Mirror plane and spin direction

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Newstein
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Consider a system with a mirror axis (bulk projected surface), I want to know the direction of spin polarization on the mirror axis. The result is that the spin is perpendicular to the mirror axis, but I don't understand the reason.
If someone have related references, please recommend to me. Thanks!
 

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You'll find it easier to understand if you wrote out a more complete description of the system and where the spin polarization is observed.
 

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