  The interaction between two magnetic spheres in microwave cavities is studied
by Mie scattering theory beyond the magnetostatic and rotating wave
approximations. We demonstrate that two spatially separated dielectric and
magnetic spheres can be strongly coupled over a long distance by standing
cavity modes. The interactions splits acoustical (dark) and optical (bright)
modes in a way that can be mapped on a molecular orbital theory of the hydrogen
molecule. Breaking the symmetry by assigning different radii to the two spheres
introduces "ionic" character to the magnonic bonds. These results illustrate
the coherent and controlled energy exchange between objects in microwave
cavities.
