Charge trapping by iodine ions in photorefractive Sn₂P₂S₆ crystals

In addition to serving as a model system for complex ferroelectric behavior,^1–3 tin hypothiodiphosphate (Sn₂P₂S₆, or simply SPS) is a photorefractive semiconductor with fast response times and high gain factors in the visible and near-infrared.^4–17 A transient peak in the temporal dynamics of the two-beam coupling in this material has been attributed to contributions from two types of movable charges.^6,12,13 A fast grating is formed by optically excited charge carriers, while a slower grating appears because of a redistribution of thermally excited (optically inactive) carriers of opposite sign. These space-charge gratings are out-of-phase and thus compensate each other. The different characteristic build-up times for the two gratings lead to an initial peak in the two-beam coupling and then a decrease within tens of seconds to a lower steady-state value. Another important feature of the photorefractive effect in some SPS crystals is the enhancement caused by optical sensitizing (i.e., exposing a crystal to light in the 530–675 nm range before writing a grating).^4,13,14

To increase the two-beam coupling and also to explain variations in the photorefractive response observed among SPS crystals grown at different times and by different methods, all the point defects that may serve as traps for photoexcited electrons and holes in this highly compensated semiconductor need to be identified. Electron paramagnetic resonance (EPR), with its narrow linewidths and high sensitivity, is a suitable experimental technique to explore the wide range of intrinsic and extrinsic point defects that can be present in SPS crystals.^18–20 Exposure to appropriate wavelengths of light allows electrons and holes to be redistributed among the donors and acceptors that are introduced during growth. Self-trapping of charge may also occur. At all times, the crystal will remain electrically neutral. This redistribution of charge as a result of illumination, although stable at low temperatures, will be transient at room temperature and forms the basis of the photorefractive effect. Thus far, photoinduced EPR has been used to identify hole-like small polarons (Sn³⁺),²¹ electron-like small polarons (Sn⁺),¹⁷ singly ionized sulfur vacancies,²² singly ionized tin vacancies,²³ and two Sb-related defects.^24–26 In each case, the resolved hyperfine structure in the EPR spectrum provides the critical information that allows a specific defect model to be assigned.²⁷ 

In the present paper, we investigate the charge-trapping role of iodine ions in an SPS crystal. This crystal was unintentionally doped with iodine (as a result of the growth method) and, at the same time, was deliberately doped with tellurium. Recent work shows that the Te ions replace Sn and S ions and thus provide both electron and hole trapping sites that are active during an illumination.²⁸ This leaves the important question: What site (Sn, P, or S) does an iodine ion occupy in an SPS crystal? Iodine is often found in crystals as a negative ion (I⁻) with the [Kr]4d¹⁰5s²5p⁶ closed-shell configuration. An example from the alkali halide family is sodium iodide (NaI), a widely used scintillator material. There are other examples, such as the well-known nonlinear optical crystal LiIO₃, where iodine is a positive ion (I⁵⁺) with the [Kr]4d¹⁰5s² closed-shell configuration. Our initial expectation was that an iodine ion in SPS would act the same as Te ions and occupy a S or Sn site. However, neither of these sites (S or Sn) for the iodine ions is supported by our present EPR data. Instead, our observation of a very large hyperfine interaction with only one ³¹P nucleus indicates that iodine ions in SPS crystals occupy a phosphorous site and can trap an electron following an illumination at low temperature with sub-bandgap laser light. Before light, the iodine is part of a nonparamagnetic (IPS₆)⁴⁻ molecular ion (i.e., no unpaired spins). After light, the extra electron converts this molecular ion to a paramagnetic (IPS₆)⁵⁻ unit. A complete set of EPR angular dependence data for the ¹²⁷I and ³¹P hyperfine interactions, coupled with predictions of Fermi contact parameters and spin density distribution from quantum chemistry calculations, support this (IPS₆)⁵⁻ model for an electron trapped by an iodine ion in SPS crystals.

