Photoinduced trapping of charge at sulfur vacancies and copper ions in photorefractive Sn₂P₂S₆ crystals

Tin hypothiodiphosphate crystals (Sn₂P₂S₆, or simply SPS) are a photorefractive material with fast response times and high gain factors in the visible and near-infrared spectral regions.^1–3 Thus far, the photorefractive effect has been investigated in undoped, Sb-doped, and Te-doped SPS crystals.^4–14 Studies show that the temporal dynamics of the two-beam coupling in this material has contributions from two types of movable charge.^9,10,13 Optically excited charge carriers form “fast” gratings, while a redistribution of thermally excited carriers of opposite sign forms “slower” compensating gratings. There remain opportunities, beyond the improvements achieved thus far with Sb and Te doping, to enhance the photorefractive response of SPS by identifying additional optically active defects with favorable properties. Increasing the number of desirable defects and decreasing the number of undesirable defects is a major goal for most optical and electronic materials. In SPS crystals, specific defects are needed that increase the photorefractive gain, provide faster response, and extend the sensitivity to longer wavelengths in the infrared. Unwanted defects in this material may provide compensating gratings that limit the gain and slow the response. An experimental technique that has proven useful to identify and characterize intrinsic and extrinsic point defects in SPS crystals is electron paramagnetic resonance (EPR).^15,16 The relatively sharp lines in the EPR spectra allow g matrices and hyperfine matrices to be fully determined and defect models to be established.^14,17–24 A recent example of the successful use of EPR is the identification of iodine as a major electron trap unintentionally introduced into SPS during growth.²⁴ 

In the present paper, we use EPR to investigate the charge-trapping roles of sulfur vacancies and copper impurities in an SPS crystal. The three electronic states of a group VIA anion vacancy (V²⁺, V⁺, and V⁰) are a major focus of our experiments. Other than oxygen, group VIA vacancies, and especially sulfur vacancies, have not been widely studied, despite their often critical roles in controlling the electrical and optical properties of many chalcogenides and related materials. All three charge states of the sulfur vacancy are active in our SPS crystal, thus giving us a unique experimental opportunity to more fully characterize a group VIA anion vacancy. Computational studies of nonstoichiometric effects in SPS crystals have explored the role of sulfur vacancies.^25,26

Our SPS crystal was doped during growth with Cu⁺ (3d¹⁰) ions. These transition-metal ions occupy Sn²⁺ sites.²⁷ Doubly ionized sulfur vacancies (⁠$VS2+$⁠) were also formed during growth, as these vacancies are needed to provide charge compensation for the closed-shell Cu⁺ ions (one $VS2+$ vacancy compensates two Cu⁺ ions). Illuminating the crystal with 532 or 633 nm laser light, while at temperatures near and below 70 K, converts the Cu⁺ ions to Cu²⁺ (3d⁹) ions and converts the sulfur vacancies to singly ionized vacancies (⁠$VS+$⁠) and neutral vacancies (⁠$VS0$⁠), with one and two trapped electrons, respectively. During an illumination, the copper ions serve as a source of electrons and the sulfur vacancies serve as traps for electrons. In conventional semiconductor notation, the Cu⁺ ions are A⁻ acceptors and the Cu²⁺ ions are A⁰ acceptors. For the missing sulfur ions, the $VS2+$ vacancies are D⁺⁺ donors, the $VS+$ vacancies are D⁺ donors, and the $VS0$ vacancies are D⁰ donors.

The $VS+$ vacancies and the Cu²⁺ ions, each having one unpaired electron spin, are directly observed with EPR, whereas the presence of nonparamagnetic neutral $VS0$ vacancies is determined by monitoring changes in the intensity of the $VS+$ EPR spectrum. Golden et al.¹⁸ have previously fully characterized the EPR spectrum from the $VS+$ vacancies. The same approach is followed in the present study for the Cu²⁺ ions, with the angular dependence of the EPR spectrum used to determine a complete set of spin-Hamiltonian parameters. In addition to establishing the presence of Cu²⁺ ions and $VS+$ and $VS0$ vacancies, EPR provides information about the thermal stabilities of these defects. An activation energy of 194 meV is obtained from the analysis of five Cu²⁺ isothermal decay curves taken at temperatures in the 74–82 K range. This activation energy describes the release of electrons from $VS0$ vacancies to the conduction band. In addition to the Cu²⁺ and $VS+$ spectra, a third photoinduced EPR signal in our Cu-doped crystal, observed below 40 K, is assigned to Ni⁺ (3d⁹) ions at Sn²⁺ sites. An angular study provides the g matrix for these Ni⁺ ions. Since they are present as Ni²⁺ ions in the as-grown crystal, these acceptors are deeper (i.e., farther from the valence band) than the Cu acceptor ions in SPS crystals and possibly have a level in the upper half of the gap.

