The magnetic properties of hematite $(\alpha -{\mathrm{Fe}}_2{\mathrm{O}}_3)$ 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 $T\gtrsim 100\mathrm{K}$ 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, ${\tau }_0=(6\mathrm{}\pm 4)\times {10}^{-11}\mathrm{s}$ and the magnetic anisotropy energy barrier, $E_{\mathrm{bm}}{/k=590\mathrm{}}_{-120}^{+150\mathrm{}}\mathrm{K}.$ A lower value of the pre-exponential factor, ${\tau }_0{=1.8\mathrm{}}_{-1.3}^{+3.2\mathrm{}}\times {10}^{-11}\mathrm{s},$ and a significantly lower anisotropy energy barrier $E_{\mathrm{bm}}^{\mathrm{magn}}/k=305\mathrm{}\pm 20\mathrm{K}$ 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 (111) 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.

Neutron scattering is used to characterize the magnetism of the vortices for the optimally doped high-temperature superconductor La _2-x Sr _x CuO ₄ ( x = 0.163) in an applied magnetic field. As temperature is reduced, low-frequency spin fluctuations first disappear with the loss of vortex mobility, but then reappear. We find that the vortex state can be regarded as an inhomogeneous mixture of a superconducting spin fluid and a material containing a nearly ordered antiferromagnet. These experiments show that as for many other properties of cuprate superconductors, the important underlying microscopic forces are magnetic.