A ferroelectric–paraelectric phase change occurs at 64 °C in Sn₂P₂S₆ crystals. Below this temperature, the crystals are monoclinic with space group Pc (No. 7) and point group m. Lattice constants at room temperature^29,30 are a = 9.378 Å, b = 7.488 Å, c = 6.513 Å, and β = 91.15°. The b axis is perpendicular to the mirror plane of the crystal, and β is the angle between the a and c directions. When analyzing the angular dependence of the EPR spectrum, the crystal is treated as orthorhombic and the slight deviation from 90° between the a and c axes is ignored. Both covalent and ionic behaviors occur in the Sn₂P₂S₆ crystals. As shown in Fig. 1, the building blocks for constructing an SPS crystal are Sn²⁺ ions and (P₂S₆)⁴⁻ molecular ions. The Sn²⁺ ions have a significant ionic nature, whereas the (P₂S₆)⁴⁻ anionic groups have strong covalent P–P and P–S bonds.^31–33 There are no unpaired spins in these Sn²⁺ ions and (P₂S₆)⁴⁻ groups. In the low-temperature ferroelectric phase of this material, there are two slightly inequivalent tin sites, two slightly inequivalent phosphorous sites, and six inequivalent sulfur sites. Above 64 °C, in the paraelectric phase, the two tin sites are equivalent and the two phosphorous sites are equivalent, but the sulfur sites remain inequivalent.³⁰ 

The Sn₂P₂S₆ crystal used in the present investigation was grown at Uzhhorod University by the chemical vapor transport method using SnI₄ as the transport agent.^34,35 A small portion of the iodine from the carrier gas entered the growing crystal. This is an expected effect, with ZnSe providing an early example of unintentional doping by the iodine transport agent during chemical vapor transport growth.^36,37 In addition to the inadvertent incorporation of iodine, our SPS crystal was deliberately doped during growth by adding 1% (by weight) of tellurium to the starting materials. These tellurium ions play a direct role, at low temperatures, in allowing electrons to be trapped at iodine ions. The sample for the EPR experiments, cut from the larger as-grown boule, was rectangular in shape with the a, b, and c axes normal to the faces. Dimensions were ∼2 mm on a side.

A Bruker EMX spectrometer, operating near 9.39 GHz, was used to take the EPR spectra. The sample temperature was controlled by adjusting the flow of cold helium gas through an Oxford Instruments ESR-900 cryostat attached to a Bruker ER4103TM cylindrical microwave cavity. A helium–neon laser (producing 12 mW at 633 nm) was used to convert defects within the crystal to their paramagnetic charge states. The optical absorption edge of SPS crystals is near 530 nm at room temperature³⁸ and shifts to 500 nm for temperatures below 100 K.³⁹ 

Figure 2 shows two EPR spectra from the iodine-related trapped electron defect in our Sn₂P₂S₆ crystal. They were both taken at 20 K, with the magnetic field along the b direction in the upper spectrum and along the c direction in the lower spectrum. The multi-step process used to produce this new defect in the Te-doped sample is described in Sec. IV D. Each spectrum in Fig. 2 consists of two sets of six lines, with stick diagrams above the spectra identifying individual lines within each set. Based on a comparison to an EPR pitch sample provided by Bruker, our estimate of the concentration of defects responsible for the spectra in Fig. 2 is 1.1 × 10¹⁷ cm⁻³.

The hyperfine patterns observed in Fig. 2, i.e., two sets of six lines, suggest that the responsible defect has one unpaired electron spin (S = 1/2) interacting with two nuclear spins (I = 1/2 and I = 5/2). Both the I = 1/2 nucleus and the I = 5/2 nucleus must be very near 100% abundant because there are no observable I = 0 lines in the spectra in Fig. 2. Obvious choices for these nuclei are ³¹P and ¹²⁷I. Phosphorus is a constituent of Sn₂P₂S₆ crystals; thus, it is reasonable to assign the I = 1/2 interaction to the 100% abundant ³¹P nuclei. Other possible 100% abundant I = 1/2 nuclei are ¹H, ¹⁹F, ⁸⁹Y, ¹⁰³Rh, ¹⁶⁹Tm, and combined ²⁰³Tl and ²⁰⁵Tl. These latter two isotopes have I = 1/2, with similar magnetic moments, and together appear as 100% abundant. The hyperfine parameters (isotropic Fermi contact and anisotropic dipole–dipole) determined in Sec. IV B for the I = 1/2 interaction are larger than the predicted maximum values^40,41 for ¹H, ⁸⁹Y, and ¹⁰³Rh, thus removing these nuclei from consideration. Fluorine, thulium, and thallium, as well as yttrium and rhodium, are not expected to be unintentionally present in our SPS crystal at the ∼1 × 10¹⁷ cm⁻³ concentration level measured for our EPR spectrum.

