1. Introduction

The Yttrium Aluminum Garnet monocrystals (Y₃Al₅O₁₂ abbreviated YAG) containing both trivalent and tetravalent chromium ions have been intensively studied for over thirty years. This very well-known host material doped with Cr⁴⁺ ions is of particular interest due to its applications in laser systems. The Cr⁴⁺:YAG crystal, which exhibits fluorescence in the broad spectral range of 1300 - 1600 nm, can be used as an active material in tunable near-infrared lasers [1,2]. However, such crystals are mainly utilized as saturable nonlinear absorbers in the range of 800 - 1200 nm, that provides passive Q-switching of near infra-red (NIR) lasers, especially for 1.064 µm emission of Nd:YAG in both high power and microchip lasers [3–8]. Y. Kaliski, in an excellent review paper, described a number of applications of Cr⁴⁺ ions - doped crystals in laser physics, systems and technology [8].

A special class of miniature infra-red (IR) lasers represent diode-pumped passively Q-switched Nd:YAG microlasers that offer such desirable features as sub nanosecond, multikilowatt pulses at high repetition rate [6,7]. In this type of microlasers, the Nd³⁺:YAG gain medium and Cr⁴⁺:YAG saturable absorber form the monolithic Nd³⁺:YAG/Cr⁴⁺:YAG planar structure produced by two main techniques: thermal bonding of active plate to plate of saturable absorber developed in the MIT Lincoln Laboratory [6,7] or liquid-phase epitaxy (LPE) proposed for this purpose in the 1990s by CEA/LETI [9–11]. Also, pulsed laser deposition (PLD) could be an alternative method [12,13]. In an epitaxial microlasers, the lasing material is formed by the Nd³⁺:YAG substrate and the Cr⁴⁺:YAG epitaxial layer acting as a passive Q-switch. The passive modulation process utilizes the nonlinear dependence of Q-switching medium absorption on the energy density of incident radiation at a given wavelength. This means that the transmittance of the Cr⁴⁺:YAG absorber, at rising energy of a laser beam with a wavelength of about 1 µm, increases up to the saturation point and above the material becomes transparent. Since the switching is done by laser radiation, the passive modulator does not require external control or power supply. This feature allows to construct a compact microlaser, integrating the pumping laser diode in a single housing [7,10].

In recent years, particular progress has been made in the field of diode-pumped passively Q-switched Nd:YAG lasers and microlasers with Cr⁴⁺:YAG absorber both based on transparent ceramics [16–18]. Currently, transparent laser ceramics seem to be the most promising material for all kinds of solid-state lasers. The authors of the paper [18], based on their laser experiments, conclude that Cr⁴⁺:YAG ceramics is a more efficient material for passive Q-switching of 1 µm lasers compared to the monocrystalline counterpart.

The YAG crystal is cubic and belongs to the Ia_3d space group, with eight formula units in a unit cell which can be expressed by the formula [C₃][A₂][D₃]O₁₂, where C, A, D represent dodecahedral, octahedral and tetrahedral sites. During bulk crystal growth by a standard Czochralski method, chromium is incorporated into the YAG crystal as a trivalent ion replacing the Al³⁺ ion at the octahedral site. In the case when the Cr ion should have a different valence (4+) than the other cations in YAG lattice, the charge imbalance could be compensated by divalent ions, such as Ca²⁺ [5] or Mg² [14]. The Cr⁴⁺ ions enter both tetrahedral and octahedral sites. The Ca²⁺ and Mg²⁺ ions substitute yttrium at dodecahedral sites in YAG lattice. A broad absorption band of Cr,Ca:YAG or Cr,Mg:YAG centered at about 1 µm, which determines Q-switching properties, is attributed to Cr⁴⁺ ions at tetrahedral sites. It has also already been demonstrated, that the post-growth annealing in an oxidizing atmosphere causes an increase in the concentration of tetrahedrally coordinated Cr⁴⁺ (tetra) ions [15,19,20,25]. The similar observations have been also reported for Cr,Mg:YAG [21–23] however, not for Cr,Ca:YAG [24] epitaxial saturable absorbers fabricated by the LPE method.

