Iron-oxygen vacancy defect association in polycrystalline iron-modified $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ antiferroelectrics: Multifrequency electron paramagnetic resonance and Newman superposition model analysis

By utilizing multifrequency electron paramagnetic resonance (EPR) spectroscopy, the iron functional center in ${\mathrm{Fe}}^{3+}$-modified polycrystalline lead zirconate $\left(\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3\right)$ was studied. The single phase polycrystalline sample remained orthorhombic and antiferroelectric down to $20\mathrm{K}$ as confirmed by high-resolution synchrotron powder diffraction. The ${\mathrm{Fe}}^{3+}$ ions were identified as substituting for ${\mathrm{Zr}}^{4+}$ at the B-site of the perovskite $\mathrm{AB}{\mathrm{O}}_3$ lattice. Similarly as found for ${\mathrm{Fe}}^{3+}:\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3$ [Meštrić et al., Phys. Rev. B 71, 134109 (2005)], the value of the fine-structure (FS) parameter $B_2^0$ is only consistent with a model in which a charged ${({\mathrm{Fe}}_{\mathrm{Zr}}^{\prime }–V_{\mathrm{O}}^{••})}^{•}$ defect associate is formed. In contrast to a well defined iron functional center in lead titanate $\left(\mathrm{Pb}\mathrm{Ti}{\mathrm{O}}_3\right)$ with FS parameters exhibiting variances of less than 3%, a strong broadening of the EPR powder pattern was observed in lead zirconate, indicating a much larger variance of FS parameters. It is suggested that the apparent broad distribution of fine-structure parameters arises from the system’s capability to realize different oxygen vacancy positions in the first coordination shell around the iron site. This proposed model of a small number of distinct iron-oxygen vacancy sites is supported by the observation that corresponding $B_2^0$ and orthorhombic $B_2^2$ FS parameters of these sites are anticorrelated, a property not expected for random distributions of fine-structure parameters.

Figure 1

Observed and calculated diffraction patterns of $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ obtained from high-resolution synchrotron powder diffraction at $20\mathrm{K}$ (top) together with its difference curve (bottom). Discrepancies between the observed and calculated diffraction pattern are due to real-structure effects caused by the domain structure of the compound. Wavelength $\lambda =0.0499256\mathrm{nm}$.

Figure 2

$240\mathrm{GHz}$ EPR spectra of ${\mathrm{Fe}}^{3+}:\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ (ii,iv), compared to numerical spectrum simulations (i,iii). (a) Energy level scheme assuming the external field along the $y$-axis $(\theta =\varphi =90°)$ with indicated “allowed” $(\Delta m_S=\pm 1)$ EPR transitions at $240\mathrm{GHz}$. (b) and (c) EPR spectra at 15 and $4.8\mathrm{K}$. (d) Orientation dependence of resonance lines for the polar angles $(\varphi ,\theta )$ relative to the external field orientation.

Figure 3

X-band EPR spectra of ${\mathrm{Fe}}^{3+}:\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ (iii), compared to numerical spectrum simulations. (i,v) Numerical spectrum simulations invoking extreme values of the FS parameters (cf. Table ). (ii) Numerical spectrum simulation with the sum over the six basic EPR spectra taken with equal weight. (iv) Numerical spectrum simulation assuming a single-site model with large FS-strain.

Figure 4

Schematic representation of the distribution of FS parameters used for spectral simulation. (a) and (b) Single-site model necessitating the use of large strain values (full width half maximum of a Gaussian distribution) of $\delta B_2^0=0.1\mathrm{GHz}$, $\delta B_2^2=0.8\mathrm{GHz}$ for the $X$-band (a) and $\delta B_2^0=1.8\mathrm{GHz}$, $\delta B_2^2=0.8\mathrm{GHz}$ for the $240\mathrm{GHz}$ case (b). (c) Multi-site model invoking a basis set of six different sites with identical strain values $\delta B_2^0=0.20\mathrm{GHz}$ and $\delta B_2^2=0.23\mathrm{GHz}$ used for simulation at all mw frequencies.

Figure 5

X-band EPR spectra of ${\mathrm{Fe}}^{3+}:\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ (ii) as compared to simulations assuming a six-site model. (iii) Correlation and (i) anti-correlation of the FS-parameters $B_2^0$ and $B_2^2$.

Figure 6

$240\mathrm{GHz}$ EPR spectra of ${\mathrm{Fe}}^{3+}:\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ (iii) as compared to simulations assuming a six-site model. (iv,v) Correlation and (iv) anticorrelation of the FS parameters $B_2^0$ and $B_2^2$. The “stick-spectra” (ii,v) show the superposition of all six constituent EPR spectra.

Figure 7

(a) Unit cell of $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$. (b) Oxygen octahedron of $\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$ selected for Newman superposition calculations.

Figure 8

Newman superposition calculations for $B_2^0$ (a) and (b) and $B_2^2$ (c) and (d) for ${\mathrm{Fe}}^{3+}:\mathrm{Pb}\mathrm{Zr}{\mathrm{O}}_3$. (a) and (c) Oxygen vacancy at position $\mathrm{O}{2}^{\prime }\left(1\right)$. (b) and (d) Oxygen vacancy at position $\mathrm{O}{2}^{\prime }\left(2\right)$. The solid horizontal lines represent the experimental mean values for $B_2^0$ and $B_2^2$, and the dashed horizontal lines mark the range of values for $B_2^0$ and $B_2^2$ spanned by the six constituent EPR spectra. The full line represents the Newman superposition calculations with an associated oxygen vacancy, and the dashed lines stand for calculations assuming a complete octahedron. The distance $d$ is defined according to a line connecting ${\mathrm{O}}^{2-}$ and the original ${\mathrm{Zr}}^{4+}$ position, with the positive direction towards the ${\mathrm{O}}^{2-}$ position.