593.
31. H. Xu, D. Lee, J. He, S. B. Sinnott, V. Gopalan, V. Dierolf and S. R. Phillpot, Stability of intrinsic defects and defect clusters in LiNbO₃ from density functional theory calculations, Phys. Rev. B: Condens. Matter Mater. Phys., 2008, 78, 174103.
32. Y. Li, W. G. Schmidt and S. Sanna, Intrinsic LiNbO₃ point defects from hybrid density functional calculations, Phys. Rev. B: Condens. Matter Mater. Phys., 2014, 89, 094111.
33. M. Fontana, K. Chah, M. Aillerie, R. Mouras and P. Bourson, Optical damage resistance in undoped LiNbO₃ crystals, Opt. Mater., 2001, 16, 111–117.
34. F. Abdi, M. Aillerie, P. Bourson, M. D. Fontana and K. Polgar, Electro-optic properties in pure LiNbO₃ crystals from the congruent to the stoichiometric composition, J. Appl. Phys., 1998, 84, 2251–2254.
35. H. Bo, Q. Meng, H. Hu, H. Zhao, Z. Zhang, Q. Zhang and C. Zhang, Temperature-dependent ferroelectric properties of near stoichiometric lithium niobate single crystal, Appl. Phys. A: Mater. Sci. Process., 2018, 124, 691.
36. G. Wang, F. Wang, L. Xie, D. Wang, W. Song, Y. Sang, H. Liu, X. Zhao and F. Yu, Near stochiometric LiNbO₃ crystal: the Piezoelectric features and the shear horizontal guided wave transducer for structural health monitoring up to 650 °C, ACS Appl. Mater. Interfaces, 2024, 16, 47902–47911.
37. F. Wang, D. Sun, Q. Liu, Y. Song, F. Zhang, W. Zhou, Y. Sang, D. Wang and H. Liu, Growth of large size near-stoichiometric lithium niobate single crystals with low coercive field for manufacturing high quality periodically poled lithium niobate, Opt. Mater., 2022, 125, 112058.
38. S. Wang, Y. Shan, D. Zheng, S. Liu, F. Bo, H. Liu, Y. Kong and J. Xu, The real-time dynamic holographic display of LN:Bi,Mg crystals and defect-related electron mobility, Opto-Electron. Adv., 2022, 5, 210135.
39. G. Nava, P. Minzioni, W. Yan, J. Parravicini, D. Grando, E. Musso, I. Cristiani, N. Argiolas, M. Bazzan, M. V. Ciampolillo, A. Zaltron, C. Sada and V. Degiorgio, Zirconium-doped lithium niobate: photorefractive and electro-optical properties as a function of dopant concentration, Opt. Mater. Express, 2011, 1, 270.
40. X. Zhang, G. Liang and Z. Xu, Defect structure and holographic storage properties of LiNbO₃:Zr:Fe:Cu crystals with various Li/Nb ratios, Opt. Mater., 2019, 96, 109318.
41. M. N. Palatnikov, A. V. Kadetova, L. A. Aleshina, O. V. Sidorova, N. V. Sidorov, I. V. Biryukova and O. V. Makarova, Growth, structure, physical and chemical characteristics in a series of LiNbO3:Er crystals of different composition grown in one technological cycle, Opt. Laser Technol., 2022, 147, 107671.
42. K. Kasemir, K. Betzler, B. Matzas, B. Tiegel, T. Wahlbrink, M. Wöhlecke, B. Gather, N. Rubinina and T. Volk, Influence of Zn/In codoping on the optical properties of lithium niobate, J. Appl. Phys., 1998, 84, 5191–5193.
43. J. G. Marques and K. Lorenz, Lattice location of Hf and its interaction with other impurities in LiNbO₃: a review, Opt. Eng., 2014, 53, 060901.
44. K. Lengyel, L. Kovács, Á. Péter, K. Polgár and G. Corradi, The effect of stoichiometry and Mg doping on the Raman spectra of LiNbO₃:Mg crystals, Appl. Phys. B, 2007, 87, 317–322.
45. D. Sun, Y. Leng, Y. Sang, X. Kang, S. Liu, X. Qin, K. Cui, B. K. Wan Hairul Anuar, H. Liu and Y. Bi, Nd:MgO:LiTaO₃ crystal for self-doubling laser applications: growth, structure, thermal and laser properties, CrystEngComm, 2013, 15, 7468.
