Effect of Mn doping on magnetodielectric properties of polycrystalline BiFeO3 ceramics

Oxygen octahedra distortion‐induced multiferroic properties of Er and Zr co‐doped BiFeO3 nanoparticles

“…The tilt angle of FeO 6 octahedra along [1 1 1] direction can be obtained by using $$$$\begin{equation}cos{\theta _1} = \frac{{2 - 5co{s^2}{\varphi _1}}}{{2 + co{s^2}{\varphi _1}}}\end{equation}$$$$ $$$$\begin{equation}cos{\theta _2} = \frac{{1 - 4co{s^2}{\varphi _1}}}{3}\end{equation}$$$$where θ 1 and θ 2 denote the Fe–O–Fe bond angles correlated with a tilting angle ( φ ) of the FeO 6 octahedra 28 . The tilt angles ( φ ) of Bi 1− x Er x Fe 1− y Zr y O 3 ( x = .05, .1; y = 0, .02, .05) samples are found to be 12.5°, 13.1°, 14.6°, 16.3°, 24.1°, and 13.5°, respectively.…”

“…To understand further, the average value of the magnetic moment is determined for all the samples 28 . The magnetic moments of all the samples are determined to be .00821, .00174, .02094, .00666, .00642, and .00372 μ B /Fe, respectively.…”

“…where θ 1 and θ 2 denote the Fe-O-Fe bond angles correlated with a tilting angle (φ) of the FeO 6 octahedra. 28 The tilt angles (φ) of Bi 1−x Er x Fe 1−y Zr y O 3 (x = .05, .1; y = 0, .02, .05) samples are found to be 12.5 Here, the tilt angle increases with an increase in the codoping concentration of Er 3+ (via Bi site) and Zr 4+ (via Fe site), respectively. Kubel and Schmid 29 studied the crystal structure of BiFeO 3 and reported that the tilt angle of oxygen octahedra lies between 11 • and 14 • due to the rotation of the pair of oxygen octahedra within a unit cell.…”

“…Hence, the antiferromagnetic ordering To understand further, the average value of the magnetic moment is determined for all the samples. 28 The magnetic moments of all the samples are determined to be .00821, .00174, .02094, .00666, .00642, and .00372 μ B /Fe, respectively. The decrease in magnetic moments is due to the concentration of nonmagnetically active Zr 4+ ions in the Fe 3+ site, which perturbs the corkscrew spin arrangement and releases the latent magnetization, thereby deviating the macroscopic magnetization in the structure.…”