  Future information technology demands ultimately fast, low-loss quantum
control. Intense light fields have facilitated important milestones, such as
inducing novel states of matter, accelerating electrons ballistically, or
coherently flipping the valley pseudospin. These dynamics leave unique
signatures, such as characteristic bandgaps or high-order harmonic radiation.
The fastest and least dissipative way of switching the technologically most
important quantum attribute - the spin - between two states separated by a
potential barrier is to trigger an all-coherent precession. Pioneering
experiments and theory with picosecond electric and magnetic fields have
suggested this possibility, yet observing the actual dynamics has remained out
of reach. Here, we show that terahertz (1 THz = 10$^{12}$ Hz) electromagnetic
pulses allow coherent navigation of spins over a potential barrier and we
reveal the corresponding temporal and spectral fingerprints. This goal is
achieved by coupling spins in antiferromagnetic TmFeO$_{3}$ with the locally
enhanced THz electric field of custom-tailored antennas. Within their duration
of 1 ps, the intense THz pulses abruptly change the magnetic anisotropy and
trigger a large-amplitude ballistic spin motion. A characteristic phase flip,
an asymmetric splitting of the magnon resonance, and a long-lived offset of the
Faraday signal are hallmarks of coherent spin switching into adjacent potential
minima, in agreement with a numerical simulation. The switchable spin states
can be selected by an external magnetic bias. The low dissipation and the
antenna's sub-wavelength spatial definition could facilitate scalable spin
devices operating at THz rates.
