Size effect of surface magnetic anisotropy in Cu₂O nanoparticles

The thermal deviation of the saturation magnetization of Cu₂O nanoparticles shows the size effect of a surface magnetic anisotropic energy gap, which is in contrast to the diamagnetism characteristic of bulk Cu₂O. The thermal deviation of the saturation magnetization exhibits an exponential variation, which is a clear departure from the Bloch T^3/2 law expected for isotropic systems, signaling the onset of magnetic anisotropy, presumably due to the high surface-to-volume ratio of the nanoparticles and the surface atoms which gives rise to polarized moments. We assume a uniaxial anisotropy and adopt the Heisenberg model for the H_a-aligned moment-carrying Cu₂O nanoparticles. It is known that the uniaxial anisotropy results in a gap in the energy dispersion. The surface magnetic anisotropic energy gap can be obtained from the fit and decreases with the reducing particle size.