The present work demonstrates that neutral sulfur vacancies (⁠$VS0$⁠) can be produced in a Sn₂P₂S₆ crystal during exposure to laser light. It is known from past experimental studies that doubly ionized sulfur vacancies (⁠$VS2+$⁠) are easily formed when compensating acceptors are present, and thus are a common defect, in nearly all SPS crystals.^14,18,19,23 Until now, however, they were thought to only convert to the singly ionized charge state (⁠$VS+$⁠) during illumination. Future efforts that model the room-temperature photorefractive response of the SPS crystals will need to include the photoinduced formation of short-lived neutral sulfur vacancies (⁠$VS0$⁠).

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. This crystal was doped during growth by adding 1.0% (by weight) of copper metal to the starting materials, with Cu being transported to the growing crystal in the same manner as Sn. In addition to the copper ions, a small concentration of nickel ions was also present in the as-grown crystal. The source of these unintentional nickel ions is believed to be the copper. Small samples, suitable for the EPR experiments, were cut from the as-grown boule. These samples were cubes, approximately 2 mm on a side, with the a, b, and c axes along the edges.

Below 64°C, Sn₂P₂S₆ crystals are monoclinic with space group Pc (No. 7) and point group m. The lattice constants at room temperature^28,29 are a = 9.378 Å, b = 7.488 Å, c = 6.513 Å, and β = 91.15°, with β being the angle between the a and c directions. Following the usual convention, the b axis is perpendicular to the mirror plane of the crystal. A ball-and-stick representation of the SPS crystal is shown in Fig. 1. Covalent and ionic behavior occurs in Sn₂P₂S₆ crystals, as both Sn²⁺ ions and (P₂S₆)⁴⁻ anionic groups are present.^30–32 In its low temperature ferroelectric phase, the SPS crystal has two inequivalent tin sites, two inequivalent phosphorous sites, and six inequivalent sulfur sites.²⁹ 

The EPR spectra were taken near 9.39 GHz with a Bruker EMX spectrometer and a Bruker ER4103TM cylindrical microwave cavity. An Oxford Instruments helium flow system controlled the sample temperature. Small magnetic field corrections were made with the aid of a MgO:Cr³⁺ crystal (the isotropic g value for Cr³⁺ ions in MgO is 1.9800). Three cw light sources, with powers in the 10–100 mW range, were used: a 532 nm frequency-doubled Nd:YAG laser, a 633 nm helium–neon laser, and a 1064 nm Nd:YAG laser. The SPS crystals have an optical absorption edge near 530 nm at room temperature.³³ A shift to approximately 500 nm occurs below 100 K.³⁴ 

Figure 2 shows EPR spectra taken from our copper-doped Sn₂P₂S₆ crystal during exposure to 532 nm laser light. These data were obtained at 64 K with the magnetic field parallel to the a, b, and c directions in the crystal. There were no observable EPR signals before applying the light. In Fig. 2(a), the set of four equally spaced hyperfine lines centered at 320.9 mT is assigned to Cu²⁺ ions and the slightly structured line at 341.1 mT is assigned to singly ionized sulfur vacancies (⁠$VS+$⁠). The present study is the first detailed report of the Cu²⁺ EPR spectrum in SPS crystals. In contrast, the EPR signal from the sulfur vacancy was identified by Golden et al.¹⁸ in 2014 and has been observed since then in a variety of SPS crystals. The barely resolved structure in the $VS+$ signal is due to weak hyperfine interactions (slightly unequal and nearly isotropic) with two ³¹P nuclei. These vacancies are in the doubly ionized charge state before exposure to the laser light, with no trapped electrons. They trap one or two electrons during illumination. A few smaller EPR lines located on the high-field side of the spectra in Fig. 2 are unidentified.

