Correlation of magnetic properties, morphology and structural parameters in Mn$_{0.5}$Zn$_{0.5}$Fe$_{2}$O$_{4}$ nanoparticles

The effect of structural and morphology parameters on the magnetic behavior of Mn$_{0.5}$Zn$_{0.5}$Fe$_{2}$O$_{4}$ Nanoparticles is presented. The samples were prepared by chemical co-precipitation method on mica substrates at temperatures between 60-90 \r{ }C. The particle sizes were obtained using AFM ($\sim $ 3-15 nm) and MFM. Magnetization measurements have been adjusted for a system of non-interacting nanoparticles with a volume distribution according to: $M(T,H,t)=\frac{m_o ^2H}{2T}\int\limits_0^{V_C } {dVf(V)} V^2$ Where m$_{o}$ is magnetization of the single particle, V$_{c}$ is critical volume and $f(V)$ is distribution size function. Blocking temperature T$_{B}$, magnetization of the single particle, anisotropy energy density and size distribution were obtained as function of the average particle size. The dependence of parameters such as M$_{s}$ and H$_{c}$ has been determines as function of the temperature and correlated with the particle sizes.