# [Wien] Magnetization axis, SOC, and rotation

```Dear WIEN2K users and developers,
```
```
I have a question regarding the magnetization direction in SOC calculations.

For a general magnetization axis, the Sz component is defined to be along this
axis. But then, along which direction are laying Sx and Sy ( I know that their
mean value is zero but I'm interested in matrix elements for given bands).

Let's take a tetragonal system and call 100 the x-axis, 010 the y-axis and 001
the z-axis. If one sets the magnetization along the z-axis, then the Sz
component is the one along the 001, right ?

But now, if I set the magnetization axis to be the crystallographic x-axis,
then the Sz component ( psi_up^2 - psi_dn^2 ) is along the x-axis, i.e. the
crystallographic basis is not the same as the basis for the spin.

But then, what about the x/y axis in the spin-basis ? I would say that in that
case, the z-axis has been rotated along the y axis so that we have
z -> x   ( Sz is along the crystallographic x axis)
x -> -z  ( Sx is along the crystallographic -z axis)

y -> y   ( Sy is along the crystallographic y axis)

If this is correct, then what about a magnetization along the 110
crystallographic axis ?

Is it a rotation of 90° along an axis which is perpendicular to the z-axis and
to the 110 axis ?

Thank you in advance for any answer or hint on this topic,

Best regards,

Leandro
```
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