I learned from a source that when external magnetic field is applied, parallel spin/spin up has lower energy than spin down. But why? How does this relate to two like poles of magnets facing each other and two unlike poles facing each other?

 

Source:https://mriquestions.com/energy-splitting.html

7 hours ago, King E said:

I learned from a source that when external magnetic field is applied, parallel spin/spin up has lower energy than spin down. But why? How does this relate to two like poles of magnets facing each other and two unlike poles facing each other?

 

Source:https://mriquestions.com/energy-splitting.html

It's like a compass needle. The configuration it spontaneously takes up is the one aligned with the Earth's magnetic field because that is the state of lowest energy. The opposite orientation is the one with the highest energy. The lowest energy is when the N pole of the needle is facing the S pole from the surrounding field, i.e. you have N-(S-N)-S rather than N-(N-S)-S.

That's what the animated diagram in the link is illustrating. However in the case of the electron or nucleus, the quantum-allowed orientations are only partially aligned with or against the prevailing field, hence the 2 diagonal orientations shown in the animation.