Antennas are the quintessential means to communicate information wirelessly over long distances via electromagnetic waves. Traditional antennas have two shortcomings that have prevented miniaturization: (1) their radiation efficiencies plummet and (2) they radiate isotropically when miniaturized to small fractions of the radiated wavelength. Here, we report a new genre of non-classical antennas that overcome these limitations by employing non-traditional principles and harnessing topological insulators. An alternating charge current of frequency 1-10 GHz injected into a thin film of a three-dimensional topological insulator (3D-TI) injects a spin current of alternating spin polarization into a periodic array of cobalt nanomagnets deposited on the surface of the 3D-TI. This generates spin waves in the nanomagnets, which radiate electromagnetic waves in space, thereby implementing an antenna. The frequency of the electromagnetic wave is the same as that of the current. The antenna dimension is only 0.6-1.8% of the free space wavelength and yet it radiates with an efficiency several orders of magnitude larger than the theoretical limit for conventional antennas. Furthermore, it radiates anisotropically (despite being a "point source") and one can change the anisotropic radiation pattern by changing the direction of the injected alternating charge current, which changes the spin wave patterns within the nanomagnets because of spin-momentum locking in the 3D-TI. This enables beam steering without the use of a phased array. We have overcome several limitations of classical antennas by harnessing the quantum mechanical attributes of a quantum material, namely a 3D-TI.