The I = 5/2 nucleus contributing to the spectra in Fig. 2 must be extrinsic in origin since there are no isotopes of Sn and S that have I = 5/2. Possible assignments for this nucleus include ²⁷Al, ⁵⁵Mn, ¹²⁷I, ¹⁴¹Pr, and combined ¹⁸⁵Re and ¹⁸⁷Re, as they are the only isotopes with I = 5/2 and 100% abundance. Of these, ¹²⁷I is the only realistic candidate since aluminum, praseodymium, and rhenium are not expected to be significant residual impurities in SPS crystals. A quite different EPR spectrum with S = 5/2 has already been assigned to Mn²⁺ ions occupying Sn²⁺ sites in Mn-doped Sn₂P₂S₆ crystals,⁴² thus eliminating manganese from consideration. The use of the iodine-containing carrier gas during the chemical-vapor-transport growth of our crystal greatly strengthens the assignment of the I = 5/2 hyperfine lines in Fig. 2 to ¹²⁷I nuclei. Furthermore, a search of the literature reveals a series of previously reported EPR spectra that show similar resolved hyperfine patterns from ¹²⁷I nuclei.^43–48 

Numerous less intense EPR lines are present in the spectra in Fig. 2, in addition to the two intense sets of six lines identified by the stick diagrams. The majority of these smaller lines, located between the larger lines, are attributed to partially allowed transitions (Δm_I = ±1 and Δm_I = ±2) arising from a nuclear electric quadrupole interaction for the ¹²⁷I nuclei.^46,48,49 In general, the strength of a quadrupole interaction depends on the product of the electric quadrupole moment of the nucleus and the electric field gradient at the nucleus. The ¹²⁷I nucleus has a large quadrupole moment,⁵⁰ and the electric field gradients at nuclei in the low-symmetry monoclinic SPS crystals are also large; thus, significant nuclear electric quadrupole effects are expected in the iodine EPR spectra. A few lines in the 330–350 mT region of the spectra are assigned to holes trapped at Te ions on S sites,²⁸ electrons trapped at S vacancies,²² and holes trapped at Sn vacancies.²³ 

Complete sets of angular dependence data were taken for the iodine-related defect. These results, shown in Fig. 3, provide information about the g matrix and the ¹²⁷I and ³¹P hyperfine matrices. The positions of the EPR lines, plotted as discrete points in Fig. 3, were acquired in three planes (a–b, b–c, and c–a), as the crystal was rotated relative to a fixed direction of the magnetic field. Overlapping of lines made it difficult to precisely locate the positions of lines near the centers of the spectra. In addition, in the c–a plane, locating the positions of the allowed lines was more challenging because of the increased intensities of nuclear-quadrupole-related partially allowed lines. When the ¹²⁷I hyperfine interaction becomes smaller relative to the nuclear quadrupole interaction (as it does in the c–a plane), the “forbidden” lines become more intense.

In the monoclinic structure of the SPS crystal, with the b axis normal to the mirror plane, a paramagnetic point defect can have two crystallographically equivalent orientations, i.e., sites. These two physically different orientations of the same defect, at different locations within the crystal, are related to each other by the symmetry elements of the crystal (in the present case, the mirror plane) and thus are crystallographically equivalent. The two defect orientations will have the same set of principal values, but a different set of principal-axis directions for each matrix in the spin Hamiltonian (see the next paragraph). The direction of the external applied magnetic field relative to the principal-axis directions of these matrices determines the positions (and spacings) of lines in the EPR spectrum for each orientation. When the two orientations are said to be magnetically equivalent, their EPR spectra are identical (i.e., they overlap). They separate into two similar, but easily distinguished, spectra when the two orientations are magnetically inequivalent. In our SPS crystal, the two crystallographically equivalent orientations of the iodine-related defect are magnetically equivalent when the magnetic field is along the a, b, or c directions, and they are also magnetically equivalent for all angles when the magnetic field is rotated in the a–c plane. In Fig. 3, as expected, there is a splitting into two branches in the a–b and b–c planes, but no splitting in the a–c plane.

