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About the non-collinear projected magnetization formula used by vasp.

Posted: Fri Apr 01, 2022 7:06 am
by hszhao.cn@gmail.com
For LNONCOLLINEAR=.TRUE., i.e., spin-orbit coupling case, the following formula is used by vasp to calculate the non-collinear projected magnetization:
1/2 \sum _{\mu ,\nu =1}^{2}\sigma _{\mu \nu }^{j}\langle \chi _{n{\bf {k}}}^{\mu }|Y_{lm}^{\alpha }\rangle \langle Y_{lm}^{\alpha }|\chi _{n{\bf {k}}}^{\nu }\rangle
But the formula, in my opinion, is still a little complicated. Would you please explain to me the physical meaning and the work logic behind it?

Regards,
HZ