Two-dimensional double nanoparticle(DNP) arrays are demonstrated theoretically, supporting the interaction between out-of-plane magnetic plasmons and in-plane lattice resonances, which can be achieved by tuning the nanoparticle height or the array period due to the height-dependent magnetic resonance and the periodicity-dependent lattice resonance. The interplay between the two plasmon modes can lead to a remarkable change in resonance lineshape and an improvement on magnetic field enhancement. Simultaneous electric field and magnetic field enhancement can be obtained in the gap region between neighboring particles at two resonance frequencies as the interplay occurs, which presents "open" cavities as electromagnetic field hot spots for potential applications on detection and sensing. The results not only offer an attractive way to tune the optical responses of plasmonic nanostructure, but also provide further insight into the plasmon interactions in periodic nanostructure or metamaterials comprising multiple elements.
