Neutron study of magnetic excitations in $8\text{−}\mathrm{nm}$ $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles

By use of inelastic neutron scattering we have studied magnetic fluctuations in $8\text{−}\mathrm{nm}$ particles of antiferromagnetic $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ (hematite) as a function of temperature and applied magnetic fields. The fluctuations are dominated by uniform excitations. Studies have been performed on both coated (noninteracting) and uncoated (interacting) particles. We have estimated the magnetic anisotropy energy and found that the data are in good agreement with the value obtained from Mössbauer spectroscopy. The energy ${\epsilon }_0$ of the uniform excitations depends strongly on the uncompensated moment, which is caused by finite-size effects, and we have estimated the size of this moment from the experimental neutron data. The field dependence of ${\epsilon }_0$ for the interacting nanoparticles differs strongly from that of the noninteracting nanoparticles, and this is a result of the influence of exchange interaction between the particles.

Figure 1

TEM images of the $8\text{−}\mathrm{nm}$ $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles. (a) The noninteracting (coated) particles and (b) the interacting (noncoated) particles. The coating is seen as an amorphous layer around the particles.

Figure 2

Inelastic neutron data for $8\text{−}\mathrm{nm}$ $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles. (a), (b) Energy scans with ${\epsilon }_f=3.7\mathrm{meV}$ at constant scattering vector ${\tau }_{003}$ at 10 and $150\mathrm{K}$, respectively, for the noninteracting nanoparticles. Similar data for the interacting nanoparticles are shown in (c) and (d). The thin line represents the fit to the model as explained in the text and the bold line in (b) and (d) shows the contribution from just the collective magnetic excitations. The asymmetric tails is at $\epsilon <0.05\mathrm{meV}$ are a part of the background, as explained in Sec. 3. In each series of measurements, the spectra obtained at the lowest temperatures and zero applied field have been normalized to the same maximum intensity at ${\epsilon }_0=0\mathrm{meV}$.

Figure 3

Inelastic neutron data for the $8\text{−}\mathrm{nm}$ $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles. (a), (b) Energy scans with ${\epsilon }_f=3.7\mathrm{meV}$ at constant scattering vector ${\tau }_{003}$ at $100\mathrm{K}$ at an applied magnetic field of 0 and $6\mathrm{T}$, respectively, for the noninteracting nanoparticles. Similar data for the interacting nanoparticles are shown in (c) and (d). The thin line represents the fitted model as explained in the text, and the contribution from the just collective magnetic excitations is shown by the bold line.

Figure 4

Mössbauer spectra of the $8\text{−}\mathrm{nm}$ $\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3$ nanoparticles at various temperatures from $18\mathrm{K}$ to room temperature. (a) Data for the noninteracting particles and (b) data for the interacting particles.

Figure 5

The area fraction as a function of (a) temperature and (b) field at $T=100\mathrm{K}$. The fit to Eq. (9), which only applies at low temperatures, is shown by the solid line in (a). The data points for the interacting nanoparticles in (b) have been multiplied by 5 for clarity.

Figure 6

The average observed hyperfine field $⟨B_{\mathrm{obs}}⟩$ obtained from the Mössbauer data, as a function of temperature. The lines are linear fits to the data.

Figure 7

Position of the inelastic peaks as a function of (a) temperature and (b) field at $T=100\mathrm{K}$. The solid lines in (a) show the linear extrapolation to $T=0\mathrm{K}$ and in (b) the dotted line represents Eq. (8).

Figure 8

Width of the inelastic peaks as a function of (a) temperature and (b) field at $T=100\mathrm{K}$.