Controlling the size of nanoparticles using a magnetic field: a sphere packing approach.

We present an analytical framework that predicts and controls nanoparticle size through external magnetic fields, uniting first-principles thermodynamics with a sphere packing approach. Calibrated to diamagnetic silver nanoparticles (20 nm at zero field and 5 nm at 250 mT), the model yields a closed-form relation between radius and field that reproduces the observed shift in most-probable size. Within the limits of classical capillarity and spherical demagnetization, the field lowers the nucleation barrier and drives the distribution toward smaller particles. Our results are robust for radii above [Formula: see text] nm ([Formula: see text] atoms). Below this scale non-extensive effects likely dominate, as discussed in detail in Supplementary Information. The approach generalizes to both diamagnetic and paramagnetic systems and the limitations expected for very small or ferromagnetically ordered nanoparticles are discussed.