The effect where atomic energy levels split under an external magnetic field is the Zeeman effect. More precisely, a magnetic field can split a spectral line into several components because it shifts the energies associated with different electron motions and spins.
The effect was discovered in 1896 by Dutch physicist Pieter Zeeman. He observed that spectral lines from heated atoms changed when a strong magnetic field was applied. Zeeman and Hendrik Lorentz received the 1902 Nobel Prize in Physics for their work on the phenomenon.
The Zeeman effect is closely related to the Stark effect, but the fields differ: the Zeeman effect is caused by a magnetic field, while the Stark effect is caused by an electric field. The Paschen–Back effect is a high-field regime in which the usual coupling between an electron’s orbital and spin angular momentum is disrupted, so it is not the general name for magnetic splitting.
Because the separation between Zeeman components depends on magnetic-field strength, astronomers use the effect to detect and measure magnetic fields on the Sun, other stars, and in plasmas. The split lines can also show distinctive polarization.