The effect of demagnetization on the susceptibility of single-domain particles and assemblies

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 this is true for macroscopic multi-domain magnetic materials, we explain why magnetic nanoparticles in a single-domain state do not suffer from this limitation. For single-domain particles, the differences between demagnetization factors along the principal axes are relevant and can influence susceptibility but do not limit it to an upper value as in the case for multi-domain particles. We experimentally validated this result on spherical nanoparticles with varying diameters (9–150 nm) and varying volume fractions (0.1–47 vol. %). In agreement with our predictions, we measure single-domain particle susceptibilities largely above 3, in fact up to more than 250. Moreover, contrary to an existing model for assemblies of particles, we find that the susceptibility of materials composed of non-interacting single-domain particles in a non-magnetic matrix scales linearly with the volume fraction of particles. This implies that high susceptibilities (>100) are achievable for nanoparticle-based composites and is relevant for the design of magnetically soft materials that are operational at MHz–GHz frequencies with negligible power losses.