The following spin Hamiltonian describes the EPR angular dependence shown in Fig. 3,

An electron Zeeman term is included, along with hyperfine and nuclear Zeeman terms for the two nuclei (subscript 1 refers to the ¹²⁷I nucleus and subscript 2 refers to the ³¹P nucleus). Here, S, I₁, and I₂ are the spin operators and B is the external magnetic field. The electron and nuclear Bohr magnetons are β and β_n, respectively. Each matrix (g, A₁, and A₂) in Eq. (1) has six independent parameters: three principal values and three Euler angles that describe the principal-axis directions. The values for these parameters were determined by fitting the experimental results in Fig. 3.

The spin Hamiltonian in Eq. (1), after being rewritten as a 24 × 24 matrix (S = 1/2, I₁ = 5/2, and I₂ = 1/2), was repeatedly diagonalized as the 18 parameters were systematically varied during a least-squares fitting process. Input data for the fitting were the 290 magnetic field values corresponding to the discrete points in Fig. 3. There are two sets of parameters that give equally good fits if only data from the a–b, b–c, and c–a planes are used. We determined the correct set by collecting additional data from b to the midpoint between a and c. The final best-fit values for the spin-Hamiltonian parameters are listed in Table I. Positive signs are assigned to the principal values of the hyperfine matrices, as the magnetic moments of the ³¹P and ¹²⁷I nuclei are positive. For each matrix, the set of three Euler angles describing the principal-axis directions has been converted to three (θ, ϕ) pairs. The polar angle θ is defined relative to the c axis of the crystal, and the azimuthal angle ϕ is defined relative to the a axis with positive rotation being from a toward b in the plane perpendicular to c. In Table I, the principal-axis directions are for one of the two crystallographically equivalent orientations of the defect. Directions for the other orientation are obtained by applying a reflection through the mirror plane of the crystal. In Fig. 3, the solid lines were generated using the final best-fit values for the spin Hamiltonian parameters from Table I. The good agreement between the calculated curves and the discrete experimental points in Fig. 3 verifies that the correct set of spin-Hamiltonian parameters has been determined.

The principal-axis directions for the g matrix and the ³¹P hyperfine matrix in Table I are not near the P–P or P–S bond directions in the crystal. The direction of the unique principal axis (A₃) of the ¹²⁷I hyperfine matrix, however, is reasonably close to the P–P bond direction. The θ and ϕ values in Table I for A₃ are 92.6° and 291.1°, and the corresponding θ and ϕ values for the P–P interatomic axis obtained from Ref. 29 are 110.9° and 307.8°. The Δθ and Δϕ differences are 18.3° and 16.7°, respectively.

A large hyperfine interaction with only one phosphorous nucleus is the critical feature in the EPR spectrum that allows a model to be proposed for the iodine-related defect. In the regular SPS lattice, phosphorous ions are always present as pairs, adjacent to each other in the (P₂S₆)⁴⁻ anionic groups (see Fig. 1). Earlier EPR studies of defects in SPS crystals have verified this pairing by showing equal, or nearly equal, hyperfine interactions with two phosphorous nuclei.^22,23,25 The large phosphorous interaction in our present spectra indicates that a P₂S₆ unit must be involved, but the lack of a resolved interaction with a second phosphorous nucleus strongly suggests that one of the two phosphorous ions has been replaced by another ion. Iodine, with its I = 5/2 nuclear spin, is the obvious choice for the ion that replaces a phosphorus. A small fraction of the regular (P₂S₆)⁴⁻ molecular ions are replaced by (IPS₆)⁴⁻ units in the as-grown crystal (see Fig. 4). The original (P₂S₆)⁴⁻ groups are not paramagnetic (i.e., have no unpaired spins), and the (IPS₆)⁴⁻ units also are not paramagnetic. When an electron is trapped at low temperatures as a result of illumination, these latter units convert to paramagnetic (IPS₆)⁵⁻ units with S = 1/2. The large phosphorous hyperfine interaction strongly supports that an electron, instead of a hole, is trapped at the (IPS₆)⁴⁻ unit. A hole would be more localized on the sulfur ions and thus give a smaller ³¹P interaction.

