Mössbauer spectroscopy study of the superparamagnetism of ultrasmall $\epsilon$-Fe$_2$O$_3$ nanoparticles

The superparamagnetism of an ensemble of $\epsilon$-Fe$_2$O$_3$ nanoparticles with a mean size of 3.9 nm dispersed in a xerogel SiO$_2$ matrix is studied by the Mössbauer spectroscopy method. It is shown that most nanoparticles at room temperature are in the superparamagnetic (unblocked) state. As the temperature decreases, the progressive blocking of the magnetic moments of the particles occurs, which is manifested in the Mössbauer spectra as the transformation of the quadrupole doublet into a Zeeman sextet. The analysis of the relative intensity of the superparamagnetic (quadrupole doublet) and magnetically split (sextets) spectral components in the range of 4–300 K provides the particle size distribution, which is in agreement with the transmission electron microscopy data. The values of the effective magnetic anisotropy constants ( $K_{\mathrm{eff}}$) are determined, and the contribution of surface anisotropy ($K_S$) is estimated for particles of various sizes. It is shown that the quantity $K_{\mathrm{eff}}$ is inversely proportional to the particle size, which indicates the significant contribution of the surface to the magnetic state of the $\epsilon$-Fe$_2$O$_3$ nanoparticles with the size of several nanometers.