  The recent boost in data transfer rates puts a daring strain on information
technology. Sustaining such a growth rate requires the development of sources,
detectors and systems working in the so-called TeraHertz (THz) gap covering the
frequency window from 0.1 to 10 THz (1 THz = 10$^{12}$~Hz). This gap represents
a challenge for conventional electronic devices due to carrier transit delays
($\sim$1-10ps), as well as for photonic devices due to thermal fluctuations
(300K$\sim$6THz). Nonetheless, designing efficient, room-temperature THz
sources would constitute a key enabler to applications spanning from
high-resolution imaging to extreme wide band wireless communication. Whereas
high-harmonic generation in solid is usually limited to less than ten
harmonics, broadband THz emission has been demonstrated using laser-induced
superdiffusive spin currents in magnetic bilayers composed of a ferromagnet
deposited on top of a noble metal. While promising, this technique presents the
major disadvantage of necessitating optical pumping and hence lacks
scalability. Here, we demonstrate that extremely high harmonic emission can be
achieved by exploiting conventional spin pumping, without the need of optical
excitation. We show that when the spin-orbit coupling strength is close to the
s-d exchange energy, a strongly non linear regime resulting from resonant spin
flip scattering occurs leading to the generation of a thousand of harmonics at
realistic antiferromagnetic precession frequencies, thereby enhancing both spin
and charge dynamics by two orders of magnitude, and allowing for an emission at
frequencies above 300 THz.