Estimates of the concentrations of defects responsible for the spectra in Fig. 2(a), based on a comparison to an EPR pitch sample provided by Bruker, are 5.7 × 10¹⁷ cm⁻³ for the Cu²⁺ ions and 6.1 × 10¹⁶ cm⁻³ for the $VS+$ vacancies. The difference between these two concentrations is attributed to the large number of nonparamagnetic $VS0$ vacancies that are also created by the laser light. If no other defects participate, the concentration of Cu²⁺ ions is expected to be equal to the concentration of $VS+$ vacancies plus twice the concentration of $VS0$ vacancies, i.e., [Cu²⁺] = [$VS+$] + 2[$VS0$]. Using this charge neutrality condition, we estimate that the concentration of $VS0$ vacancies in Fig. 2(a) is about 2.5 × 10¹⁷ cm⁻³. The light forms approximately four times more neutral vacancies than singly ionized vacancies.

The energy of the photons from the 532 nm laser used to generate the Cu²⁺ ions and the $VS+$ vacancies in Fig. 2 is 2.33 eV, a value close to the bandgap of SPS. This suggests that a primary defect production mechanism for the 532 nm light is the simultaneous formation of electrons and holes in the conduction and valence bands as a result of the direct pumping of electrons across the gap. A portion of these “free” electrons and “free” holes are immediately trapped at sulfur vacancies and Cu ions, respectively. The remainder of the electrons and holes generated with the 532 nm light quickly recombine, radiatively or nonradiatively.

The EPR spectra in Fig. 2 can also be produced at 64 K with below-bandgap 633 nm (1.96 eV) laser light. For these lower energy photons, two production mechanisms are possible: (1) electrons are excited from Cu⁺ ions to the conduction band, with these electrons then becoming trapped at $VS2+$ vacancies and forming $VS+$ and $VS0$ vacancies, or (2) electrons are excited from the valence band to $VS2+$ vacancies, with the holes left in the valence band becoming trapped at Cu⁺ ions and forming Cu²⁺ ions. We were unable to experimentally determine which mechanism is more likely. The first mechanism, however, is of special interest because it allows the 633 nm photons to directly form $VS0$ vacancies.

The effects of longer wavelength 1064 nm (1.16 eV) laser light are very different. Cooling the Cu-doped SPS crystal in the dark and then illuminating at 64 K with 1064 nm light did not produce detectable EPR spectra. We also observed that Cu²⁺ and $VS+$ signals produced at 64 K by the 532 or 633 nm laser (and remaining thermally stable after removing the visible light) were quickly destroyed at this temperature by the 1064 nm laser light. Possible mechanisms for this destruction of the paramagnetic charge states with the near-infrared light are (1) excitation of electrons from the valence band to Cu²⁺ ions with the holes left behind recombining with electrons at the $VS+$ and $VS0$ vacancies or (2) excitation of electrons from $VS+$ and $VS0$ vacancies to the conduction band followed by the recombination of these electrons with holes at the Cu²⁺ ions. Although green and red laser light are expected to readily form gratings in the Cu-doped SPS crystals, our present results suggest that a significant photorefractive response will not be produced with 1064 nm laser light in SPS crystals doped only with Cu.

The Cu²⁺ EPR spectrum in Fig. 2(a) has the characteristic pattern of four lines expected from hyperfine interactions with ⁶³Cu and ⁶⁵Cu nuclei. A stick diagram above the spectrum in Fig. 2(a) identifies these lines. Natural abundances of the two isotopes are 69.15% and 30.85%, respectively. Both isotopes have an I = 3/2 nuclear spin and their nuclear magnetic moments are similar. Together, these properties are responsible for the observed four-line spectrum. Individual lines from the ⁶³Cu and ⁶⁵Cu nuclei are resolved in some EPR studies,³⁵ especially at the low- and high-field ends of the spectrum. This, however, is not the case in the present study because of the large widths of the lines. The spacing between the primary Cu lines in Fig. 2, representing the strength of the hyperfine interaction with the ⁶³Cu and ⁶⁵Cu nuclei, has a strong angular dependence. This is seen when comparing the spectra in Figs. 2(b) and 2(c) with the spectrum in Fig. 2(a). The spacing varies from 7.8 mT when the magnetic field is along the a direction to nearly zero when the field is along the c direction. Spin-Hamiltonian parameters describing this angular dependence are determined in Sec. III C.

