Optical trapping with optical magnetic field and photonic Hall effect forces

Optical trapping offers robust nanoscale control of matter but, to date, has been dominated by the interaction between a material's electric polarizability, α_e, and the electric part of light, therefore defined by electric-field intensity-gradient forces. Magnetic light-matter interactions, despite their potential to reshape optical trapping research, have remained experimentally unrealized. This paper addresses this long-standing deficiency by realizing optical magnetic field-associated trapping of high-index (i.e., Si) nanoparticles. Experiments, validated by our theoretical framework and Maxwell stress tensor calculations, reveal the essential role of a material's magnetic polarizability, α_m, and electric-magnetic scattering forces arising from the photonic Hall effect. This magnetic contribution allows exploration of stable trapping, distinct from purely electric-field control. Our findings open avenues for nanoparticle manipulation beyond conventional paradigms, enable previously unexamined optical matter formation driven by magnetic interactions, and suggest unexplored N-body effects and symmetry-breaking dynamics in optical matter systems.