I wrote an article on the history of magnetic amplifiers: https://spectrum.ieee.org/the-vacuum-tubes-forgotten-rival

The quick summary is that magnetic amplifiers started in the US in 1901, but Germany came up with much better magnetic alloys during World War II. This led to a post-war boom in mag amps, which were used in industrial control, aerospace, and computers such as the Univac Solid State. These magnetic materials also led to core memory. Transistors mostly killed off mag amps, although PC power supplies used them into the 1990s.