The behavior of chromium ions in the yttrium-aluminum garnet lattice seems to be quite peculiar. Chromium ions can adopt different valences and occupy different positions in the crystal lattice. Thus, control of the concentration and lattice position of chromium ions in Cr,Mg:YAG epi-layers similarly to monocrystals is possible by thermal oxidation and reduction processes. The efficiency of thermal treatment of the layers in creating of Cr⁴⁺ ions occupying tetrahedral sites depends on temperature, atmosphere, and the concentration of both Cr ions and charge-compensating ions. The information concerning the study of the dynamics, mechanisms, and effectiveness of chromium ion valence transformation in Cr⁴⁺: YAG bulk crystals and ceramics can be found in many papers, for example in [17–20,25–27]. In the case of Cr⁴⁺:YAG epitaxial layers, the number of papers focused on the problems of chromium ions recharging processes during the thermal treatment is very limited [21–23]. During high-temperature annealing in an oxidizing atmosphere of both monocrystals and Cr,Mg:YAG ceramics the content of Cr^4 +(tetra) ions is established by two parallel reactions: oxidation of Cr^3 +(octa) to Cr^4 +(octa) ions and position conversion of Cr^4 +(octa) ions with Al^3 +(tetra) ions. For ceramic absorbers the second reaction is faster than Cr³⁺ to Cr⁴⁺ oxidation [26].

The liquid-phase epitaxy method allows to grow Cr,Mg:YAG layers in which the as grown concentration of tetrahedrally coordinated Cr^4 +(tetra) ions is much higher than that obtained in the Cr,Mg:YAG monocrystals after high temperature oxidation. The high concentration of Cr⁴⁺ ions is the most needed property of the Cr,Mg:YAG layers in epitaxial Nd³⁺:YAG/Cr⁴⁺:YAG microlaser due to the technological limitations of the LPE process practically allowing the deposition of layers with a maximum thickness of about 200 - 250 µm [28]. For an efficient Q-switching, the total population of Cr^4 +(tetra) ions in an epi-layer of epitaxial microlaser should be comparable to the total content of such ions in a monocrystalline absorber of almost the same active area but several mm thick, used to create a structure of bonded microlaser.

In Cr,Mg:YAG epi-layers heavily doped with Cr and Mg ions the concentration of Cr^4 +(tetra) ions can be effectively controlled by thermal treatment in a suitable atmosphere. Considering the valence state transition of octahedral coordinated chromium ions, it would be appropriate to determine the relative concentration of Cr³⁺ ions. The change of a content of Cr^3 +(octa) ions, after high temperature annealing, is troublesome to estimate from UV and VIS absorption spectra. This is due to the fact that most of the absorption bands of chromium (for all valences) are quite broad and overlapping.

Thus, we suppose that in the case of paramagnetic Cr³⁺ ions in Cr⁴⁺:YAG epi-layers, the electron spin resonance (ESR) technique can provide more information than optical methods despite the negative opinion on this question [20]. The authors of paper [20] have stated that ESR measurements did not show any noticeable changes in the ESR spectrum of the Cr,Mg:YAG monocrystal after thermal oxidation or reduction. The electron spin resonance (ESR) spectroscopy is one of the most important methods when investigating paramagnetic ions and defects in crystals. The measurements of ESR spectra allow, in many cases, to determine the chemical nature of a paramagnetic defect, its charge state, and position in the crystal structure. The analysis of the width of the resonance lines of a given ion or paramagnetic defect provides an estimate of its concentration in the crystal. In our case, it is important that the analysis of the width of the resonance lines of a Cr³⁺ ion may allow to determine its concentration in the crystal.

It should be noted that XPS is a more versatile method compared to ESR for determining the concentration, valence state and lattice position of dopants in YAG layers.

The aim of this work was to fabricate Cr,Mg:YAG layers with different concentrations of Cr^4 +(tetra) ions by means of liquid phase epitaxy, and to determine the influence of annealing processes on the concentration changes of Cr⁴⁺ (tetra) and Cr^3 +(octa) ions. A possibly diversified set of samples consisting of epitaxial Cr,Mg:YAG/YAG structures differing in both the concentration of Cr and Mg ions and the ratio of these concentrations may provide suitable material for testing the usefulness of the ESR method for monitoring annealing induced valence changes. Our expectations have been confirmed. To the best of our knowledge, we can report for the first time on the satisfactory use of the ESR method in determining the changes of Cr^3 +(octa) ions concentration in Cr,Mg:YAG layers caused by thermal treatment of samples. The optical spectroscopic measurements and ESR investigation confirmed the capability of obtaining saturable absorber material in the form of epitaxial layers.

