Effect of the cobalt concentration on the magnetic properties of Co$_{1-x}$Mg$_{x}$Fe$_2$O$_4$ nanocrystals

Nanoparticles of Co$_{1-x}$Mg$_{x}$Fe$_2$O$_4$ with $x$ equal to $0, 0.2, 0.4, 0.6, 0.8$, and $1.0$ have been synthesized. For all values of x, they are nanocrystals with a cobalt ferrite structure and an average linear size $(56 \pm 3)$ nm. Based on the analysis of the Mössbauer effect spectra, the Co$^{2+}$ ions were shown to occupy only octahedral positions at all values of $x$. The experimentally obtained dependence of the nanoparticles magnetization on $x$ corresponds to the dependence calculated using the Mössbauer effect data, except for the sample with $x = 1.0$. The effective magnetic anisotropy constant estimated for $0$ K from the analysis of the coercive force temperature dependences decreases from $5.27 \times {{10}^{6}}$ at $x = 0$ to $1.29 \times {{10}^{6}}$ erg/cm$^3$ at $x = 0.8$ and drops sharply to $4 \times {{10}^{4}}$ erg/cm$^3$ at $x = 1.0$.