Spin waves across three-dimensional, close-packed nanoparticles.

Inelastic neutron scattering is utilized to directly measure inter-nanoparticle spin waves, or magnons, which arise from the magnetic coupling between 8.4 nm ferrite nanoparticles that are self-assembled into a close-packed lattice, yet are physically separated by oleic acid surfactant. The resulting dispersion curve yields a physically-reasonable, non-negative energy gap only when the effective is reduced by the inter-particle spacing. This renormalization strongly indicates that the dispersion is a collective excitation between the nanoparticles, rather than originating from within individual nanoparticles. Additionally, the observed magnons are dispersive, respond to an applied magnetic field, and display the expected temperature-dependent Bose population factor. The experimental results are well explained by a limited parameter model which treats the three-dimensional ordered, magnetic nanoparticles as dipolar-coupled superspins.