2. Experimental procedure

2.1 LPE growth

The epitaxial Cr,Mg:YAG layers ware prepared using liquid phase epitaxy developed previously also at the Institute of Electronic Materials Technology (now Łukasiewicz Research Network - Institute of Microelectronics and Photonics) [29]. Using our own original procedures, we have produced the Cr⁴⁺:YAG/Nd:YAG epitaxial structures for passively Q-switched microlasers. Such structures with deposited mirror coatings generated pulses at repetition rate up to 15 kHz, with pulse length in the range of 0.8–2 ns (FWHM), pulse energy 6 µJ and peak power of up to 3 kW [29].The equipment for LPE growth of garnet layers was constructed at IEMT. The layers were grown from a supercooled molten garnet-flux high temperature solution in the air atmosphere. The Cr,Mg:Y₃Al₅O₁₂ layer constituent oxides (Al₂O₃, Y₂O₃, Cr₂O₃ and MgO) were dissolved in flux (PbO-B₂O₃) to form a high-temperature solution. The layers designed for annealing, optical and ESR measurements were grown on both sides of the polished <111 > oriented, 20 mm in diameter YAG substrates using the isothermal dipping technique with rotation of the horizontally held substrate in a Pt holder. As mentioned earlier, to create a tetravalent state of chromium ions, co-doping with cations of valence (2+), such as Mg or Ca, is necessary. Due to the smaller ionic radius of Mg²⁺ than Ca²⁺ ion we have chosen magnesium as the dopant that stimulates the formation of Cr⁴⁺ ions in the garnet host. The Ca²⁺ ions can only enter into the dodecahedral sites, which causes an essential increase of the lattice constant. The growth of high-quality garnet epitaxial films is limited by the effect of strains induced by lattice mismatch. During film growth with magnesium as charge compensating dopant only a part of chromium ions substitute Al³⁺ ions as Cr⁴⁺ ions, while the rest remains in the 3 + valence state in dependence on Cr₂O₃/Al₂O₃ ratio in the melt. The epitaxial Cr,Mg:YAG films were grown with different concentration of Cr₂O₃ and mole ratio Cr₂O₃ to MgO in the melt ranging from 10 to 2. The high-quality films were deposited at temperatures in the range from 1000^oC to 1050 °C with thickness between 35–85 µm. For simplicity, we use in the paper Cr/Mg, Mg/Al and Cr/Σ to denote Cr₂O₃/MgO, MgO/Al₂O₃ mole ratio and molar fraction of Cr₂O₃ in the melt, respectively.

2.2 XRD measurements

The garnet layer of Cr,Mg:YAG composition is in fact a solid solution with properties depending on the concentration of cations locating in the different lattice sites. The lattice mismatch between epitaxial layer and substrate was measured using X-ray high resolution diffraction method (HRXRD). Diffraction measurements were performed by means of X-ray quasi parallel double-crystal arrangement with 400 reflection on a Ge monochromator and symmetrical reflection 444 YAG of Cu Kα₁ radiation. The composition of the layer and thus the lattice mismatch depends on the melt compositions. The changing concentration of Cr and Mg ions replacing Al ions in the YAG lattice results in a linear change in the value of the epi-layer lattice constant according to the Vegard’s rule. The XRD measurements in symmetric reflections allowed to determine the lattice mismatch Δa^⊥/a_S = (a_S - a_F^⊥)/a_S in the direction perpendicular to the substrate-layer interface. Based on such measurements, the relaxation state of the layers cannot be precisely determined, as well as Δa/a_S in the film plane. Figure 1 shows the difference in lattice constants between the YAG substrate and the Cr,Mg:YAG layer Δa^⊥/= a_S – Δa^⊥ as a function of Cr/Σ. The a_S and a_F are the substrate and layer lattice constants, respectively.

 

Fig. 1. The difference between Cr,Mg:YAG film and YAG substrate lattice constant as a function of Cr₂O₃ mol fractions in the melt.

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According to the XRD measurements, the value of Δa^⊥ in obtained Cr,Mg:YAG/YAG epitaxial structures calculated from the angular separation of X-ray rocking curves of the substrate and layer, otherwise defined as diffraction peaks, varies from +0.002 Å to –0.002 Å. The XRD results indicate that the Cr,Mg:YAG films were in slight compression (a_F > a_S) or expansion (a_F < a_S) and exhibited an elastic adaptation to the YAG substrate. The doping of the layers with chromium and magnesium ions led to the acceptable mismatch values which fall in the range from –0.02 Å to +0.01 Å [30]. The cracking of the doped YAG layer occurs for Δa^⊥ > 0.01 Å, while for value of Δa^⊥ below - 0.02 Å the so-called faceting growth is observed. Such a mismatch range guarantees the growth of a monocrystalline layer [30]. The Cr₂O₃ concentration in the melt Cr/Σ = 0.024 and Cr/Mg = 4 ensures equalization of the lattice constant of Cr,Mg:YAG film and YAG substrate (Δa^⊥ = 0). The half width of the rocking curve (FWHM = 14’’) of the layer without lattice mismatch is close to the value measured for YAG substrate and indicates the excellent crystallinity of obtained films.

