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Keywords:

  • EPR spectra;
  • rare-earth aluminum borates;
  • spin-Hamiltonian parameters;
  • superposition model

Abstract

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References

The EPR spectra of Gd3+ ion replacing Y3+ or rare-earth (RE) ions in aluminum borates REAl3(BO3)4 (RE = Y3+, Eu3+, Tm3+) have been studied. The spin-Hamiltonian parameters of an impurity Gd3+ ion in these crystals were determined. The basic atom coordinates in the structure of TmAl 3 (BO3)4 crystal have been established. Distortions of the Gd3+ ion nearest environment were analyzed within the framework of the superposition model of zero-field splitting. The inline image parameter change in isomorphic aluminum borates is shown to be determined by change of the angle between the Gd3+[BOND]O2− bond and the C3-axis.

1 Introduction

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References

The borates with general formula REM3(BO3)4, where RE are the trivalent rare-earth ions or yttrium and M = Al, Fe, Ga, Cr, attract extensive attention due to their distinctive luminescent and nonlinear optical properties. The ability of borates to accommodate a high concentration of RE dopants combined with good chemical and physical properties allow consideration of them as a promising and perspective media for solid-state lasers [1-3].

An opportunity to introduce into the borates the rare-earth ions along with ions of the iron group makes them attractive from the point of view of magnetism, since an interaction of two magnetic subsystems determines their magnetic and magnetoelectric properties [4-6].

The optical spectrum of RE ions and crystal-field analysis of aluminum borates have been reported [7-14]. A number of previously publications cover investigations of EPR spectra both of ions of the iron chemical group [15-19] and rare-earth ions [9, 20-22].

Since an impurity ion introduced into a crystal determines its physical properties, the interest in the energy states, the location of impurities and crystal structure distortions that they create is the subject of many including current studies [23, 24].

Electron paramagnetic resonance (EPR) is a very informative method to determine the symmetry of the active center, its charge state, direction of the magnetic axis and, in some cases, the location of the compensator if an impurity ion charge does not coincide with the charge of the replaced ion of the host lattice.

However, even for isovalent replacement an impurity ion distorts the local environment. Such distortions can be determined by analyzing the spectrum changes with axial and all-round pressure [25] or by using an empirical superposition model, which has shown its adequacy in the analysis of local distortions created by impurity ions [26-32].

In the present work, a comparison of the EPR spectra parameters in the isomorphic Gd3+ ion-doped YAl3(BO3)4, EuAl3(BO3)4, and TmAl3(BO3)4 crystals has been carried out. The analysis of spectra was performed within a superposition model of zero-field splitting using the crystallographic measurements data.

2 Crystal structure and details of the experiment

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References

The rare-earth aluminum borates REAl3(BO3)4 crystallize in the huntite structure of CaMg3(BO3)4 with the spatial group R32.

The REAl3(BO3)4 crystals with the impurity of 0.2% Gd3+ have been obtained from a solution in a melt as a result of spontaneous crystallization. Potassium molybdate K2Mo3O10 was used as a solvent. The preliminary synthesized aluminum borate was added in a solvent. Moreover, an excess quantity of 10% B2O3 and corresponding quantity of Gd2O3 were added into the mixture. Growth of a crystal was realized by cooling of a solution from 1150 to 900 °C at a speed of 2 °C h−1, followed by a slow cooling of the furnace to room temperature. The transparent, well-faceted crystals with sizes of 2–3 mm were obtained.

The lattice parameters and ion coordinates in the structures of YAl3(BO3)4 and EuAl3(BO3)4 crystals were established in Refs. [33, 34]. In this work, X-ray diffraction measurements of the structure of TmAl3(BO3)4 were first performed. The basic atom coordinates in the structure of TmAl3(BO3)4 crystal are shown in Table 1. The parameters of trigonal cell for three crystals are shown in Table 2. Figure 1 shows the crystal structure of TmAl3(BO3)4 in a plane perpendicular to the C3-axis. In Fig. 1, the nearest environment of the rare-earth ion is marked off by solid lines, and in Fig. 2 it is shown in more detail.

