I'm not an expert, but I presume "magnetic monopole antenna" refers to a monopole antenna[1] with some affiliation with magnetics. I presume the word "magentic" came from this description in the article:
The key part of an oscillator is the resonant tank circuit: an inductor and a capacitor. Energy sloshes back and forth between the inductor’s magnetic field and the capacitor’s electric field at a resonant frequency determined by the capacitance and inductance. In the new circuit, the team used the antenna itself as the inductor in the resonant tank. Because it was acting as an inductor, the antenna radiated using changing magnetic field instead of an electric field...
Though I don't follow the meaning of this paragraph, what with the energy sloshing. I guess it comes down to the antenna being used as an inductor.