2.3 Transmission spectra

The presence of Cr⁴⁺ ions in the layers, especially those with tetrahedral coordination, was confirmed by a transmittance spectra. The optical transmission spectra of epitaxial structures were measured using Perkin Elmer Lambda 900 spectrophotometer with a step of 0.5 nm. The transmission spectra of Cr,Mg:YAG/YAG structures which were grown from the melts with different Cr₂O₃ and MgO concentration are presented in Fig. 2. In order to determine the value of the absorption coefficient of the layers, the transmission measurements were carried out separately for the substrate and the epitaxial structure. The absorption coefficient was calculated according to the following formula:

 

Fig. 2. Comparison of transmission spectra of Cr,Mg:YAG/YAG structures obtained from solutions with different concentrations of Cr₂O₃ and MgO.

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Fig. 3. Absorption spectrum of Cr,Mg:YAG epitaxial layers. The absorption lines were assigned according to [25].

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Due to approximation of the absorption spectrum shown in Fig. 3 by the sum of the components described by the Lorenz function, a series of lines was obtained, which were then attributed to absorption bands characteristic for chromium ions with different charge states and sites in the YAG lattice.

For identifying the series of transitions characteristic for chromium ion, we have taken benefit of the energy level diagrams of Cr⁴⁺ ions in the tetrahedrally and octahedrally coordinated sites as well as energy level diagram of Cr³⁺ ions residing in the octahedral sites of YAG as presented in [25]. These bands connected to the successive transitions are depicted below:

In the investigated layers, the positions of the maxima of the absorption bands are shifted from a few to several nm, relative to the position of the bands determined for the Cr⁴⁺:YAG crystal and depend on the concentration of chromium ions in the epitaxial layer. The expected property of the obtained layers is the presence of a broad band absorption in the range from 800 to 1200 nm. This band is typical of oxide crystals containing Cr⁴⁺ ions in tetrahedral positions. In the absorption spectrum of the Cr,Mg:YAG layer, compared to that of the Cr⁴⁺:YAG crystal, an additional band can be detected in the 700 nm - 800 nm range with a maximum for the wavelength λ_max = 760 nm. Haibo et al. [24] have first observed this absorption line in Cr,Ca:YAG epitaxial layers and attributed its origin to the ²B₁(²E) → ²E(²T₂) transition of tetrahedrally coordinated Cr⁵⁺ ions [24]. Ishii and co-workers, in a theoretical paper focusing on the multiplet structure of Cr⁴⁺ and Cr⁵⁺ ions in tetrahedral sites of a YAG crystal, accepted the possibility of such transition for the Cr⁵⁺ ion [31]. The chromium ion with valence (5+) was also observed in a garnet crystal of Cr:Ca₃Ga₂Ge₃O₁₂ composition [32]. The absorption band near 760 nm becomes noticeable in Cr,Mg:YAG layers starting at a value of the molar fraction of Cr₂O₃ in the solution Cr/Σ= 0.018. The starting molar ratios of Cr₂O₃/Σ and mole ratios of Cr₂O₃/MgO, MgO/Al₂O for which the tested structures from 5 to 23 were deposited, are given in Table 1.

Table 1. Comparison of the absorption coefficients α (λ= 1064 nm), N concentrations of Cr⁴⁺ ions at tetrahedral positions before (0) and after the annealing process (T). N_A and N_D denote concentrations calculated from the absorption and energy transmission measurements respectively and Δα = α_T - α_o

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The influence of Cr₂O₃ and MgO concentrations in the solution on the value of absorption coefficient α at the wavelength λ = 1064 nm is illustrated in Fig. 4(a) and 4(b). As can be seen from Fig. 4, the content of Cr⁴⁺ ions in tetrahedral positions is mainly determined by the concentration of Cr₂O₃, as well as by the total amount of Cr₂O₃+ MgO in the solution. At the fixed value of Cr/Σ (samples 9,13 and 16,19) an increase of the amount of MgO leads to an increase in the value of α (λ = 1064 nm).