Table 1. Basic atom coordinates in the structure of TmAl3(BO3)4 crystal
atomx/ay/bz/c
Tm000
Al0.55576 (30)00
B1000.5
B20.45216 (122)00.5
O10.85364 (50)00.5
O20.58726 (76)00.5
O30.43925 (55)0.13745 (49)0.52308 (69)
Table 2. The spin-Hamiltonian parameters (1) describing the EPR spectra of Gd ion3+ in the EuAl3(BO3)4, YAl3(BO3)4, and TmAl3(BO3)4 crystals. The inline image parameters are specified in units of 10−4 cm−1 at room temperature
crystalg||ginline imageinline imageinline image
EuAl3(BO3)41.981 ± 0.0021.982 ± 0.005280.18 ± 0.12−12.95 ± 0.080.61 ± 0.12
YAl3(BO3)41.989 ± 0.0021.986 ± 0.005386.15 ± 0.11−12.95 ± 0.070.35 ± 0.11
TmAl3(BO3)1.986 ± 0.0021.989 ± 0.005431.1 ± 0.13−12.08 ± 0.080.41 ± 0.12
image

Figure 1. Crystal structure of the TmAl3(BO3)4 crystal. The C3-axis is perpendicular to the plane of the figure.

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image

Figure 2. Rare-earth ion (R) surrounded by nearest O2− ligands in the structure of aluminum borates.

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The unit cell of RE-aluminum borates contains Z = 3 formula units. Trigonal prisms, octahedra, and triangles formed by oxygen ions are coordination polyhedra of RE3+, Al3+, and B3+ ions, respectively. RE ions are located on the rotary C3-axis in slightly deformed prisms, in which the top and bottom triangles are slightly turned from each other. The Al3+ ions occupy the positions in oxygen octahedra that, being coupled by edges, form the twisted columns elongated along the C3-axis. The B1 and B2 atoms are located in oxygen triangles of two types: B1 atoms are in triangles that are perpendicular to the triple axes and alternate with Y-prisms, and B2 atoms are in the triangles that connect the twisted columns from Al-octahedra among themselves.

The X-ray diffraction measurements were carried out at a laboratory Bragg–Brentano diffractometer (X'Pert Pro Alpha1 MPD, Panalytical) equipped with a monochromator and position-sensitive linear detector (the setup has been described in Ref. [35]). The measurements were performed at temperature of 26 ± 2 °C. Crystallographic characterization and structure refinement were done with help of Full prof. 2k program [36]. In refinements, a pseudo-Voigt profile-shape function was assumed. The following parameters were refined: scale factor, lattice parameters, atomic position, isotropic atomic displacement parameters, peak shape parameters, systematic lineshift parameters. The background was then set manually.

For the EPR spectra studies, an X-band Bruker spectrometer was used. The measurements have been carried out in a temperature range of 300–5 K.

3 Fine structure of EPR spectrum

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References

The gadolinium trivalent ion has a half-filled electronic shell with a 4f7 configuration. The ground 8S7/2 multiplet is characterized by an absence of orbital moment (L = 0) and the spin moment value of S = 7/2. The eightfold degenerate level of a free trivalent gadolinium ion being placed in trigonal crystal field of europium-aluminum borate is split into four Kramers doublets. The EPR spectrum consists of seven absorption lines resulting from both intradoublet and interdoublet transitions (Fig. 3). In the spectrum of Gd3+ ion in EuAl3(BO3)4 the satellites arranged symmetrically relative to the spectrum center are clearly observed. Lines of this kind, but less pronounced, are visible in the YAl3(BO3)4 crystal. It is entirely possible that the additional absorption lines are connected with the spin–spin interaction of Gd3+ ions placed in the chains along the C3-axis.

image

Figure 3. EPR spectra of Gd3+ ion in the EuAl3(BO3)4,YAl3(BO3)4, and TmAl3(BO3)4 crystals. Magnetic field is directed along the C3-axis.

