Magnetic anisotropy and quantized spin waves in hematite nanoparticles

We report on the observation of high-frequency collective magnetic excitations, $\hslash \omega \approx 1.1\mathrm{meV}$, in hematite $\left(\alpha \text{−}{\mathrm{Fe}}_2{\mathrm{O}}_3\right)$ nanoparticles. The neutron scattering experiments include measurements at temperatures in the range 6–300 K and applied fields up to 7.5 T as well as polarization analysis. We give an explanation for the field- and temperature dependence of the excitations, which are found to have strongly elliptical out-of-plane precession. The frequency of the excitations gives information on the magnetic anisotropy constants in the system. We have in this way determined the temperature dependence of the magnetic anisotropy, which is strongly related to the suppression of the Morin transition in nanoparticles of hematite. Further, the localization of the signal in both energy and momentum transfer brings evidence for finite-size quantization of spin waves in the system.

Figure 1

Inelastic neutron scattering data measured at $\kappa =1.50{\mathrm{\AA }}^{-1}$, close to ${\mathbf{\tau }}_{101}$. (a) Logarithmic plot of the data at zero applied field at the indicated temperatures. The arrows indicate the position of the high-frequency collective magnetic excitation. (b) Linear plot of the data in applied fields at $T=200\mathrm{K}$. The data are displaced by (a) a factor of 100 and (b) a constant. The solid lines represent fits as described in the text. The feature at 0.6 meV in (a) is a background signal as discussed in the text.

Figure 2

(a) Area $\left(A^{-}\right)$ and (b) position $\left({\epsilon }_0^{-}\right)$ of the inelastic peak as a function of temperature in zero field. (c) Area $\left(A^{-}\right)$ and (d) position $\left({\epsilon }_0^{-}\right)$ of the inelastic peak as a function of applied field at 200 K. The lines show fits as described in the text.

Figure 3

(a) Diffraction data on hematite at 200 K. (b) Constant-$\epsilon$-scan measured at $\epsilon =1.1\mathrm{meV}$ at 200 K. The solid lines are fits to the peaks multiplied with the Debye-Waller factor plus a sloping background. (c) Polarization data on hematite measured at 200 K in the non-spin-flip channel (엯) and the spin-flip channel (●). The straight lines represent fits as described in the text. The main panel shows the inelastic intensity measured at the antiferromagnetic reflection at $\kappa =1.50{\mathrm{\AA }}^{-1}$. The lower straight lines are the corresponding analyzer-turned background in the two channels. The inset shows diffraction data.

Figure 4

(Color online) The scattered inelastic intensity at 200 K and zero field as a function of scattering vector, $\kappa$ (horizontal) and energy transfer, $\hslash \omega$ (vertical). The bar to the right represents the color scale. The solid lines show the dispersion relation of bulk hematite with anisotropy gaps of 1.1 and 0.26 meV, as discussed in the text. The data have been normalized as described in Ref. 18.

Figure 5

Temperature dependence of ${\kappa }_1\left(K_1\right)$. The solid line represents our results for the hematite nanoparticles. The dashed line represents the value for bulk hematite (Ref. 8).

Figure 6

Illustration of the scattering geometry for a powder sample when $\mathbf{\kappa }={\mathbf{\tau }}_{\left(101\right)}$. The [001] direction makes an angle, $\alpha \sim 72°$, to the [101] direction.