46. F. Wang, X. Kang, L. Liang, W. Song, D. Sun, J. Wang, H. Liu and Y. Sang, Yb sensitized near-stoichiometric Er:LiNbO₃ single crystal: A Matrix for optical communication and upconversion emission, Cryst. Growth Des., 2018, 18, 1495–1500.
47. J. M. Cabrera, Hydrogen defects in LiNbO₃ and applications, Radiat. Eff. Defects Solids, 1995, 136, 79–83.
48. J. M. Cabrera, J. Olivares, M. Carrascosa, J. Rams, R. Müller and E. Diéguez, Hydrogen in lithium niobate, Adv. Phys., 1996, 45, 349–392.
49. J. Wen, L. Wang, Y. Tang and H. Wang, Enhanced resistance to photorefraction and photovoltaic effect in Li-rich LiNbO₃:Mg crystals, Appl. Phys. Lett., 1988, 53, 260–261.
50. J. E. Midwinter, Lithium niobate: Effects of composition on the refractive indices and optical second-harmonic generation, J. Appl. Phys., 1968, 39, 3033–3038.
51. Y. Kong, B. Li, Y. Chen, Z. Huang, S. Chen, L. Zhang, S. Liu, J. Xu, H. Liu, Y. Wang, W. Yan, X. Xie, X. Li, L. Shi, W. Zhang and G. Zhang, Photorefractive Effects, Materials, and Devices, OSA, La Colle sur Loup, 2003, p. 53.
52. T. R. Volk, V. I. Pryalkin and N. M. Rubinina, Optical-damage-resistant LiNbO₃:Zn crystal, Opt. Lett., 1990, 15, 996.
53. Y. Kong, J. Wen and H. Wang, New doped lithium niobate crystal with high resistance to photorefraction—LiNbO₃:In, Appl. Phys. Lett., 1995, 66, 280–281.
54. S. Sulyanov and T. Volk, Lattice parameters of optical damage resistant In-doped LiNbO₃ crystals, Crystals, 2018, 8, 210.
55. J. K. Yamamoto, K. Kitamura, N. Iyi, S. Kimura, Y. Furukawa and M. Sato, Increased optical damage resistance in Sc₂O₃-doped LiNbO₃, Appl. Phys. Lett., 1992, 61, 2156–2158.
56. L. Wang, S. Liu, Y. Kong, S. Chen, Z. Huang, L. Wu, R. Rupp and J. Xu, Increased optical-damage resistance in tin-doped lithium niobate, Opt. Lett., 2010, 35, 883.
57. P. Minzioni, I. Cristiani, J. Yu, J. Parravicini, E. P. Kokanyan and V. Degiorgio, Linear and nonlinear optical properties of Hafnium-doped lithium-niobate crystals, Opt. Express, 2007, 15, 14171.
58. P. Galinetto, F. Rossella, I. Cristiani, P. Minzioni, V. Degiorgio and E. P. Kokanyan, Structural and optical properties of hafnium-doped lithium-niobate crystals, Phys. Status Solidi C, 2007, 4, 1372–1375.
59. Y. Kong, S. Liu, Y. Zhao, H. Liu, S. Chen and J. Xu, Highly optical damage resistant crystal: zirconium-oxide-doped Lithium Niobate, Appl. Phys. Lett., 2007, 91, 081908.
60. L. Sun, F. Guo, Q. Lv, H. Yu, H. Li, W. Cai, Y. Xu and L. Zhao, Increased optical damage resistance of Zr:LiNbO₃ crystals, Cryst. Res. Technol., 2007, 42, 1117–1122.
61. K. Buse, F. Jermann and E. Krätzig, European Materials Research Society Symposia Proceedings, Elsevier, 1995, vol. 48, pp. 237–240.
62. E. Krätzig and H. Kurz, Photo-induced currents and voltages in LiNbO₃, Ferroelectrics, 1976, 13, 295–296.
63. F. Caccavale, C. Sada, F. Segato, L. D. Bogomolova, N. A. Krasil’nikova, Yu. N. Korkishko, V. A. Fedorov and T. V. Morozova, Copper–lithium ion exchange in LiNbO₃, J. Mater. Res., 2000, 15, 1120–1124.