The experimental spin Hamiltonian parameters in Table I provide information about the distribution of the unpaired spin within the (IPS₆)⁵⁻ molecular ion. Each hyperfine matrix can be separated into an isotropic part a and an anisotropic part B, with U being the identity matrix,

The Fermi contact interaction, proportional to the unpaired spin density ρ_s at the nucleus, is represented by the scalar a, while the angular-dependent magnetic dipole–dipole coupling between the unpaired electron and the nucleus is represented by the traceless matrix B,^18–20 

The hyperfine matrices A, from Eq. (2), are rewritten in the following form:

Here, b is the axial part of the dipole–dipole interaction and b′ describes the deviation from axial symmetry. Table II gives the values for a, b, and b′ obtained from the ¹²⁷I and ³¹P hyperfine matrices in Table I.

The results for b and b′ in Table II show that the anisotropic ¹²⁷I hyperfine interaction is axial (b′ is much less than b). This is consistent with the unique (A₃) principal-axis direction for ¹²⁷I in Table I being close to the P–P direction (or for our model, the I–P direction). In other words, a major portion of the unpaired spin density contributing to the dipole–dipole interaction for the ¹²⁷I nucleus is distributed symmetrically about the I–P direction. In contrast, Table II shows that the anisotropic ³¹P interaction is strongly nonaxial (b′ is greater than b). This suggests that a significant portion of the unpaired spin density on the phosphorus may be in a p-type orbital oriented perpendicular to the I–P axis. There will also be spin density located along the I–P direction between the iodine and phosphorus and around the iodine. Having the spin density distributed in two orthogonal directions about the ³¹P nucleus will result in a dipole–dipole interaction that is strongly nonaxial, in agreement with the b and b′ values reported for this nucleus in Table II.

Reference atomic values, obtained from ab initio calculations, are available to help interpret hyperfine parameters.^40,41 They are often used to analyze the unpaired spin composition of a defect in terms of s and p orbitals. This approach provides a rudimentary, but useful, picture of the ground state of a defect. For the ³¹P nucleus, Fitzpatrick et al.⁴¹ predicted that a 100% occupied phosphorous 3s orbital has a Fermi contact value of 10 201 MHz. Our experimental value of 1769 MHz for a from Table II, when compared with this prediction, suggests that 17.3% of the unpaired spin in the (IPS₆)⁵⁻ defect is in a phosphorous 3s orbital. Similarly, a comparison of our experimental value of 114 MHz to the value of 316.7 MHz (2/5 of 791.7 MHz) predicted by Fitzpatrick et al.⁴¹ for the phosphorous anisotropic (dipolar) parameter b suggests that 36.0% of the unpaired spin in the defect is in a phosphorous 3p orbital. The angular factor of 2/5 is used in this determination of the 3p contribution.⁴⁰ 

Morton and Preston⁴⁰ provided the only reference atomic values in the literature for the ¹²⁷I nucleus. They predicted that a 100% occupied iodine 5s orbital has a Fermi contact value of 41 600 MHz and a 100% occupied iodine 5p orbital has a value of 812 MHz (2/5 of 2031 MHz). Our experimental value of 386 MHz for a suggests that 0.9% of the unpaired spin is in an iodine 5s orbital, and our value of 139 MHz for b suggests that 17.1% is in an iodine 5p orbital. Fitzpatrick et al.⁴¹ suggested that the early predictions of Morton and Preston⁴⁰ should be lowered by 20% because of approximations made when implementing the Hartree–Fock method. This may especially be the case for the “heavier” atoms in the Periodic Table such as iodine. Thus, we expect that our percentages of 5s and 5p contributions to the (IPS₆)⁵⁻ group should be increased by at least 20%.

The general conclusions from this cursory analysis of the experimental hyperfine parameters are that ∼50% of the unpaired spin is centered on the participating phosphorous ion, about 20% is associated with the iodine ion, and the remainder is distributed over the six neighboring sulfur ions. The only isotope of sulfur that has a nonzero nuclear spin (³³S with I = 3/2) is just 0.75% abundant, and thus, its hyperfine lines are too weak to detect in the EPR spectra.