In addition to the ⁶³Cu and ⁶⁵Cu hyperfine, there are superhyperfine lines in the Cu²⁺ spectra in Fig. 2 caused by interactions of the Cu²⁺ ion (on a Sn²⁺ site) with ¹¹⁷Sn and ¹¹⁹Sn nuclei at two adjacent Sn²⁺ sites (referred to as Sn_A and Sn_B). The natural abundances of the ¹¹⁷Sn and ¹¹⁹Sn isotopes are 7.68% and 8.59%, respectively, and they both have an I = 1/2 nuclear spin. Individual lines from the two Sn isotopes are not resolved in Fig. 2 because their nuclear magnetic moments are similar. These Sn-related superhyperfine lines are best seen in Fig. 2(c). Stick diagrams below this spectrum identify the lines. The pair of lines at 321.4 mT and 340.8 mT in Fig. 2(c) is symmetrically located about the primary Cu²⁺ line at 331.2 mT and are due to ^117,119Sn nuclei on the neighboring Sn_A site. The line at 302.9 mT, and its counterpart near 359 mT, are due to ^117,119Sn nuclei on the neighboring Sn_B site. Interference (i.e., overlap) with the nearby lines from the singly ionized sulfur vacancy (⁠$VS+$⁠), as well as other weak unidentified lines, makes it difficult to clearly see the high-field component of this latter pair.

Hyperfine lines, from ^117,119Sn nuclei, are also present on the low- and high-field sides of the Cu²⁺ spectra in Figs. 2(a) and 2(b). These lines are again more clearly seen on the low-field side because interference from other signals obscures their presence on the high-field side. As the center Cu²⁺ line in Fig. 2(c) splits into four lines in Figs. 2(a) and 2(b), so also will each of the ^117,119Sn lines. For example, where there are two ^117,119Sn lines on the low-field side in Fig. 2(c), there will be eight lines on the low-field side in Figs. 2(a) and 2(b). All eight lines are not seen in these latter spectra because some overlap each other and some are underneath the more intense primary Cu²⁺ lines. A careful look at the three spectra in Fig. 2 shows that these ^117,119Sn interactions are isotropic with hyperfine splittings of 19.4 mT and 56.3 mT. Morton and Preston³⁶ predict that an unpaired spin in a 5 s orbital on a Sn ion will have an isotropic hyperfine value of 1255 mT (the 20% reduction suggested by Fitzpatrick et al.³⁷ is included in this value). Our combined values of 19.4 and 56.3 mT indicate that approximately 6.0% of the Cu²⁺ unpaired spin is located on the two neighboring Sn²⁺ ions. We also expect that a portion of the unpaired electron spin from the Cu²⁺ ion is in s and p orbitals on each of its eight nearest-neighbor S²⁻ ions. Superhyperfine lines from the sulfur nuclei, however, are too weak to observe in the Cu²⁺ spectra in Fig. 2. The natural abundance of ³³S is 0.75% (this is the only sulfur isotope with a nuclear magnetic moment).

The angular dependence of the Cu²⁺ EPR spectrum was acquired in three planes (a-b, b-c, and c-a). In Fig. 3, the discrete points are the experimental positions of the lines. As described in Ref. 24, a paramagnetic point defect has two crystallographically equivalent orientations, i.e., sites, in the monoclinic SPS crystals. These two crystallographically equivalent orientations of the Cu²⁺ ions are magnetically equivalent when the magnetic field is along the a, b, or c directions. The two sites are also magnetically equivalent for all angles when the magnetic field is rotated in the a–c plane. By magnetically equivalent, we simply mean that the two sites have identical EPR spectra. This expected behavior of a point defect in an SPS crystal is illustrated in Fig. 3. The EPR spectrum splits into two branches when the direction of the magnetic field is rotated from a to b and from b to c but does not split when the field is rotated from a to c.