 

Fig. 4. The influence of Cr/Σ a) and (Cr + Mg)/Σ b) in the solution on the absorption coefficient value of Cr,Mg:YAG layers at 1064 nm wavelength

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2.4 Thermal oxidation

The obtained Cr,Mg:YAG/YAG epitaxial structures were annealed in the ambient atmosphere (clean room) with humidity in the range of 35–45% at temperatures in the range of 1100 - 1150 °C for a period of 5 - 6 hours, i.e. conditions that ensure the maximum achievable content of recharged and transferred Cr⁴⁺ ions into the tetrahedral sites [19,22]. The samples were then cooled down to room temperature as quickly as possible within several minutes in order to freeze the annealing induced changes. Like the authors of the papers [23,28], we have observed the increase of absorption at about 1 µm corresponding to the ³A₂ → ³T₂ transition of tetrahedrally coordinated Cr⁴⁺ ions in Cr,Mg:YAG films. The changes of absorption spectra in the 500 - 1300 nm range, induced by the annealing process of two Cr,Mg:YAG/YAG epitaxial structures numbered 22 and 23 obtained from solutions with different concentrations of Cr₂O₃ and MgO oxides, are shown in Fig. 5.

 

Fig. 5. The absorption spectra of samples 22 and 23 before and after oxidation (T).

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The content of chromium ions in the layer and, ultimately, the amount of Cr⁴⁺ ions in the tetrahedral positions, which determine the value of the absorption coefficient α (λ = 1064 nm) depends on the initial concentration of Cr₂O₃ and the molar ratio of Cr₂O₃ to MgO in the high-temperature solution. During the epitaxy process of Cr,Mg:YAG layers, an oxidation reaction of the Cr³⁺ (octa) ions takes place in the presence of Mg²⁺ ions and oxygen vacancies V_O(2-) in solid state, which leads to the formation of the Cr⁴⁺ ions. The results of absorption and energy density-dependent transmission measurements of Cr,Mg:YAG layers exposed to an oxidizing. process showed an increase of the concentration of Cr⁴⁺ (tetra) ions. Following the authors of the paper [25], a brief description of solid-phase reactions causing an increase of the amount of Cr⁴⁺ ions is shown below. The Cr⁴⁺ ion is formed by the following reaction occurring in the layer:

Next, the Cr⁴⁺ ion, by changing the position with the Al³⁺ ion, switches the coordination (from 6 to 4) moving to a tetrahedral site.

It may be observed in Fig. 5 that the absorption band of Cr⁵⁺ ions at about 760 nm almost disappeared after annealing, We suppose that this phenomenon is probably related to the oxidation of the Cr⁵⁺ (tetra) to Cr⁶⁺ (tetra) ion with an absorption band around 400 nm (Fig. 3, peak 1). Such oxidation reaction requires charge compensation by the Mg²⁺ ion. Sugimoto et al. [15] have stated that the oxidation process of Cr,Ca:YAG crystals produces a Cr⁶⁺ as well as Cr⁴⁺ ions, depending on dopant concentrations and annealing conditions. If the assumption of Cr⁶⁺ ion formation is correct, this would mean that chromium could exist in trivalent, tetravalent, pentavalent and hexavalent states in heavily doped Cr,Mg:YAG layers.

The values of the absorption coefficient α for the wavelength of 1.064 µm before and after annealing, with the estimated concentrations of Cr⁴⁺ ions at tetrahedral positions, are summarized in Table 1. In the case of samples numbered 5 and 9, the values of absorption coefficient α (λ= 1064 nm) are similar to those for typical bulk Cr,Mg:YAG monocrystals [14]. The effect of annealing on increasing of the absorption coefficient value by several percent is similar to that observed in monocrystals.

For example: the composition of the high-temperature solution for the growth of the layers such as in sample 22, expressed in moles, is as follows: PbO – 2,64, B₂O₃ - 0.22, Y₂O₃ -0.01174, Al₂O₃ - 0.0587, Cr₂O₃ – 0.05283, MgO - 0.01761.

For the remaining samples, it was found that as a result of annealing of Cr,Mg:YAG layers, independently of the initial concentration of Cr₂O₃ and MgO in the high temperature solution, the value of the absorption coefficient α(λ = 1064 nm) increased much more, by about 40–60%. This observation is valid for Cr₂O₃ and MgO concentrations used by us in the epitaxy processes.

The information contained in the paper [21] may be helpful in explaining such a significant increase in the value of the absorption coefficient. The authors of the paper [21] have found that in as-grown Cr,Mg:YAG layers Cr^4 +(octa) ions represent nearly 50% of all octahedrally coordinated chromium ions. The above observation concerned the epitaxy of Cr,Mg:YAG layers at molar ratio MgO/Al₂O₃ > 0.1 and Cr₂O₃ concentration in the high temperature solution of about 0.45 wt. %. Under very close conditions we have grown the investigated structures 13 - 23 as shown in Table 1. The significantly increased population of Cr^4 +(octa) ions in layers compared to Cr,Mg:YAG crystals explains the higher efficiency of creating Cr⁴⁺ ions in tetrahedral positions during oxidation. In the layers, more Cr^4 +(octa) ions participate in position switching which is a faster and energetically more favorable process compared to the recharging of Cr³⁺ ions.

