Could the paleomagnetism and the present magnetic field somehow influence the movements of tectonic plates?

However, the lower mantle is a semiconductor with a significant thermal gradient, which induces electrical gradient via thermoelectricity. This paper suggests this effect can be strong enough to actually be a source of geomagnetism. If true, it is also strong enough to interact with geomagnetic field to produce mechanical forces, which would manifest as a depth-oriented gradient of East-west drag.

Another paper claims both geomagnetism and plate tectonics have the same cause: Global coupling at 660 km is proposed to explain plate tectonics and the generation of the earth's magnetic field.