The angular dependence of the Cu²⁺ ions is described by the following spin Hamiltonian:

An electron Zeeman term, a hyperfine term, and a nuclear Zeeman term are included. In Eq. (1), S and I are the spin operators; B is the external magnetic field; and β and β_n are the electron and nuclear Bohr magnetons, respectively. In general, g and A matrices each have six independent parameters. These are the three principal values and the three Euler angles that define the principal-axis directions. We determine values for these 12 parameters by fitting the experimental results in Fig. 3. When determining these parameters, we ignore the slight deviation from 90° for the angle between a and c (i.e., the crystal is regarded as orthorhombic).

The spin Hamiltonian in Eq. (1) was rewritten as an 8 × 8 matrix (S = 1/2, I = 3/2). A least-squares fitting routine, based on the energy eigenvalues obtained from diagonalizations of this matrix, was then used to determine the “best” values for the 12 parameters. The EPR selection rules ΔM_S = ± 1 and Δm_I = 0 are followed. Input data for the fitting were the 189 pairs of magnetic field values and microwave frequencies representing the experimental points in Fig. 3. For reasons described in Ref. 24, data taken from b to the midpoint between a and c were also included. Table I contains the final spin-Hamiltonian parameters. To aid in the visualization of the directions of the principal axes, each set of Euler angles is converted in Table I to polar and azimuthal (θ,ϕ) pairs of angles. We define θ relative to the c axis and ϕ relative to the a axis with positive rotation being from a toward b in the plane perpendicular to c. Applying a reflection through the mirror plane of the crystal will give the principal-axis directions for the second of the two crystallographically equivalent sites for the Cu²⁺ ions. Since the lines from ⁶³Cu and ⁶⁵Cu nuclei are not resolved in our EPR spectra, the hyperfine parameters in Table I represent an “average” of the two isotopes. The solid lines in Fig. 3 were generated using the parameters in Table I.

It is interesting to compare the spin-Hamiltonian parameters in Table I with parameters obtained from Cu²⁺ EPR spectra in other materials. A wide range of g values have been reported, ranging from g_∥ = 0.20 and g_⊥ = 1.549 in GaN³⁸ to g₁ = 1.9998, g₂ = 2.1538, and g₃ = 2.7796 in LiGaO₂.³⁹ This wide variation can be theoretically explained (1) by considering strong admixtures of spin and orbital states due to competing spin–orbit and crystal-field interactions and (2) by allowing significant orbital reduction factors caused by covalency (which spreads the d states onto the neighboring ions) and possible admixtures of the Cu 4p states into the d states.^38,40–42 For the Cu²⁺ ions in SPS, we suggest that the g values in Table I, all between 2.01 and 2.11, result from a combination of a weak crystal field and significant covalent overlap with neighboring Sn and S ions. Our observation of superhyperfine interactions with two neighboring Sn ions, reported in Sec. III B, supports this delocalized model.^43,44

Figure 4 shows the time evolution of thermally induced changes in the intensities of the EPR signals from singly ionized sulfur vacancies (⁠$VS+$⁠) and Cu²⁺ ions. These data were taken at 78 K after removing the 532 nm laser light. The Cu²⁺ signal has a large initial drop during the first 300 s (a decrease of approximately 67%) and then approaches a nonzero equilibrium level. The inset of Fig. 4 shows that during this initial 300 s interval, the signal from the $VS+$ vacancies grows significantly (the increase is 67%). The behaviors illustrated in Fig. 4 are caused by the thermal decay of neutral sulfur vacancies (⁠$VS0$⁠). When the light is on the crystal, $VS0$ and $VS+$ vacancies and Cu²⁺ ions are all produced. Then, when the light is removed (at t = 0 in Fig. 4), electrons are thermally released from the $VS0$ vacancies. This increases the number of $VS+$ vacancies (as only one electron is released from each $VS0$ vacancy) and, at the same time, decreases the number of Cu²⁺ ions. The released electrons moved to Cu²⁺ ions and restore a portion of the Cu⁺ ions that were present before illumination. Beyond 600 s in Fig. 4, all the $VS0$ vacancies have decayed and the concentrations of the $VS+$ vacancies and the Cu²⁺ ions are the same (∼1.1 × 10¹⁷ cm⁻³). These remaining defects compensate each other (with one electron trapped at a sulfur vacancy for each hole trapped at a Cu ion) and are stable at 78 K.