3. ESR measurements and discussion

ESR measurements have been performed on the number of Cr,Mg:YAG/YAG epitaxial structures with different concentration of chromium ions in the layer. The samples were investigated using a Bruker ESP-300 X-band spectrometer operating at a microwave frequency of about 9.4 GHz with a reflection rectangular cavity in the TW₁₀₂ mode. Magnetic field modulation at 100 kHz and phase sensitive detection were used to record the derivatives of the absorbed microwave power. For operation at variable temperatures between 4 to 300 K, the spectrometer was equipped with a helium gas flow Oxford Instruments ES-910 cryostat. The information on specific layer parameters which are necessary for comparison and analysis of the recorded ESR spectra are listed in Table 2. where: H and h are the thicknesses of the YAG substrate and Cr,Mg:YAG layer, respectively; M is the mass of the measured epitaxial structure; Δm is the mass of the layer; S is the field under the lines of Cr³⁺ ion; and S_E/S_T is the field ratio of the post-epitaxy and annealed samples.

Table 2. Summary of some parameters of the investigated Cr,Mg:YAG/YAG/Cr,Mg:YAG epitaxial structures

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The amount of chromium ions incorporated into the layer, independent of their charge state, reflects the initial concentration of Cr₂O₃ in the high-temperature solution, is denoted as the molar fraction of Cr/Σ in Table 2. The initial Cr₂O₃/MgO (Cr/Mg) molar ratio decides on the concentration of Cr⁴⁺ ions in the layer. The layer and the substrate thickness values given in Table 2, as well as the mass of the measured structure, are required to determine the mass of the layer itself and its volume in the structure. Knowledge of the volume and area under the resonance lines, originated from paramagnetic Cr³⁺ ions, will allow to compare their relative concentrations in the layers.

The measurements of ESR spectra of chromium ions in YAG monocrystals have been the subject of many studies since as early as the 1960s, the results of which are presented, for example, in papers [33,34]. The ESR spectrum in a YAG crystal depends on the charge state and lattice position of chromium ions. The observed resonance lines were assigned to Cr³⁺ ions occupying octahedral positions. By contrast, Cr⁴⁺ ions do not appear in the ESR spectrum. The ESR spectroscopy is based on the study of the energy levels of active paramagnetic centers which, in the presence of a constant magnetic field, have unpaired electron spin (e.g., for Cr³⁺ ion S = 3/2). A sample of the tested material is placed in a uniform magnetic field to which a high-frequency magnetic field is directed perpendicularly. For a fixed configuration of the two fields, changing the intensity of the constant field, several lines related to the resonant absorption of microwave energy can be observed.

The set of these lines is defined as the ESR spectrum of the investigated center in a given crystal. Knowing the spectrum of the Cr³⁺ ion in YAG crystal, one can attempt to determine the relative concentration of this dopant. The resonance lines of Cr³⁺ ions in the garnet structure are strongly anisotropic. Comparison of these lines for different samples is possible for the same orientation of the magnetic field vector in the layer. Since the layers were deposited on <111 > oriented substrate, the direction of the magnetic field should be changed in the plane (111) i.e. the sample being rotated around the <111 > axis. In order to compare and to establish the position of the Cr^3 +(octa) ion lines in the ESR spectrum of Cr,Mg:YAG layer the ESR spectrum of the Cr:YAG crystal was measured. The ESR spectrum of the crystal was recorded for a magnetic field directed parallel to the C₂ axis (direction <110>) i.e. H II C₂ and is presented in Fig. 6.

 

Fig. 6. The ESR spectrum of Cr³⁺ ions in monocrystalline samples in the H II C₂ direction.

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The ESR spectra of the epitaxial structures were then measured for the same magnetic field direction, namely H II C₂. To determine the dopant concentration based on ESR spectrum, one should estimate the area of the field under the resonance lines attributed to the dopant and then compare it with the reference sample. In the case of the investigated layers, a comparison has been made between post-epitaxy and annealed structures based on two resonance lines of Cr³⁺ ion at higher magnetic field with an intensity in 500–600 mT range.

