Demagnetisation effects in single-domain particles

According to the classical laws of magnetism, the shape of magnetically soft objects limits the effective susceptibility. For example, spherical soft magnets cannot display an effective susceptibility larger than 3. Although true for macroscopic multi-domain magnetic materials, we explain why magnetic nanoparticles in a single-domain state do not suffer from this limitation. We show that the differences between demagnetisation factors along principal axes are relevant and can influence susceptibility for single-domain particles, but do not limit the susceptibility as in the case for multi-domain particles. We validate this result experimentally on spherical nanoparticles with varying diameter (8 to 150 nm) and varying volume fraction (0.1 to 47 vol%). In agreement with our predictions, we measure susceptibilities largely above 3, in fact up to more than 250, for single-domain particles. Moreover, contrary to an existing model, we find that the susceptibility of non-interacting single-domain particles in a non-magnetic matrix scales simply linearly with the volume fraction of particles.