  We investigate tripartite coupling between phonons, magnons and photons in a
periodic array of elliptical magnetostrictive nanomagnets delineated on a
piezoelectric substrate to form a two-dimensional two-phase multiferroic
crystal. A surface acoustic wave (phonons) of 5 - 35 GHz frequency launched
into the substrate causes the magnetizations of the nanomagnets to precess at
the frequency of the wave, giving rise to spin waves (magnons). The spin waves,
in turn, radiate electromagnetic waves (photons) into the surrounding space at
the surface acoustic wave frequency. Here, the phonons couple into magnons,
which then couple into photons. This tripartite phonon-magnon-photon coupling
is exploited to implement an extreme sub-wavelength electromagnetic antenna
whose measured radiation efficiency and antenna gain exceed the theoretical
limits for traditional antennas by more than two orders of magnitude at some
frequencies. Micro-magnetic simulations are in excellent agreement with
experimental observations and provide insight into the spin wave modes that
couple into radiating electromagnetic modes to implement the antenna.