Several steps were involved in producing the specific charge state of the defect responsible for the EPR spectra in Fig. 2. There were no EPR signals detected after the crystal was initially cooled to 20 K while being kept in the dark. The crystal was then exposed at 20 K to sub-bandgap 633 nm laser light for 5 min. This exposure did not, by itself, form the iodine-related defects seen in Fig. 2, and another step was needed for their production. After removing the light, the crystal was warmed to near 100 K and held there for 2 min. Then, the crystal was immediately returned to 20 K where the spectra shown in Fig. 2 were recorded.

A large number of Te ions deliberately added to the crystal during growth play an important role in the production of the iodine-related EPR spectrum. During the initial illumination at 20 K, holes are trapped at Te ions substituting for S ions and electrons are trapped at Te ions substituting for Sn ions. Detailed descriptions of the EPR spectra from these Te-related defects have been reported.²⁸ Nonparamagnetic Te⁴⁺ (5s²) ions that replace Sn²⁺ (5s²) ions during growth trap two electrons and form Te²⁺ (5s²5p²) ions during the exposure to laser light at 20 K. Then, when the crystal is warmed in the dark to near 100 K, the two trapped electrons are thermally released from the Te²⁺ ions. This restores the Te⁴⁺ ions. Many of the released electrons annihilate holes trapped by Te ions at S sites, but a significant portion moves to iodine ions occupying phosphorous sites and forms the S = 1/2 iodine-related defect responsible for the EPR spectra in Fig. 2. Although the EPR signal for the iodine defect is easily produced at 100 K in Te-doped SPS, it slowly decays over several minutes when the crystal is subsequently held constant near 50 K. To prevent thermal decay of the signal, the crystal was always quickly cooled back to 20 K after the 100 K production step.

Trapping of electrons by iodine has also been observed in an SPS crystal that did not contain tellurium ions,²¹ thus demonstrating the broader significance of our present study. The three highest field lines in our iodine related EPR spectrum when the magnetic field is along the b direction (see the upper spectrum in Fig. 2) correspond directly to the very weak lines near 375 mT, 397 mT, and 419 mT in Fig. 2 in Ref. 21. The defect responsible for these lines was not identified in that early work. However, as a result of the current investigation, they can now be assigned to electrons trapped by iodine ions. The iodine spectrum in Ref. 21 was produced at 25 K with 442 nm light in an SPS crystal doped with Ag, with hole-like small polarons and possibly Ag ions on Sn sites serving as the defects that trap the compensating holes. This Ag-doped crystal was grown at Uzhhorod University by the chemical vapor transport method using SnI₄ as the transport agent.

A relatively simple quantum chemistry calculation supports our model of an (IPS₆)⁵⁻ molecular ion for the EPR-active iodine-related defect in SPS. The eight-ion cluster in Fig. 4 is used, where the relative positions of the ions are the same as in the P₂S₆ groups in the regular crystal. One of the phosphorous ions is replaced by an iodine ion. The coordinates of the eight ions are given in Table III (the iodine is at the origin and the z direction is along the I–P bond). Unrestricted Hartree–Fock (UHF) and second-order Møller–Plesset perturbation theory (UMP2), as implemented in Gaussian 16,⁵¹ is used to determine the ground state of the unpaired spin (i.e., the trapped electron) in this cluster. With this electron included, the net charge of the cluster is −5 and the spin multiplicity is 2. Geometry optimization is not done. The dgdzvp basis set (double zeta valence plus polarization) is used.⁵² Yurieva et al.⁵³ and Siiskonen and Priimagi⁵⁴ showed that this basis set performs well for iodine. Table IV includes the calculated Fermi contact parameters, the Mulliken charges, and the spin densities for the eight ions in the (IPS₆)⁵⁻ cluster, and Fig. 5 shows the results from Gaussian 16 for the distribution of spin density.