An activation energy describing the thermal release of electrons from the neutral sulfur vacancies (⁠$VS0$⁠) is obtained by monitoring the decay of Cu²⁺ ions. Using the Cu²⁺ spectrum for this purpose is necessary because the $VS0$ vacancies do not have unpaired spins and thus cannot be directly monitored with EPR. Figure 5 shows a set of isothermal decay curves for the Cu²⁺ EPR signal. These curves were taken at 74, 76, 78, 80, and 82 K after illuminating the crystal with 532 nm laser light. The EPR spectrometer was operated in a kinetics mode (i.e., a time sweep) with the field fixed at 317.0 mT, corresponding to the second Cu²⁺ hyperfine line in Fig. 2(a).

A general-order kinetics model^45–48 allows an activation energy to be extracted from the isothermal decay curves in Fig. 5. This model was recently used to determine the Mg^0/− level in a β-Ga₂O₃ crystal.⁴⁹ The analysis starts with the differential equation,

In Eq. (2), n represents the decreasing concentration of Cu²⁺ ions after removal of the 532 nm light (as electrons are released from $VS0$ vacancies), t is the time, b is the parameter that describes the order of the kinetics, E is the activation energy, and T is the temperature. The pre-exponential factor s′ is the “attempt-to-escape frequency” and the parameter b represents the “order” of the decay (b is usually between 1 and 2). First-order kinetics (b = 1) corresponds to no retrapping of an electron at a $VS0$ vacancy after its initial release (i.e., electrons move directly to Cu²⁺ ions after being released from the $VS0$ vacancies). Second-order kinetics (b = 2) describes the repeated retrapping and release of electrons at $VS0$ vacancies after the initial release. First-order decay curves are single exponentials, whereas second-order decay curves are nonexponential with long tails.

The solution to Eq. (2), for b > 1, is

where n₀ is the initial concentration of $VS0$ vacancies (when the laser light is removed). Equation (3) is rewritten in the following form:

The five isothermal decay curves in Fig. 4 are separately plotted as (n/n₀)^1−b vs time, after removing the approximate 20% offset due to the Cu²⁺ ions that remain after all of the neutral $VS0$ vacancies have decayed. The segment of time used is terminated at 200 s for 74 K, 150 s for 76 K, 120 s for 78 K, 90 s for 80 K, and 90 s for 82 K. For each curve, the longer times are avoided because of the slight uncertainty associated with removing the contributions of Cu²⁺ ions that remain after the $VS0$ vacancies have decayed. For each plot, the value of b is adjusted between 1 and 2 until a straight line emerges. This process gives b = 2 for each decay curve, thus indicating that significant retrapping is occurring. The five straight lines used to determine the b values have different slopes. From Eq. (4), these slopes are

where the index i = 1–5 corresponds to the five temperatures where decay curves were obtained. Taking the natural logarithm of each side of Eq. (5) gives

According to Eq. (6), a plot of ln(m_i) vs 1/T_i yields a straight line with a slope of –E/k. This approach is implemented in Fig. 6 where a plot with five points, one for each of our isothermal decay curves, has been generated. The slope of the best-fit straight line in Fig. 6 gives an activation energy of E = 194 meV for the thermal decay of photoinduced neutral sulfur vacancies (⁠$VS0$⁠) in Sn₂P₂S₆ crystals. An estimate of the uncertainty in this value of E is ±10 meV.

The singly ionized $VS+$ vacancies and Cu²⁺ ions that remain after the neutral $VS0$ vacancies have thermally decayed (see Figs. 4 and 5) are thermally destroyed when the crystal is further warmed to 120 K (this restores the crystal to its pre-illuminated state). We have not established in the present study whether the $VS+$ vacancies become unstable near 120 K and release electrons that move to the Cu²⁺ ions or the Cu²⁺ ions become unstable and release holes that move to the $VS+$ vacancies. Results reported in Ref. 18 suggest that it is the $VS+$ vacancies that become unstable near 120 K, as the SPS crystal used in that earlier investigation did not contain significant amounts of Cu ions.