Taking into account the differences in the volume of the measured layers and spectrum measurement parameters, the values of the fields under the resonance lines of the Cr³⁺ ion were calculated according to the formula given by Pool [35]. The results are summarized in Table 2. The shape changes of the Cr³⁺ ion resonance lines caused by annealing are shown for example for layers 5 and 16 in Fig. 7. The ESR measurements were carried out at liquid helium temperature (6 K). An increase in temperature caused a decrease in the intensity of resonance lines of Cr³⁺ ions.

 

Fig. 7. A part of the ESR spectrum of samples 5 and 16 showing Cr³⁺ lines for the H II C2 direction pre- and post-oxidation

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The measurements of the amplitude and width of the Cr³⁺ line as a function of the power of the microwave signal were performed also at the lowest temperature. The dependences obtained for as grown samples 5, 16 and 23 are shown in Fig. 8 and 9.

 

Fig. 8. The intensity of Cr³⁺ ions lines versus microwave power for layers 5,16, 23

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Fig. 9. The Cr³⁺ ions line width as a function of microwave power for layers 5, 16, and 23

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According to the dependencies presented in Figs. 8 and 9, the lines for structure 5 with the lowest Cr ions content saturate the fastest, while for the most heavily Cr ions doped structure 23 the slowest. As could be expected, the presented experimental results indicate lower stresses in epitaxial structures with lower doping levels. Moreover, for all samples, we have observed a reduction in the width of Cr³⁺ resonance lines after annealing compared to the width of these lines in the post-epitaxy layers. This observation may indicate that annealing caused a more unform distribution of paramagnetic centers and a some reduction in the local crystal lattice distortions of Cr,Mg:YAG layers.

The calculation results presented in Table 2 show also that an increase in the initial Cr₂O₃ concentration in the high temperature solution is generally followed by an increase in the intensity of Cr³⁺ resonance lines. An increase of the concentration of MgO with unchanged content of Cr₂O₃ leads to a decrease in the intensity of the lines associated with Cr³⁺ ions as observed for unannealed samples 9 and 13, and samples 16 and 19. The result was as expected, because the presence of more Mg²⁺ ions increases the concentration of Cr⁴⁺ ions, which are not visible in the ESR spectrum. Annealing in an oxidizing atmosphere should cause an increase in the amount of Cr⁴⁺ ions in the Cr,Mg:YAG crystal. The annealing process resulted in an increase of the values of absorption coefficient α at λ =1064 nm in the Cr,Mg:YAG/YAG epitaxial structures summarized in Tables 1 and 2 what clearly indicates a higher concentration of tetrahedrally coordinated Cr⁴⁺ ions in the annealed samples.

The shapes of the resonance lines associated with Cr³⁺ ions were changed after the annealing process, such as shown in Fig. 7 for structures 5 and 16. To evaluate changes of the content of Cr³⁺ ions in the layer after the annealing process we have used, as a determinant of changes, the ratio of the field under the lines of Cr³⁺ ions in the sample after the epitaxy S_E to the field under these lines for the annealed sample S_T. When the S_E/S_T field ratio was greater than 1 the concentration of Cr³⁺ ions in the layer decreased due to an increase in Cr⁴⁺ ions as indicated by the absorption measurements. Such a situation was observed for the structures numbered 5 and 9 and is well described in the literature for crystals, ceramics or epitaxial layers of Cr,Mg:YAG composition [17–23,25–28]. The change in valence from (3+) to (4+) and the localization switching of the chromium ion proceeds according to reactions 2 and 3 (see 2.4).

For all other structures crated by highly doped Cr and Mg YAG layers summarized in Table 2, the ratio of S_E/S_T fields is less than 1. Such a completely unexpected result indicates a significant increase of 20% to 75% in the content of Cr^3 +(octa) ions in the layer accompanied also by an increase in the amount of Cr⁴⁺ (tetra) ions confirmed by the absorption measurements. Of course, it should be noted, that the total population of chromium ions in the layer is constant. The concentration of Cr ions in the layers estimated for the chromium segregation coefficient k_Cr = 0.0065 [41] reached 2 × 10²⁰cm^-3 (sample 9) and 5 × 10²⁰cm^-3 (sample 23), respectively. The concentrations of Cr⁴⁺ ions in tetrahedral positions after oxidation are in the range of (1 - 3)x10¹⁸cm^-3 i.e. about 1% of the total amount of Cr ions. Thus, one can see for what quantity of octahedrally coordinated Cr³⁺ ions the .changes observed by the ESR method occur.

