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We report on the observation of high-frequency collective magnetic excitations, ប Ϸ 1.1 meV, in hematite ͑␣-Fe 2 O 3 ͒ 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.

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