The Fermi contact parameters for the ¹²⁷I and ³¹P nuclei in Table IV provide the most direct evidence that the (IPS₆)⁵⁻ unit is the correct model for our iodine-related EPR spectrum. For the ³¹P nucleus, the calculated value of 1815 MHz is very close to the experimental value of 1769 MHz, with the difference being only 2.6%. For the ¹²⁷I nucleus, the calculated value of 760 MHz is approximately a factor of 2 greater than the experimental value of 386 MHz. This latter result is encouraging, especially when considering the challenge of calculating the Fermi contact values for heavy ions such as iodine where relativistic effects are important.⁵⁵ Although the predicted Fermi contact parameters for the six sulfur nuclei are all small in Table IV, the values for S2 and S5 are larger than the other four values. These are the two sulfur ions (S2 and S5) that are farthest apart and are seen in the upper right and lower left portions of Fig. 5.

The predicted spin densities in Table IV are also informative. They agree, in large part, with the earlier results in Sec. IV C, where the distribution of the spin in s and p orbitals was estimated using the experimental spin-Hamiltonian parameters. The predicted value of 0.1847 in Table IV for the spin density at the iodine ion is close to the estimate of 20%. The predicted values of 0.3342 for the phosphorous ion and 0.4811 for the sum of the sulfur ions in Table IV are not significantly different from the estimates of 50% and 30%, respectively.

Future computational efforts using advanced quantum chemistry modeling methods and a more versatile basis set are expected to provide a complete set of precise spin-Hamiltonian parameters for an (IPS₆)⁵⁻ molecular ion embedded in an SPS crystal. These results, when compared to the present experimental spin-Hamiltonian parameters, will allow the model for our EPR-active iodine defect to be further refined by including spin-density sharing with Sn ions as well as relaxation effects (i.e., small shifts in the relative positions of ions within the molecular unit).

An electron-trapping defect responsible for an iodine-related EPR spectrum in ferroelectric and photorefractive Sn₂P₂S₆ crystals has been identified. Iodine enters the photorefractive crystal as an unintentional impurity during growth by the chemical vapor transport method (when SnI₄ is used as the carrier gas). It substitutes for a phosphorous ion in a constituent (P₂S₆)⁴⁻ anion and produces (IPS₆)⁴⁻ units. Paramagnetic (IPS₆)⁵⁻ units are then formed in the crystal when electrons are trapped at the (IPS₆)⁴⁻ units after an exposure at 20 K to 633 nm laser light and the subsequent release of electrons from Te-associated defects upon warming to 100 K. The angular dependence of the EPR spectrum provides a complete set of spin-Hamiltonian parameters describing the g matrix and the ¹²⁷I and ³¹P hyperfine matrices. The experimental values for the isotropic Fermi contact and the anisotropic dipole–dipole interactions, extracted from these matrices, allow estimates to be made for the distribution of the unpaired spin on the phosphorous and iodine ions. Quantum chemistry modeling (UHF/UMP2), using a small cluster approach and a dgdzvp basis set, supports the (IPS₆)⁵⁻ description of the trapped electron.

A primary focus of the present study has been to investigate charge trapping by defects in SPS crystals, with the goal of improving the photorefractive response of the material. Although many of the SPS crystals used in photorefractive studies have been grown by the chemical vapor transport method, there has been no mention thus far in the literature that iodine may have entered the crystals. This incorporation of iodine in significant concentrations is now shown to occur, and moreover, the isolated iodine ions are shown to serve as traps for electrons. Future studies are needed that explore the influence (positive or negative) of the iodine impurities on the photorefractive response of the SPS crystals. These studies should address the competing (or complementing) roles of intentional impurities, such as Sb and Te, unintentional native defects, such as sulfur and tin vacancies, and the iodine ions. If warranted, future growth procedures may need to be modified to minimize or maximize the amount of iodine taken up by an SPS crystal.

Work at the Air Force Research Laboratory was supported under Contract No. FA8650-16-D-5404 from the Air Force Office of Scientific Research. Work performed at Uzhhorod National University was supported by the Science and Technology Center of Ukraine and the European Office of Aerospace Research and Development (STCU/EOARD; Project No. P438b). The views expressed in this paper are those of the authors and do not necessarily reflect the official policy or position of the United States Air Force or the Department of Defense.

The data that support the findings of this study are available within the article.