diamagnetism, paramagnetism and ferromagnetism can be fully explained only using quantum theory

The magnetic properties of certain materials (e.g. why an unmagnetized piece of iron sticks to a magnet of either polarization), the way permanent magnets work, is best explained by quantum mechanics.

However, the electromagnetic force itself doesn’t “arise” from quantum mechanics, and you can explain things like electromagnets and a lot of common electric circuits (until you need a transistor) quite well without considering quantum mechanics.

Usually you take the “classical” formula for a force and to inform your quantum mechanical model of particles, and that’s how you can arrive at things like deriving how permanent magnets work with the help of w quantum mechanics.

Generally, a lot of material science and chemistry is inherently quantum mechanical because the way atomic orbitals and molecular bonds work is heavily quantum mechanical.