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Take hydrogen atom as example. The 2P orbital will split due to spin-orbit coupling to the $^{2}P_{3/2}$ and $^{2}P_{1/2}$ terms. The term $^{2}P_{1/2}$ has anti-parallel orientation of electron spin and orbital angular moment and is lower in energy than the $^{2}P_{3/2}$ which has parallel spin and orbital angular moment.

Why is that and not the other way around? From electrodynamics we know that magnetic potential energy is minimal when two magnetic dipoles are parallel which confuses me here.

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    $\begingroup$ Are you sure on the statement about aligning dipoles? Dipoles align with magnetic fields, and the field of a dipole is such that a neighbouring dipole will anti-align. $\endgroup$ – diracula Mar 6 '17 at 21:46
  • $\begingroup$ Hm... no I am not sure about that. Looks like I assumed that since magnetic dipole in external homogeneous magnetic field will align to be parallel then that also must be true for the external field created by another magnetic dipole. I tried to find some article about magnetic dipole-dipole energy and when it is minimum but I couldn't... all I find is magnetic dipole energy in external field. If you have some helpful link please let me know or maybe you could write answer below with basic formulas that proves this. Thanks for your comment. $\endgroup$ – matori82 Mar 7 '17 at 1:08
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The magnetic potential energy of two magnetic dipoles is minimal when the magnetic dipoles are anti-parallel. You can easily check this with two bar magnets.This also explains why anti-parallel electron spin and orbital angular momentum (and thus anti-parallel magnetic dipole moment) gives, in general, lower energies than parallel orientation.

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  • $\begingroup$ Could you derive that minimal energy for magnetic dipole-dipole interaction is when they are anti-parallel, or provide some link with derivation? That would be very helpful. Thanks for your answer! $\endgroup$ – matori82 Mar 7 '17 at 1:10
  • $\begingroup$ @matori82 - You can find the expression for the potential energy of two magnetic dipoles here: en.wikipedia.org/wiki/Magnetic_dipole–dipole_interaction $\endgroup$ – freecharly Mar 7 '17 at 1:17

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