The observed effect could probably be explained by assuming that for higher starting concentrations of Cr₂O₃ some of the Cr³⁺ ions being incorporated into the layers are located at dodecahedral positions while Mg²⁺ ions enter octahedral ones [36]. Such a supposition is legitimized by the observations of Dong and Lu [36] and Lupei and others [37], who concluded that in garnet crystals including YAG, a few to several percent of ions occupying octahedral sites can switch positions with ions located in dodecahedral sites. During annealing, Mg²⁺ ions diffuse to dodecahedral sites and Cr³⁺ ions migrate to octahedral sites. The explanation is simple, but unfortunately not supported by any experimental indications related to the layer growth process.

Looking for an alternative explanation, we suppose that in the Cr,Mg:YAG layers, the content of Mg²⁺ ions may indirectly affect the observed changes in the amount of Cr³⁺ after thermal oxidation. The increase in the amount of Cr³⁺ ions after oxidation starts from structure 13 for which, relative to structure 9, the Cr/Mg value in the high-temperature solution decreases significantly from 8.88 to 2.5. In other words, the amount of MgO increases at a constant level and content of the other layer constituent oxides in the solution (see Table 1).

Ya. Zakharko and co-workers reported in the paper [21] that in Cr,Mg:YAG epitaxial layers deposited from the solution of a proper composition there exist the Cr²⁺ centres. The existence of Cr²⁺ ions (6-coordinate, octahedral) with ionic radii of about 80 pm induced by the doping of Mg²⁺ ions was confirmed by investigation of thermo-stimulated luminescence [21]. It is reasonable to assume that the high temperature oxidation can promote the process Cr²⁺ → Cr³⁺, which leads to increase of Cr³⁺ concentration analogously to the influence of oxidation on ions transformation from Cr²⁺ to Cr³⁺ in Cr:Mg₂SiO₄ crystals [38]. We believe that this strictly qualitative explanation regarding the increase of Cr³⁺ ion concentration can be accepted.

It should be mentioned that in Cr,Mg:YAG crystals the Mg²⁺ dopant can be accumulated due to creating of oxygen vacancies V_o^2- during growth without forming Cr⁴⁺ ions [39]. The oxygen vacancies are compensating the excess charge of Mg²⁺. Also, in the highly doped Cr,Mg:GGG epitaxial layers the transformation of chromium ions valence state Cr³⁺ → Cr⁴⁺ can be assured not only by charge compensation by Mg²⁺ ions but by creation of oxygen vacancies. The elimination of oxygen vacancies during high temperature oxidation results in transformation of Cr⁴⁺ (octa) to Cr³⁺ ions [40]. The increase in the amount of Cr^3 +(octa) ions after oxidation of Cr,Mg:GGG confirms the enhancement of luminescence intensity in the red spectral range [40]. We could not find comparable and convincing confirmation such in the case of the Cr,Mg:YAG layers. So, the supposition about the role of Cr²⁺ ions leading to the increase of the amount of Cr^{3 +}ions in octahedral sites during the oxidative annealing seems least controversial.

4. Conclusions

In this paper, to the best of our knowledge, we report for the first time on the effective use of ESR technique to monitor paramagnetic Cr³⁺ ions in epitaxial Cr,Mg:YAG saturable absorber. In order to obtain suitable material for the study, we have successfully grown, by means of LPE technique, the epitaxial Cr,Mg:YAG layers from the high-temperature solution with various concentrations of Cr₂O₃ and molar ratio Cr₂O₃ /MgO ranging from 10 to 2. The high quality Cr,Mg:YAG layers with thickness 35–85 µm were deposited on YAG substrates at temperatures in the range from 1000 °C to 1050 °C.

The optical transmission measurements of the layers confirmed the successful obtaining of saturable absorption material for which the value of the absorption coefficient α (λ = 1064 nm) > 5 cm^-1. Thus, the as-grown concentration of tetrahedrally coordinated Cr⁴⁺ ions exceeds 10¹⁸cm^-3 and is an order of magnitude higher as compared to typical Cr⁴⁺:YAG monocrystals. The high-temperature annealing (> 1100 ° C) in an oxidizing atmosphere led to an increase in the value of the absorption coefficient α (λ = 1064 nm) and the Cr⁴⁺ ions concentration in tetrahedral sites, respectively, by about fifty percent.

The ESR investigations allowed us to observe changes in the concentration of octahedrally coordinated Cr³⁺ ions in Cr,Mg:YAG layers caused by high-temperature oxidation. We have tried to clarify the unexpected increase in Cr³⁺ ion concentration observed after the oxidation annealing process, although it seems to us that a fully satisfactory explanation could not be found. As a result of presented here studies, we concluded that even in a well-known and studied material that has found its way into commercial laser technology, it is possible to encounter not quite-explained questions about the material's properties.