## Nonlinear magnetic response of nanostructured BiFeO3

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Abstract
08-027 Gustavo Sanguino Dias Volnistem, E.A.(Maringá State University); Dias, G.S.(Maringá State University); Leonardo, J.M.(Maringá State University); Silva, D.M.(Maringá State University); Garcia, D.(Universidade Federal de São Carlos); Eiras, J.A.(Universidade Federal de São Carlos); Santos, I.A.(Maringa State University); Bismuth Ferrite (${\mathrm{BiFeO}}_{3}$) is a multiferroic magnetoelectric material with a rhomboedrally distorted perovskite structure ($AB{O}_{3}$) and $R3c$ space group that has attracted the attention of the scientific community due to elevated Currie and Nèel temperatures (${\mathrm{T}}_{\mathrm{c}}$ ~ 370 ${}^{o}C$and ${\mathrm{T}}_{\mathrm{n}}$ ~ 830 ${}^{o}C$) making $BiFe{O}_{3}$ a promising candidate for technological applications. However, the synthesis of single-phased $BiFe{O}_{3}$ remains a challenge considering the formation of undesirable phases such as $B{i}_{25}Fe{O}_{39}$ and $B{i}_{2}F{e}_{4}{O}_{9}$ resultant from elevated temperature and longtime applied during the synthesis process. Besides that, regarding the magnetic properties, the antiferromagnetic behavior is widely reported for $BiFe{O}_{3}$ at room temperature and generally attributed to the well-known spin cycloid ordering. In this sense, the size effect on the magnetic properties of $BiFe{O}_{3}$ became an important issue since unusual magnetic behaviors has being reported for nanoparticles synthesized by wet-chemical routes with size below cycloid period (64 nm). In this study, single-phased $BiFe{O}_{3}$ samples were synthesized by high-energy ball milling followed by fast-firing sintering and, subsequently, nanostructured through high-energy ball milling at cryogenic temperature (cryomilling). The cryomilling time and ball size used as grinding medium were correlated to structural, microstructural and magnetic properties of $BiFe{O}_{3}$ nanostructured samples. Williamson-Hall analysis reveal crystallite size reduction up to 32 nm and elevated microstrain values (~ 1.1%) after 2.5 h of cryomilling. Furthermore, an unusual nonlinear magnetic behavior was observed at room temperature presenting an increase of magnetic response as the crystallite size decrease, reaching its maximum for crystallite sizes close to half of $BiFe{O}_{3}$ cycloid size. In addition, a phenomenological study based on Langevin equation were done to evaluate how linear and nonlinear are correlated to the cryomilling settings.
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