Influence of chromium concentration on the electron magnetic resonance linewidth of Cr3+ in SrTiO3

Influence of chromium concentration on the electron magnetic resonance linewidth of Cr³⁺ in SrTiO₃

Ronaldo Sergio de Biasi^I,*; Maria Lúcia Netto Grillo^II

^ISeção de Engenharia Mecânica e de Materiais, Instituto Militar de Engenharia - IME, CEP 22290-270, Rio de Janeiro, RJ, Brazil

^IIInstituto de Física, Universidade do Estado do Rio de Janeiro - UERJ, CEP 20550-013, Rio de Janeiro, RJ, Brazil

ABSTRACT

Electron magnetic resonance (EMR) spectra of Cr³⁺ ions in samples of chromium-doped strontium titanate (SrTiO₃) have been studied at room temperature for chromium concentrations between 0.20 and 1.00 mol%. According to previous studies, chromium substitutes Ti⁴⁺ sites in the lattice and its preferred valence state is Cr⁴⁺, which is EMR silent in the X-band, but the trivalent state can be produced by illumination or codoping with Nb. In the present work, the codoping method was used; the results show the electron magnetic resonance linewidth of the Cr³⁺ spectrum increases with increasing chromium concentration and that the range of the exchange interaction between Cr³⁺ ions is about 0.96 nm.

Keywords: ceramics, electron magnetic resonance, strontium titanate, chromium, niobium

1. Introduction

Strontium titanate (SrTiO₃) is a high dielectric constant ceramic material with several industrial applications^1-4, such as memory devices, oxygen sensors, electro-optical devices and flexible dielectric waveguides, whose electrical properties can be changed by the presence of transition metal and rare earth impurities such as iron and gadolinium^5,6. EMR spectroscopy is a convenient method for studying these impurities within the SrTiO₃ structure. In this work, we study the effect of chromium concentration on the EMR spectrum of Cr³⁺ in polycrystalline SrTiO₃ codoped with chromium and niobium. The importance of this investigation is twofold. First, once the effects of chromium concentration on the spectrum are known, it becomes possible to use EMR results to study the effects of other impurities^7-9 on the valence state of the chromium ion in SrTiO₃. Second, knowledge of the range of the exchange interaction between Cr³⁺ ions contributes to a better understanding of the electrical and magnetic properties^10,11 of doped strontium titanate.

2. Background

2.1. Crystal structure of strontium titanate

Strontium titanate (SrTiO₃) crystallizes in the perovskite structure¹² conforming to the space group There are two distinct cation sites, one with twelve nearest-neighbor oxygen ions, occupied by Sr atoms, and one with six nearest-neighbor oxygen atoms, occupied by Ti atoms.

2.2. EMR of chromium-doped strontium titanate

Analysis of the EMR spectrum of single-crystal chromium-doped strontium titanate¹³ shows that Cr⁴⁺ ions substitutionally replace titanium ions in the lattice. Cr⁴⁺ ions cannot be observed at X band due to a high crystal field splitting, but the trivalent state can be produced under illumination¹³ or by codoping with Nb^[14]. The spectrum of Cr³⁺ under illumination consists of a central line (g ≈ 1.978) due to ⁵⁰Cr, ⁵²Cr and ⁵⁴Cr and a hyperfine quartet due to the ⁵³Cr isotope¹³.

2.3. EMR of dilute solid solutions

The theory of dipolar broadening in diluted solid solutions was developed in Kittel and Abrahams¹⁵ and extended in de Biasi and Fernandes¹⁶ to take exchange interactions into account. The main results of the theory can be summarized as follows:

The lineshape is a truncated Lorentzian;

The peak-to-peak first derivative linewidth may be expressed as

where ΔH₀ is the intrinsic linewidth, ΔH_d is the dipolar broadening, C₁ 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.

The intensity of the absorption line is

where C₂ 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).

3. Experimental Procedure and Results

3.1. Sample preparation

The chromium/niobium doped samples used in this study were prepared from high-purity SrTiO₃ (Aldrich, 99%), Cr₂O₃ (Aldrich, 99.9%) and Nb₂O₅ (Aldrich, 99.99%) powders by grinding them together and then firing the mixture for 24 hours at 1200 ºC in air. Since niobium was intended to act as an electron donor, we used equal molar concentrations of Cr and Nb in each sample. The chromium concentrations and reagent masses are shown in Table 1. Room-temperature X-ray diffraction patterns (Figure 1) of the samples matched, within experimental error, the spectrum¹⁷ of SrTiO₃. No other phases were detected.

3.2. 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 200 mW and the modulation amplitude was 0.1 mT. The magnetic field was calibrated with an NMR gaussmeter.

Spectra of samples of SrTiO₃ doped with 0.2 and 1.0 mol% Cr and Nb are shown in Figures 2 and 3. Only the line due to the Cr³⁺ -1/2 → 1/2 transition is clearly seen; the g-value of this line is 1.978 ± 0.001, in good agreement with the value reported in Müller¹³. The lines due to the other transitions, like the Gd³⁺ lines in the same compound¹⁸, are broader because of lattice strain and are responsible, together with Cr³⁺-Cr³⁺ pairs within the range of the exchange interaction, for the feature near 0.34 T in Figures 2 and 3. Linewidth and intensity data for the Cr³⁺ -1/2 → 1/2 transition are shown in Table 2 for several chromium concentrations.

4. Discussion

The theoretical concentration dependence of the peak-to-peak linewidth ΔH_pp, given by Equation 1, is shown in Figure 4 for ΔH₀ = 0.6 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 SrTiO₃; the values of r_c were calculated from the lattice constant at room temperature as measured by X-ray diffraction¹⁷, a_o = 0.3901 nm. The experimental data are also shown in Figure 4. The experimental results fit the theoretical curve for n = 7, which corresponds, according to Table 3, to a range r_c = 0.96 ± 0.10 nm for the exchange interaction. Figure 5 shows the theoretical (Equation 3) and experimental (Table 2) intensity data, estimated using the expression I = A(ΔH_pp)², where I is the line intensity, A is the line amplitude and ΔH_pp is the peak-to-peak linewidth. The vertical scale is arbitrary and was chosen so as to provide the best fit of the experimental points to the theoretical curve for n = 7, or z(r_c) = 80. The agreement was found to be very good.

5. Conclusions

Since the linewidth and intensity of the EMR spectrum of Cr³⁺ in SrTiO₃ increase with Cr concentration and the experimental results are fitted well by a theoretical model, niobium codoping seems to be a reliable way to change the valence state of the chromium ions from Cr⁴⁺ to Cr³⁺ in substitutional titanium sites of chromium-doped strontium titanate. The fact that the range of the exchange interaction of Cr³⁺ in SrTiO₃ is much larger than in Y₂O₃^[19] (0.96 and 0.64 nm, respectively) is probably due to a more favorable bonding angle in SrTiO₃, that favors indirect exchange²⁰.

Acknowledgements

The authors thank CNPq and CAPES for financial support.

Received: July 6, 2011

Revised: May 8, 2012

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Publication Dates

• Publication in this collection
  31 May 2012
• Date of issue
  June 2012

History

• Received
  06 July 2011
• Accepted
  08 May 2012