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7

Phil's answer is absolutely correct. In non-collinear spinor calculation The spin for each state (at a specific k-point and specific band) can points towards different direction. However, since spin is still a good quantum number, we still have pairs of states in which one electron's spin points toward one direction and the other toward the opposite ...

6

Non-collinear spin doesn't mean there's no "up" and "down", it means that the natural quantisation axis (which defines "up" and "down") can vary in space. In other words, at each point in space there's a local "up" direction, but that direction may change throughout space so we no longer have a global spin ...

3

From the WIEN2k manual: LAPWSO: lapwso includes spin-orbit (SO) coupling in a 2nd variational procedure and computes eigenvalues and eigenvectors (stored in case.vectorso) using the scalar-relativistic wavefunctions from lapw1 So, after running the inputs with -so, the output files will be named with so added to the end. For instructions about plotting ...

4

Let's first break down the symbols we know in that expression: \begin{align} \mathbf{\vec{S}} &= \frac{\hbar}{2}\boldsymbol{\vec{\sigma}}\tag{1}\\ &=\frac{\hbar}{2}\left(\sigma_x \boldsymbol{\hat{x}} + \sigma_y \boldsymbol{\hat{y}} + \sigma_z\boldsymbol{\hat{z}}\right)\tag{2}\\ \end{align} {\small \mathbf{\vec{S}}_1\times \mathbf{\vec{S}}_2 = \left(...

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