64. Y. Yang, A. Adibi and D. Berben, The role of Mn in photorefractive LiNbO₃, Photorefractive Effects, Materials, and Devices, 2001, p. 101.
65. E. Krätzig, Photorefractive effects and photoconductivity in LiNbO₃:Fe, Ferroelectrics, 1978, 21, 635–636.
66. C. Prieto and C. Zaldo, Determination of the lattice site of Fe in photorefractive LiNbO₃, Solid State Commun., 1992, 83, 819–821.
67. Y. Fan, H. Li and L. Zhao, Structure and optical properties of near stoichiometric Ce:LiNbO₃ crystals, Cryst. Res. Technol., 2007, 42, 493–497.
68. X. Zhen, M. Li, C. Liu and Y. Xu, in Growth and holographic storage properties of stoichiometric Ce:LiNbO₃ crystals, ed. D. Xu and S. Ogawa,Shanghai, China, 2002, p. 422.
69. E. Lallier, Rare-earth-doped glass and LiNbO₃ waveguide lasers and optical amplifiers, Appl. Opt., 1992, 31, 5276.
70. W. Sohler, Optical Fiber Communications, OFC, 1996, pp. 251–253.
71. Y. Qian, Z. Xie, R. Wang, H. Zhang and Q. Wu, Efficient 1.54μm laser property in near- stoichiometric Er:LiNbO3 crystal, Opt. Laser Technol., 2015, 74, 173–177.
72. Y. Lu, Y. Lu, C. Xue and N. Ming, Growth of Nd³⁺-doped LiNbO₃ optical superlattice crystals and its potential applications in self-frequency doubling, Appl. Phys. Lett., 1996, 68, 1467–1469.
73. D. Z. Wang, D. H. Sun, X. L. Kang, Y. H. Sang, B. X. Yan, H. Liu and Y. Bi, Periodically poled self-frequency-doubling green laser fabricated from Nd:Mg:LiNbO₃ single crystal, Opt. Express, 2015, 23, 17727.
74. J. Capmany, E. Montoya, V. Bermúdez, D. Callejo, E. Diéguez and L. E. Bausá, Self-frequency doubling in Yb³⁺ doped periodically poled LiNbO₃:MgO bulk crystal, Appl. Phys. Lett., 2000, 76, 1374–1376.
75. M. N. Palatnikov, N. V. Sidorov, A. V. Kadetova, N. A. Teplyakova, O. V. Makarova and D. V. Manukovskaya, Concentration threshold in optically nonlinear LiNbO₃:Tb crystals, Opt. Laser Technol., 2021, 137, 106821.
76. G. Dominiak-Dzik, W. Ryba-Romanowski, M. N. Palatnikov, N. V. Sidorov and V. T. Kalinnikov, Dysprosium-doped LiNbO₃ crystal. Optical properties and effect of temperature on fluorescence dynamics, J. Mol. Struct., 2004, 704, 139–144.
77. L. Dai, Z. Yan, S. Jiao, C. Xu and Y. Xu, Effect of [Li]/[Nb] ratios on the absorption and up-conversion emission spectra in In:Yb:Ho:LiNbO₃ crystal, J. Alloys Compd., 2015, 644, 502–505.
78. A. Lorenzo, L. E. Bausa and J. G. Sole, Optical characterization of Ho³⁺ ions in LiNbO₃ and in LiNbO₃:MgO crystals, J. Phys.: Condens. Matter, 1994, 6, 1065–1078.
79. M. Quintanilla, E. Cantelar, J. A. Sanz-García and F. Cussó, Growth and optical characterization of Tm³⁺-doped LiNbO₃, Opt. Mater., 2008, 30, 1098–1102.
80. J. Lin, F. Bo, Y. Cheng and J. Xu, Advances in on-chip photonic devices based on lithium niobate on insulator, Photon. Res., 2020, 8, 1910.
81. S. Saravi, T. Pertsch and F. Setzpfandt, Lithium Niobate on Insulator: An Emerging Platform for Integrated Quantum Photonics, Adv. Opt. Mater., 2021, 9, 2100789.
