The normal musical instrument pickup uses a magnet inside a coil, and the movement of a ferromagnetic string causes changes in the magnetic field, which then induce currents in the coil.
Another possibility would be to use just a strong magnet near a string, and measuring induced currents in the string itself. This would only require a conductive string, not a ferromagnetic one.
Does anyone actually use this method? Is there a name for it, or is it useless, so no one talks about it? I tried it last night, and it works, but the signal is very low (-50 dBV, for instance, vs -5 dBV for a magnetic electric guitar pickup).