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In the works [21, 22] it was shown that the Gd3+ ion replaces Y3+ and Eu3+ ions in the YAl3(BO3)4 and EuAl3(BO3)4 crystals. In the present work, the angular dependence of the EPR spectrum of Gd3+ ion in the TmAl3(BO3)4 crystal was measured in two planes. Figure 4 presents the position of spectrum lines in the plane parallel to the C3-axis from B||C3 to BC3. In the plane perpendicular to the C3-axis the position of the absorptions lines in the magnetic field does not change. The data obtained allow us to infer that Gd3+ ion replaces Tm3+ ion and occupies a site with D3 symmetry as well as in the YAl3(BO3)4 and EuAl3(BO3)4 crystals.

image

Figure 4. Angular dependence of EPR spectrum of Gd3+ ion in the TmAl3(BO3)4 crystal at 40 K. The zero value of angle corresponds to the C3-axis.

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The spin-Hamiltonian corresponding to this symmetry is as follows [36]:

  • display math(1)

where β is the Bohr magneton, B the vector of magnetic induction, inline image the operator of electron spin, inline image the Stevens spin operators and inline image the defined parameters. The calculation of the spin-Hamiltonian parameters was performed using the program described in Ref. [20] and packet Easy Spin [39], which has given the coinciding results presented in Table 2.

As is seen in Table 2, the g-factor is practically isotropic and the spectrum is very close to the axial one. The inline image, inline image, and inline image parameters determine the initial splitting of the spectrum. Since the inline image, inline image, and inline image parameters of the spin-Hamiltonian do not significantly improve the calculation results, to describe the EPR spectrum one can be limited only by three axial parameters of the spin-Hamiltonian. The inline image parameter determining the splitting of spectrum is positive in all crystals studied. The sign of the inline image parameter was determined by comparison of the spectra obtained at room and helium temperatures. Thus, in all three crystals the low-lying state is the ±1/2 doublet, and the energy levels with quantum numbers of ±3/2, ±5/2, and ±7/2 are located at consecutively higher energy.

A decrease of temperature from 290 K down to 5 K leads to an increase of splitting in all three crystals. Figure 5 shows the change of inline image as a function of temperature for the investigated crystals. In Ref. [21], the influence of pressure on the EPR spectra of gadolinium trivalent ion in the EuAl3(BO3)4 crystal is studied. The inline image parameter was shown to increase with increasing pressure (inline image). Thus, a compression of the crystal caused by both pressure and a decrease of temperature increases the splitting of ground state.

image

Figure 5. Dependence of the inline image parameter on temperature in the EuAl3(BO3)4, YAl3(BO3)4, and TmAl3(BO3)4 crystals.

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4 Discussion

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References

Let us discuss the results obtained using the superposition model (SM) of zero-field splitting [26]. The SM model is based on the assumption that a crystal field can be expressed as the sum of axial-symmetric contributions of all the nearest ligands surrounding the paramagnetic ion.

For ions being in the S-state, the rank-two spin-Hamiltonian parameters can be presented in the following form:

  • display math(2)

where inline image is the coordinate factor defined by an angular coordinates of ligands, t2 the exponent, inline image the internal parameter and R0 the reference value defined as a result of the analysis of previously performed studies, in which the inline image parameter was determined.

In the investigated crystals, the impurity Gd3+ ion is surrounded by six O2− ions located at equal distances in the vertex of prism. Then, the expression for inline image has the form

  • display math(3)

where for O2− ligands with coordination number of six, according to Ref. [37], inline image(R0) = −(2000 ± 500) × 10−4 cm−1; t2 = 2.5 ± 1.5, and R0 = 2.699 Å; θ is the angle between Gd3+[BOND]O2− bond and the C3-axis.

Since the Gd3+ ion substitutes for RE3+ ions, the distance to the ligands, which in the crystals studied will change, can be estimated using the formula of R = Rh + (ri − rh)/2, where ri is the ionic radius of an impurity ion, rh the ionic radius of the basic lattice ion, and Rh the RE[BOND]O distance [37].