82. D. Zhu, L. Shao, M. Yu, R. Cheng, B. Desiatov, C. J. Xin, Y. Hu, J. Holzgrafe, S. Ghosh, A. Shams-Ansari, E. Puma, N. Sinclair, C. Reimer, M. Zhang and M. Lončar, Integrated photonics on thin-film lithium niobate, Adv. Opt. Photon., 2021, 13, 242.
83. F. Chen, Photonic guiding structures in lithium niobate crystals produced by energetic ion beams, J. Appl. Phys., 2009, 106, 081101.
84. Q. Li, H. Zhang, H. Zhu and H. Hu, Characterizations of Single-Crystal Lithium Niobate Thin Films, Crystals, 2022, 12, 667.
85. J. You, W. Wu, C. Jin, L. Qu, D. Zhang, J. Qi, W. Cai, M. Ren and J. Xu, Raman characterization of focused ion beam fabricated lithium niobate film, J. Appl. Phys., 2024, 135, 033101.
86. P. R. Ashley, W. S. C. Chang, C. J. Buchal and D. K. Thomas, Guided wave modulators in Ti ion implanted LiNbO₃ waveguides, J. Light Technol., 1989, 7, 855–862.
87. P. Rabiei and P. Gunter, Optical and electro-optical properties of submicrometer lithium niobate slab waveguides prepared by crystal ion slicing and wafer bonding, Appl. Phys. Lett., 2004, 85, 4603–4605.
88. T. A. Ramadan, M. Levy and R. M. Osgood, Electro-optic modulation in crystal-ion-sliced z-cut LiNbO₃ thin films, Appl. Phys. Lett., 2000, 76, 1407–1409.
89. A. M. Radojevic, M. Levy, H. Kwak and R. M. Osgood Jr., Strong nonlinear optical response in epitaxial liftoff single-crystal LiNbO₃ films, Appl. Phys. Lett., 1999, 75, 2888–2890.
90. C. Rudowicz, Concept of spin Hamiltonian, forms of zero field splitting and electronic Zeeman Hamiltonians and relations between parameters used in EPR, Magn. Reson. Rev., 1987, 13, 1–89.
91. O. F. Schirmer and D. V. D. Linde, Two-photon- and x-ray-induced Nb⁴⁺ and O⁻ small polarons in LiNbO₃, Appl. Phys. Lett., 1978, 33, 35–38.
92. H. H. Pieper and K. Schwochau, Hyperfine and superhyperfine EPR spectra of Tc(IV) and Re(IV) in tin dioxide single crystals, J. Chem. Phys., 1975, 63, 4716–4722.
93. B. R. McGarvey, The isotropic hyperfine interaction, J. Phys. Chem., 1967, 71, 51–66.
94. H. Müller and O. F. Schirmer, Microscopic structure of Nb_Li related defects in reduced undoped LiNbO₃, Ferroelectrics, 1992, 125, 319–324.
95. B. Faust, H. Müller and O. F. Schirmer, Free small polarons in LiNbO₃, Ferroelectrics, 1994, 153, 297–302.
96. W. Zheng, W. Fang, L. He and Y. Mei, Spin Hamiltonian parameters and defect structure for the X-ray-induced Nb_Li⁴⁺ center in LiNbO₃ crystal, J. Alloys Compd., 2008, 453, 32–35.
97. J. L. Ketchum, K. L. Sweeney, L. E. Halliburton and A. F. Armington, Vacuum annealing effects in lithium niobate, Phys. Lett. A, 1983, 94, 450–453.
98. K. L. Sweeney and L. E. Halliburton, Oxygen vacancies in lithium niobate, Appl. Phys. Lett., 1983, 43, 336–338.
99. L. E. Halliburton, K. L. Sweeney and C. Y. Chen, Electron spin resonance and optical studies of point defects in lithium niobate, Nucl. Instrum. Methods Phys. Res., Sect. B, 1984, 1, 344–347.
100. G. G. DeLeo, J. L. Dobson, M. F. Masters and L. H. Bonjack, Electronic structure of an oxygen vacancy in lithium niobate, Phys. Rev. B: Condens. Matter Mater. Phys., 1988, 37, 8394–8400.
101. V. Grachev, G. Malovichko and E. Kokanyan, Optimization of lithium niobate for advanced applications by variation of extrinsic and intrinsic defect subsystems, Ferroelectrics, 2001, 258, 131–140.
