Suppression of the magnetic transition in ultrasmall $\epsilon$-Fe$_2$O$_3$ nanoparticles: the size effect from nuclear forward scattering data

The features of the magnetic structure of ultrasmall $\epsilon$-Fe$_2$O$_3$ nanoparticles have been studied by the nuclear forward scattering technique using synchrotron radiation. The sample consists of isolated $\epsilon$-Fe$_2$O$_3$ nanoparticles with an average size of $\langle d\rangle = 3.8$ nm immobilized in a SiO$_2$ xerogel matrix. The time-domain spectra have been measured in the temperature range of $4$–$300$ K in zero external magnetic field and field $H = 4$ T applied in the longitudinal direction. The character of the change in the hyperfine field $H_{\text{hf}}$ as a function of the external magnetic field is the same in the entire temperature range: unlike large $\epsilon$-Fe$_2$O$_3$ particles, a monotonic increase in $H_{\text{hf}}$ is observed in the external field. These results indicate that there is no magnetic transition in the temperature range of $80$–$150$ K for ultrasmall (smaller than $ \approx 9$ nm) $\epsilon$-Fe$_2$O$_3$ particles, and the magnetic structure is noncollinear in the range of $4$–$300$ K.