Spin-glass transition in porous spheres BiFeO$_3$

Magnetic properties of porous spheres BiFeO$_{3}$ have been studied at temperatures ranging from $2$ to $300$ K. A transition to cluster spin glass state has been detected in the region of about $100$ K. The presence of the transition is confirmed by nonlinear variation of coercive force and the appearance of exchange displacement of magnetic hysteresis loops at temperature below $100$ K. Temperature dependence of magnetization for zero-field cooled regime exhibit a maximum at some temperature $T_{m}$. The function $T_{m}(H)$ ($H$ is magneic field) changes in accordance with Almeida-Thouless line. The performed measurements of the frequency dependence of AC susceptibility confirm the behavior of spin glass with spin freezing temperature $T_{f} = 116$ K. The critical index $z\nu = 2.5$ agrees well with the mean-field theory $z\nu = 2.0$.