102. A. Boker, H. Donnerberg, O. F. Schirmer and X. Feng, Two sites of Fe³⁺ in highly Mg-doped LiNbO₃, J. Phys.: Condens. Matter, 1990, 2, 6865–6868.
103. D. J. Keeble, M. Loyo-Menoyo, Y. Furukawa and K. Kitamura, Electron paramagnetic resonance of Fe³⁺ in LiNbO₃, Phys. Rev. B: Condens. Matter Mater. Phys., 2005, 71, 224111.
104. H. H. Towner, Y. M. Kim and H. S. Story, EPR studies of crystal field parameters in Fe³⁺: LiNbO₃, J. Chem. Phys., 1972, 56, 3676–3679.
105. H.-D. Pfannes, A. Putzka and J. F. Sampaio, Electronic structure and spin relaxation of Fe(III) in LiNbO₃, Hyperfine Interact., 1986, 28, 785–788.
106. R. C. Santana, M. C. Terrile, A. C. Hernandes, M. R. B. Andreeta and G. E. Barberis, Electron spin resonance study of Fe³⁺ in LiNbO₃ single crystals: Bulk and fibres, Solid State Commun., 1997, 103, 61–64.
107. M. G. Zhao and M. Chiu, Substitution site of the Fe³⁺ impurity in crystalline LiNbO₃, Phys. Rev. B: Condens. Matter Mater. Phys., 1994, 49, 12556–12558.
108. J. B. Herrington, B. Dischler and J. Schneider, An EPR investigation of Fe³⁺ and Mn²⁺ in LiNbO₃, Solid State Commun., 1972, 10, 509–511.
109. G. I. Malovichko, V. G. Grachov and E. P. Kokanyan, Widths and intensities of ESR lines of iron-group impurities in nonstoichiometric lithium niobate crystals, Phys. Solid State, 1986, 28, 1453–1458.
110. G. I. Malovichko, V. G. Grachev, O. F. Schirmer and B. Faust, New axial Fe³⁺ centres in stoichiometric lithium niobate crystals, J. Phys.: Condens. Matter, 1993, 5, 3971–3976.
111. T. Takeda, A. Watanabe and K. Sugihara, Spacing of the hyperfine sextet in Mn²⁺ ESR in LiNbO₃, Phys. Lett. A, 1968, 27, 114–115.
112. E. V. Charnaya, V. T. Gabrielyan, V. S. Kasperovich and S. Klimko, Li⁷ NMR in LiNbO₃ crystals with different nonstoichiometry, Ferroelectrics, 1997, 202, 115–119.
113. G. Corradi, H. Sothe, J.-M. Spaeth and K. Polgar, Mn²⁺ defects in LiNbO₃: an electron nuclear double resonance (ENDOR) investigation of the Mn²⁺ site and the local disorder, J. Phys.: Condens. Matter, 1990, 2, 6603–6618.
114. T. H. Yeom and S. H. Lee, Temperature dependence of Mn²⁺ paramagnetic Ion in a stoichiometric LiNbO₃ single crystal, J. Magn., 2013, 18, 221–224.
115. V. K. Jain, Superposition model analysis of zero-field splitting of Mn²⁺ in LiNbO₃, Solid State Commun., 1992, 84, 669–672.
116. D. G. Rexford and Y. M. Kim, Electron-spin resonance studies of crystal field parameters in Mn²⁺: LiNbO₃, J. Chem. Phys., 1972, 57, 3094–3098.
117. G. Corradi, H. Sothe, J.-M. Spaeth and K. Polgar, Electron spin resonance and electron-nuclear double-resonance investigation of a new Cr³⁺ defect on an Nb site in LiNbO₃:Mg:Cr, J. Phys.: Condens. Matter, 1991, 3, 1901–1908.
118. G. Corradi, I. M. Zaritskii, A. Hofstaetter, K. Polgár and L. G. Rakitina, Ti³⁺ on Nb site: A paramagnetic Jahn-Teller center in vacuum-reduced LiNbO₃: Mg: Ti single crystals, Phys. Rev. B: Condens. Matter Mater. Phys., 1998, 58, 8329–8337.