A second impurity-related EPR signal, seen near 246 mT in Fig. 7, is produced in the Cu-doped SPS crystal during an exposure at low temperature to either 532 or 633 nm laser light. The spectrum in Fig. 7 was taken at 40 K with the magnetic field aligned along the a direction. Unfortunately, there is no resolved hyperfine structure to aid in the identification of the defect. The angular dependence of this EPR signal in the a-b, b-c, and c-a planes is shown in Fig. 8. These results verify that it is an S = 1/2 defect and suggest that a transition-metal-ion, with a partially filled 3d shell, is responsible. As expected for the monoclinic structure of the SPS crystal, Fig. 8 shows a splitting into two branches in the a-b and the b-c planes, but no splitting in the a-c plane (see Sec. III C). A spin-Hamiltonian with only an electron Zeeman term (⁠$H=βS⋅g⋅B$⁠) describes the angular dependence in Fig. 8 and is used to extract principal values and principal-axis directions for the g matrix. The same fitting procedure that was used for the Cu²⁺ ions in Sec. III C is followed here, with the input data being the 46 magnetic field values corresponding to the discrete points in Fig. 8. Table II gives the results of the fitting. Again, Euler angles are converted to (θ,ϕ) pairs. These “best-fit” g matrix parameters in Table II are used to generate the solid lines in Fig. 8.

The g values in Table II are characteristic of a 3d⁹ spin system and are similar to those reported for Ni⁺ ions in other crystals.^50–52 A lack of resolved hyperfine also suggests Ni ions since only the ⁶¹Ni isotope (1.14% abundant, I = 3/2) has a non-zero nuclear magnetic moment. Equally compelling is the expectation that the Cu used in the growth will contain trace amounts of Ni since these elements are adjacent to each other in the Periodic Table. Thus, it is with a high degree of confidence that we assign the EPR signal in Figs. 7 and 8 to Ni⁺ ions. We propose that Ni²⁺ (3d⁸) ions substitute for Sn²⁺ ions during growth. They then trap an electron during an illumination at low temperature and become Ni⁺ (3d⁹) ions. The concentration of Ni⁺ ions in Fig. 7 is estimated to be 2.2 × 10¹⁶ cm⁻³. This is 25 times less than the concentration of Cu²⁺ ions in Fig. 2.

These Ni ions, like the Cu ions, are acceptors in the SPS crystal. They are present as Ni²⁺ ions in the as-grown crystal and are converted to Ni⁺ ions by the laser light, whereas the Cu ions are present as Cu⁺ ions in the as-grown crystal and convert to Cu²⁺ ions during illumination. This indicates that the Ni acceptor level is considerably deeper than the Cu acceptor level in the SPS crystals. It is possible that the Ni level is in the upper half of the gap, but studies involving Ni-doped SPS crystals are needed to make a precise determination of its position. We expect that having a level near midgap or in the upper half of the gap may allow 1064 nm laser light to produce a significant photorefractive response in Ni-doped crystals.

Sulfur vacancies and Cu impurities are studied in a single crystal of Sn₂P₂S₆, a well-known ferroelectric and photorefractive material. Doubly ionized (⁠$VS2+$⁠) sulfur vacancies and Cu⁺ ions at Sn²⁺ sites are present in the as-grown crystal. Exposing the crystal to 532 or 633 nm laser light, while below 70 K, forms stable singly ionized (⁠$VS+$⁠) and neutral (⁠$VS0$⁠) sulfur vacancies and Cu²⁺ ions, as electrons are transferred from the Cu⁺ ions to the sulfur vacancies. Electron paramagnetic resonance (EPR) is used to monitor the $VS+$ vacancies and the Cu²⁺ ions. The laser light produces approximately four times more $VS0$ vacancies than $VS+$ vacancies. An analysis of isothermal decay curves for the Cu²⁺ ions, taken at five temperatures between 74 and 82 K, gives an activation energy of 194 meV for the release of electrons from $VS0$ vacancies to the conduction band. These results suggest that neutral sulfur vacancies, when combined with a source of electrons such as Cu, may play a role in the fast photorefractive response time of Sn₂P₂S₆ crystals.

One of the authors (T.D.G.) was supported at the Air Force Institute of Technology by an NRC Research Associateship Award. Work at the Air Force Research Laboratory was supported by 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 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.