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The magnetic properties of hematite (␣-Fe 2 O 3 ) particles with sizes of about 16 nm have been studied by use of Mössbauer spectroscopy, magnetization measurements, and neutron diffraction. The nanoparticles are weakly ferromagnetic at temperatures at least down to 5 K with a spontaneous magnetization that is only slightly higher than that of weakly ferromagnetic bulk hematite. At Tտ100 K the Mössbauer spectra contain a doublet, which is asymmetric due to magnetic relaxation in the presence of an electric field gradient in accordance with the Blume-Tjon model. Simultaneous fitting of series of Mössbauer spectra obtained at temperatures from 5 K to well above the superparamagnetic blocking temperature allowed the estimation of the pre-exponential factor in Néel's expression for the superparamagnetic relaxation time, 0 ϭ(6Ϯ4)ϫ10 Ϫ11 s and the magnetic anisotropy energy barrier, E bm /kϭ590 Ϫ120 ϩ150 K. A lower value of the pre-exponential factor, 0 ϭ1.8 Ϫ1.3 ϩ3.2 ϫ10 Ϫ11 s, and a significantly lower anisotropy energy barrier E bm magn /kϭ305Ϯ20 K was derived from simultaneous fitting to ac and dc magnetization curves. The difference in the observed energy barriers can be explained by the presence of two different modes of superparamagnetic relaxation which are characteristic of the weakly ferromagnetic phase. One mode involves a rotation of the sublattice magnetization directions in the basal ͑111͒ plane, which gives rise to superparamagnetic behavior in both Mössbauer spectroscopy and magnetization measurements. The other mode involves a fluctuation of the net magnetization direction out of the basal plane, which mainly affects the magnetization measurements.

SummaryWe present a short overview of the influence of inter-particle interactions on the properties of magnetic nanoparticles. Strong magnetic dipole interactions between ferromagnetic or ferrimagnetic particles, that would be superparamagnetic if isolated, can result in a collective state of nanoparticles. This collective state has many similarities to spin-glasses. In samples of aggregated magnetic nanoparticles, exchange interactions are often important and this can also lead to a strong suppression of superparamagnetic relaxation. The temperature dependence of the order parameter in samples of strongly interacting hematite nanoparticles or goethite grains is well described by a simple mean field model. Exchange interactions between nanoparticles with different orientations of the easy axes can also result in a rotation of the sub-lattice magnetization directions.

The magnetic dynamics of two differently treated samples of hematite nanoparticles from the same batch with a particle size of about 20 nm have been studied by Mössbauer spectroscopy. The dynamics of the first sample, in which the particles are coated and dispersed in water, is in accordance with the Néel expression for the superparamagnetic relaxation time of noninteracting particles. From a simultaneous analysis of a series of Mössbauer spectra, measured as a function of temperature, we obtain the median energy barrier K Bu V m /k ϭ570Ϯ100 K and the preexponential factor 0 ϭ1.3 Ϫ0.8 ϩ1.9 ϫ10 Ϫ10 s for a rotation of the sublattice magnetization directions in the rhombohedral ͑111͒ plane. The corresponding median superparamagnetic blocking temperature is about 150 K. The dynamics of the second, dry sample, in which the particles are uncoated and thus allowed to aggregate, is slowed down by interparticle interactions and a magnetically split spectrum is retained at room temperature. The temperature variation of the magnetic hyperfine field, corresponding to different quantiles in the hyperfine field distribution, can be consistently described by a mean field model for ''superferromagnetism'' in which the magnetic anisotropy is included. The coupling between the particles is due to exchange interactions and the interaction strength can be accounted for by just a few exchange bridges between surface atoms in neighboring crystallites.

The magnetic properties of nanoparticles of antiferromagnetic materials are reviewed. The magnetic structure is often similar to the bulk structure, but there are several examples of size-dependent magnetic structures. Owing to the small magnetic moments of antiferromagnetic nanoparticles, the commonly used analysis of magnetization curves above the superparamagnetic blocking temperature may give erroneous results, because the distribution in magnetic moments and the magnetic anisotropy are not taken into account. We discuss how the magnetic dynamics can be studied by use of magnetization measurements, Mössbauer spectroscopy and neutron scattering. Below the blocking temperature, the magnetic dynamics in nanoparticles is dominated by thermal excitations of the uniform mode. In antiferromagnetic nanoparticles, the frequency of this mode is much higher than in ferromagnetic and ferrimagnetic nanoparticles, but it depends crucially on the size of the uncompensated moment. Excitation of the uniform mode results in a socalled thermoinduced moment, because the two sublattices are not strictly antiparallel when this mode is excited. The magnetic dipole interaction between antiferromagnetic nanoparticles is usually negligible, and therefore such particles present a unique possibility to study exchange interactions between magnetic particles. The interactions can have a significant influence on both the magnetic dynamics and the magnetic structure. Nanoparticles can be attached with a common crystallographic orientation such that both the crystallographic and the magnetic order continue across the interfaces.

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