119. Z. Y. Yang, C. Rudowicz and Y. Y. Yeung, Microscopic spin-Hamiltonian parameters and crystal field energy levels for the low C₃ symmetry Ni²⁺ centre in LiNbO₃ crystals, Phys. B, 2004, 348, 151–159.
120. V. G. Grachev, K. Hansen, M. Meyer, E. P. Kokanyan and G. I. Malovichko, Substitution mechanisms and location of Co²⁺ ions in congruent and stoichiometric lithium niobate crystals derived from electron paramagnetic resonance data, Mater. Res. Express, 2017, 4, 036204.
121. Q. Luo, F. Bo, Y. Kong, G. Zhang and J. Xu, Advances in lithium niobate thin-film lasers and amplifiers: a review, Adv. Photon., 2023, 5, 034002.
122. R. Jablonski, I. Pracka and M. Swirkowicz, Electron spin resonance spectra of Nd³⁺, Dy³⁺, Er³⁺ and Yb³⁺ in LiNbO₃, Zakopane, Poland, 1997.
123. V. Grachev, M. Munro, E. Kokanyan and G. Malovichko, Determination of g-tensors of low-symmetry Nd³⁺ centers in LiNbO₃ by rectification of angular dependence of electron paramagnetic resonance spectra, J. Appl. Phys., 2015, 118, 044103.
124. G. Malovichko, V. Grachev, S. Okulov, E. Kokanyan, F. Henecker, A. Hofstaetter and O. Schirmer, EPR of Nd³⁺ in congruent and nearly stoichiometric lithium niobate, Phys. Status Solidi B, 2006, 243, 409–415.
125. G. Burns, D. F. O’kane and R. S. Title, Optical and Electron-Spin-Resonance Spectra of Yb³⁺, Nd³⁺, and Cr³⁺ in LiNbO₃ and LiTaO₃, Phys. Rev., 1968, 167, 314–319.
126. N. F. Evlanova, L. S. Kornienko and L. N. Rashkovich, EPR of some rare-earth ions and Cr³⁺ in LiNbO₃, JETP, 1967, 53, 1920–1926.
127. L. Rebouta, M. F. da Silva, J. C. Soares, D. Serrano, E. Diéguez, F. Agulló-López and J. Tornero, Nonaxial sites for Er in LiNbO₃, Appl. Phys. Lett., 1997, 70, 1070–1072.
128. T. Bodziony and S. M. Kaczmarek, EPR study of low symmetry Er centers in congruent lithium niobate, Phys. Status Solidi B, 2008, 245, 998–1002.
129. S. M. Kaczmarek and T. Bodziony, Low symmetry centers in LiNbO₃ doped with Yb and Er, J. Non-Cryst. Solids, 2008, 354, 4202–4210.
130. T. Nolte, T. Pawlik and J.-M. Spaeth, EPR study of Er³⁺ in congruent LiNbO₃, Solid State Commun., 1997, 104, 535–539.
131. G. Malovichko, V. Grachev, J. Jorgensen, M. Meyer, M. Munro, B. Todt, I. Vrable, E. Kokanyan, V. Bratus and S. Okulov, Magnetic Resonance Study of Non-Equivalent Centers Created by 4f-Ions in Congruent and Stoichiometric Lithium Niobate, MRS Proc., 2008, 1111, 1111-D01–03.
132. G. Malovichko, V. Bratus1, V. Grachev and E. Kokanyan, Electron paramagnetic resonance and electron-nuclear double resonance of nonequivalent Yb³⁺ centers in stoichiometric lithium niobate, Phys. Status Solidi B, 2009, 246, 215–225.
133. C. Bonardi, C. J. Magon, E. A. Vidoto, M. C. Terrile, L. E. Bausa, E. Montoya, D. Bravo, A. Martin and F. J. Lopez, EPR spectroscopy of Yb³⁺ in LiNbO₃ and Mg:LiNbO₃, J. Alloys Compd., 2001, 323–324, 340–343.
134. M. Nakamura, S. Higuchi, S. Takekawa, K. Terabe, Y. Furukawa and K. Kitamura, Optical Damage Resistance and Refractive Indices in Near-Stoichiometric MgO-Doped LiNbO3, Jpn. J. Appl. Phys., 2002, 41, L49–L51.

---