According to Ref. [38], the ionic radii of Gd3+, Eu3+, Y3+, and Tm3+ ions are equal to 1.078, 1.087, 1.040, and 1.02 Å, respectively. Table 3 presents the unit-cell parameters for three crystals and distances between rare-earth ions and nearest O2− ligand in the host lattice as well as the same data for lattice distorted by an impurity Gd3+ ion and the bond angles. Figure 2 shows a rare-earth ion (R) surrounded by the nearest oxygen ligands in the structure of aluminum borates.

Table 3. The unit-cell parameters (a, b, c), the distances between rare-earth ion and nearest O2− ion and the bond angles in the host lattice (R[BOND]O3, θ) and in the lattice distorted by Gd3+ ion ((R[BOND]O3)1, θ1). The references indicated in the last column refer to the data for undoped crystals
crystala, bcR[BOND]O3θ(R[BOND]O3)1θ1ΔθRefs.
EuAl3(BO3)49.31225 (7)7.27477 (6)2.52453.452.51955.532.08[34]
YAl3(BO3)49.2957.2432.32154.0892.34055.601.51[33]
TmAl3(BO3)49.27166 (7)7.21394 (7)2.40955.2982.43855.870.57this work

As is seen in Table 3, in the EuAl3(BO3)4 and YAl3(BO3)4 crystals the bond angles in the undistorted lattice are less than 54.74°, wherein (3 cos2θ − 1) = 0. According to expression (3), the sign of the inline image parameter must be negative for the EuAl3(BO3)4 and YAl3(BO3)4. This does not correlate with the experimental results. In order that the calculated inline image parameters coincide with the experimental data (Table 2), the bond angles should be changed, as is shown in Table 3. The distances between the rare-earth ion and nearest O2− ion and the bond angles in the host lattice (R[BOND]O3, θ) and in the lattice distorted by an impurity Gd3+ ion ((R[BOND]O3)1, θ1) are presented in Table 3. The parameters of the model presented in Eq. (3) have a significant spread of values that determines the accuracy of the calculation of the bond angle. The exponent values are less important than the internal parameter value. The total error in determination of the bond angle is 0.6°.

Thus, a change of the bond angle contributes mainly to the transformation of value and sign of inline image parameter. To a smaller degree the bond length influences the inline image parameter value.

An increase of the inline image parameter with decreasing temperature and increasing pressure testifies that the anisotropies of both thermal expansion coefficient (α) and compressibility of crystals (σ) are qualitatively identical, namely, α|| > α and σ|| > σ. The temperature and pressure changes of the inline image parameter result from geometrical changes of a nearest environment of an impurity Gd3+ ion. Thus external pressure, temperature and rare-earth ions replacement in isomorphic row have an identical independent effect, notably angle magnification between the C3-axis and the Gd3+[BOND]O2− direction influences on the initial splitting decreasing.

5 Conclusions

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References

In the studied aluminum borates EuAl3(BO3)4, YAl3(BO3)4, and TmAl3(BO3)4, the rare-earth ions being in the lattice with D3 symmetry are substituted for the paramagnetic Gd3+ ion. In the given work, the EPR spectra of an impurity Gd3+ ion in the three isomorphic crystals are presented and the spin-Hamiltonian parameters describing the spectra are determined. X-ray diffraction measurements of the TmAl3(BO3)4 crystal structure have been first performed in addition to the known crystallographic data [33, 34] for the EuAl3(BO3)4 and YAl3(BO3)4 crystals.

The results of complex studies of the initial splitting of Gd3+ ion as a function of temperature and pressure as well as the sign of the basic inline image parameter have allowed us to conclude that the impurity Gd3+ ion distorts the nearest environment consisting of oxygen ions in such a way that the bond angle θ becomes larger than the value of 54.74° in all three crystals. In order to estimate the magnitude of distortions the superposition model of zero-field splitting for ions in the S-state was applied. It should be noted that this approach qualitatively reflects the experimental situation; however a quantitative evaluation of distortions because of the great spread of the model parameters is not very high.

References

  1. Top of page
  2. Abstract
  3. 1 Introduction
  4. 2 Crystal structure and details of the experiment
  5. 3 Fine structure of EPR spectrum
  6. 4 Discussion
  7. 5 Conclusions
  8. References