Magnetism of BiFe0.9Cr0.1O3 studied experimentally and with Monte Carlo simulations

Abstract

The sol-gel technique is used in this paper to prepare Cr-doped $\mathrm{BiFe}{\mathrm{O}}_{3}$. The magnetism of $\mathrm{Bi}{\mathrm{Fe}}_{1\text{\ensuremath{-}}\mathrm{x}}{\mathrm{Cr}}_{\mathrm{x}}{\mathrm{O}}_{3}$ with a distorted rhombohedral perovskite structure has been studied for $x=0.1$. X-ray diffraction analysis reveals that the sample is rhombohedral with the space group ${R}_{3}C$ and contains some impurity phases. The M\"ossbauer spectra at 300 and 500 K are used to determine the magnetic and impurity phase proportion as well as the valence state, electric field gradient, internal magnetic field, and electron cloud distribution of ${\mathrm{Fe}}^{3+}\mathrm{ions}$ in $\mathrm{Bi}{\mathrm{Fe}}_{0.9}{\mathrm{Cr}}_{0.1}{\mathrm{O}}_{3}$. The magnetic properties of $\mathrm{Bi}{\mathrm{Fe}}_{0.9}{\mathrm{Cr}}_{0.1}{\mathrm{O}}_{3}$ are complex. Through the zero-field-cooled/field-cooled magnetization curve, the magnetism of $\mathrm{Bi}{\mathrm{Fe}}_{0.9}{\mathrm{Cr}}_{0.1}{\mathrm{O}}_{3}$ is analyzed. According to the first-order differential of magnetization to temperature, the N\'eel temperature is determined to be $\ensuremath{\sim}134\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. It is speculated that a partial relaxation structure may exist in the system. Then the Heisenberg model simulation and experimental data are approximated using the particle swarm optimization algorithm to further analyze the magnetism and calculate the more precise phase transformation temperature. It has been determined that the exchange constants for cubic structure and relaxation structure are ${J}_{\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Cr}}=6.75\phantom{\rule{0.16em}{0ex}}\mathrm{meV}, {J}_{\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Fe}}=\ensuremath{-}6.13\phantom{\rule{0.16em}{0ex}}\mathrm{meV}, {J}_{\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Fe}}^{{}^{\ensuremath{'}}}=\ensuremath{-}1.16\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$, and ${J}_{\mathrm{Fe}\text{\ensuremath{-}}\mathrm{Cr}}^{{}^{\ensuremath{'}}}=\ensuremath{-}1.54\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$. The cubic and relaxation structures contribute 0.71 and 0.29 to magnetism, respectively. According to the Heisenberg model, the Curie temperature should be $\ensuremath{\sim}606\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, and the N\'eel temperature should be $\ensuremath{\sim}116\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The ratio of the Curie temperature to the Weiss constant is significantly >5, implying that the entire spin system is in a state of high frustration.