Electron Magnetic Resonance of Diluted Solid Solutions of Gd3+ in BaTiO3

Electron magnetic resonance (EMR) spectra of gadolinium-doped barium titanate (BaTiO3) have been studied at room temperature for gadolinium concentrations between 0.20 and 2.00 mol%. The results suggest that the Gd3+ ions occupy substitutional sites, replacing the Ba2+ ion, that the electron magnetic resonance linewidth increases with increasing gadolinium concentration, and that the range of the exchange interaction between Gd3+ ions is about 0.98 nm, of the same order as that of the same ion in other host lattices, such as strontium titanate (SrTiO3), strontia (SrO), quicklime (CaO), magnesia (MgO) and zircon (ZrSiO4). The fact that the electron magnetic resonance linewidth of the Gd3+ ion increases, regularly and predictably, with Gd concentration, shows that the Gd3+ ion can be used as a probe to study, rapidly and non-destructively, the crystallinity and degradation of BaTiO3.


Introduction
Barium titanate (BaTiO 3 ) is a traditional piezoelectric material that has been proposed for use in the microelectronics industry after studies revealed that its properties can be changed by controlling grain size 1,2 and by doping with rare earth ions 3 .EMR spectroscopy is a convenient method for studying these impurities within the BaTiO 3 structure.In this work, we study the effect of gadolinium concentration on the EMR spectrum of Gd 3+ in polycrystalline BaTiO 3 .The importance of this investigation is twofold.First, once the effects of gadolinium concentration on the spectrum are known, it becomes possible to use EMR results to study, rapidly and non-destructively, the crystallinity and degradation of BaTiO 3 .Second, knowledge of the range of the exchange interaction between Gd 3+ ions is essential for a better understanding of the magnetic properties of gadolinium-doped barium titanate.

Crystal structure of strontium titanate
At room temperature, barium titanate (BaTiO 3 ) crystallizes in the perovskite structure 4 conforming to the space group P4mm(99).There are two distinct cation sites, one with twelve nearest neighbor oxygen ions, occupied by Ba atoms, and one with six nearest neighbor oxygen atoms, occupied by Ti atoms.

EMR of barium doped barium titanate
Analysis of the EMR spectrum of single-crystal gadolinium doped barium titanate 5 shows that trivalent gadolinium ions substitutionally replace strontium ions in the lattice.The spectrum can be fitted to the Hamiltonian

EMR of dilute solid solutions
The theory of dipolar broadening in diluted solid solutions was developed in Kittel & Abrahams 6 and extended in de Biasi & Fernandes 7 to take exchange interactions into account.The main results of the theory can be summarized as follows: (I) the lineshape is a truncated Lorentzian; (II) the peak-to-peak first derivative linewidth may be expressed as where ΔH 0 is the intrinsic linewidth, ΔH D is the dipolar broadening, C 1 is a constant and f E is the concentration of substitutional ions of the paramagnetic impurity not coupled by the exchange interaction, which can be expressed as where f is the impurity concentration, z(r C ) the number of cation sites included in a sphere of radius r C , and r C the effective range of the exchange interaction.(III) the intensity of the absorption line is where C 2 is a constant.The analysis above is based on the assumption of two ion populations, one with no exchange, which is responsible for the normal paramagnetic line, and another which, due to exchange, is either EPR silent (if the coupling is antiferromagnetic) or gives rise to a much broader line (if the coupling is ferromagnetic).

Sample preparation
The gadolinium doped samples used in this study were prepared from high purity BaTiO 3 (Aldrich, 99,9%) and Gd 2 O 3 (Reacton, 99.99%) powders by grinding them together and then firing the mixture for 24 h at 1200 °C in air.The gadolinium concentrations and reagent masses are shown in Table 1.Actual Gd concentrations were determined using the Inductively Coupled Plasma (ICP) technique.Room temperature X-ray diffraction patterns (Figure 1) of the samples matched, within experimental error, the pattern 8 of BaTiO 3 .No other phases were detected.

Magnetic resonance measurements
All magnetic resonance measurements were performed at room temperature and 9.50 GHz using a Varian E-12 spectrometer with 100 kHz field modulation.The microwave power was 10mW and the modulation amplitude was 1 mT.The magnetic field was calibrated with an NMR gaussmeter.
The spectrum of a sample of BaTiO 3 doped with 0.6 mol% Gd is shown in Figure 2. It closely matches the spectrum reported by Takeda & Watanabe 9 for powdered Gd-doped BaTiO 3 .In principle, linewidth data can be extracted from any of the lines in the powder spectrum.We chose the line indicated by an arrow in Figure 2. The results are shown in Table 2 for several gadolinium concentrations.

Discussion
The theoretical concentration dependence of the peak-to-peak linewidth ΔH pp , given by Equation 2, is shown in Figure 3 for ΔH 0 = 3.3 mT and eight different ranges of the exchange interaction.The values of r C and z(r C ) for the first eight coordinate spheres are listed in Table 3, where n is the number of the order of each coordinate sphere (n = 1 includes no neighboring sites, and so on).The values of z(r C ) are those appropriate to the lattice of BaTiO 3 ; the values of r C were calculated from the lattice constants at room temperature as measured by X-ray diffraction 8 , a = 0.3990 nm, c = 0.4035 nm.The experimental data are also shown in Table 1.Gadolinium concentrations and reagent masses for the samples used in this work.concentration, expressed by the parameter C 1 , from 4.5 for MgO to 750 for BaTiO 3 .In order to investigate the question further, we plot in Figure 4 the coefficient C 1 of Equation 2as a function of the difference Δr = r Gd −r h , where r Gd the ionic radius of Gd 3+ and r h is the ionic radius of the host lattice cation (the ionic radii were taken from Shannon 15 ) for the Gd-doped compounds shown in Table 4.The results suggest that C 1 changes, in a systematic way, with the ionic radius misfit Δr.

Conclusions
The study of the EMR spectrum of Gd 3+ in BaTiO 3 shows that the peak-to-peak linewidth increases with Gd concentration.This increase is attributed to dipolar broadening and is consistent with a model based on the exchange interaction and on the misfit between the ionic radii of the doping impurity and the host cation.
The fact that the linewidth increases in a predictable way with Gd concentration suggests that gadolinium can be used as a probe to study the crystallinity and degradation of barium titanate.3, to a range r C = 0.98 nm for the exchange interaction.
In Table 4 we show the pertinent parameters for the dipolar broadening ΔH D of the Gd 3+ FMR spectrum in BaTiO 3 and in other host lattices.One can see that there is a large range of values for the rate of increase of the dipolar broadening with g = 1.995, b 2,0 = −293,6 × 10 −4 cm −1 and b 4,0 = 4.0 × 10 −4 cm -1 .

Figure 3 .
Figure 3. Concentration dependence of the peak-to-peak linewidth, ΔH pp , in Gd-doped BaTiO 3 .The circles are experimental points; the curves represent results of calculations for eight different ranges of the exchange interaction.

Figure 3 .
Figure 3.The experimental results fit the theoretical curve for n = 7, which corresponds, according to Table3, to a range r C = 0.98 nm for the exchange interaction.In Table4we show the pertinent parameters for the dipolar broadening ΔH D of the Gd 3+ FMR spectrum in BaTiO 3 and in other host lattices.One can see that there is a large range of values for the rate of increase of the dipolar broadening with

Table 3 .
Values of r c and z(r c ) for BaTiO 3 .