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 antennas sub-wavelength spatial definition could facilitate scalable spin devices operating at THz rates.
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