There are actually a few types of magnetic logic. Two production examples come to mind--and very different from each other. The first is the Univac Solid State mainframes, from a time when transistors were not considered to be reliable devices. See:
http://bitsavers.org/pdf/univac/uss/ for a bunch of documentation. The interesting thing about these is that they use majority logic.
Another production device was Eichi Goto's parametron used in NEC's NEAC 1101 system.
https://museum.ipsj.or.jp/en/computer/dawn/0017.html
Multi-aperture "hard" cores were also used.
Another more pedestrian use was the magnetic amplifier:
https://www.nutsvolts.com/magazine/article/the_magnetic_amplifier Used in very hostile environments, enables a small current or currents to control a large one.