[QE-users] How to compute spin projections?

[Hongyi Zhao]

On Thu, Mar 31, 2022 at 9:34 AM Hongyi Zhao <hongyi.zhao at gmail.com> wrote:
>
> On Wed, Mar 30, 2022 at 11:51 PM Luiz Gustavo Davanse da Silveira
> <lgsilveira at fisica.ufpr.br> wrote:
> >
> > Dear Hongyi Zhao,
> >
> > Thanks for your replys. I am answering them all at once. I tried projwfc.x
> > but got only orbital projections. I took a look at the inout documentation
> > and couldn't find an apropriate variable to compute spin projections.
> > Perhaps I am missing something but I can't realize what it would be.
> >
> > I also tried pyprocar but it doesn't support QE non-colinear calculations
> > right now.
>
> Then, the only feasible pathway may be to do the job manually
> according to the description on PROCAR file specification shown on
> vasp wiki [1]:
>
> ```
> For LNONCOLLINEAR=.TRUE. three additional projections for each ion are
> printed and the output is similar to
>
> ion      s     py     pz     px    dxy    dyz    dz2    dxz  x2-y2    tot
> 1  0.144  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.000  0.145
> 2  0.291  0.000  0.006  0.000  0.000  0.000  0.000  0.000  0.000  0.298
> 3  0.291  0.000  0.006  0.000  0.000  0.000  0.000  0.000  0.000  0.298
> tot    0.727  0.000  0.013  0.000  0.000  0.000  0.000  0.000  0.000  0.740
> 1 -0.011 -0.000 -0.000 -0.000 -0.000 -0.000 -0.000  0.000 -0.000 -0.011
> 2 -0.023 -0.000 -0.000  0.000  0.000 -0.000 -0.000  0.000 -0.000 -0.023
> 3 -0.023 -0.000 -0.000  0.000  0.000 -0.000 -0.000  0.000 -0.000 -0.023
> tot   -0.057 -0.000 -0.001  0.000  0.000 -0.000 -0.000  0.000 -0.000 -0.058
> 1 -0.142 -0.000  0.000  0.000  0.000  0.000 -0.000 -0.000 -0.000 -0.142
> 2 -0.286  0.000 -0.006 -0.000 -0.000  0.000 -0.000 -0.000  0.000 -0.293
> 3 -0.286  0.000 -0.006 -0.000 -0.000  0.000 -0.000 -0.000  0.000 -0.293
> tot   -0.715  0.000 -0.012 -0.000 -0.000  0.000 -0.000 -0.000  0.000 -0.727
> 1 -0.024 -0.000  0.000 -0.000 -0.000  0.000 -0.000  0.000 -0.000 -0.024
> 2 -0.048  0.000 -0.001  0.000  0.000  0.000 -0.000  0.000  0.000 -0.049
> 3 -0.048  0.000 -0.001  0.000  0.000  0.000 -0.000  0.000  0.000 -0.049
> tot   -0.119  0.000 -0.002  0.000  0.000  0.000 -0.000  0.000  0.000 -0.121
>
> Here the entries correspond to the projected magnetizations
>
>
> 1 / 2 \sum_{\mu, \nu=1}^{2} \sigma_{\mu \nu}^{j}\left\langle\chi_{n
> \mathbf{k}}^{\mu} \mid Y_{l m}^{\alpha}\right\rangle\left\langle Y_{l
> m}^{\alpha} \mid \chi_{n \mathbf{k}}^{\nu}\right\rangle
>
> and are calculated for the spinor of the spinor
>
> \left|\Psi_{n \mathbf{k}}\right\rangle=\left(\begin{array}{c}\chi_{n
> \mathbf{k}}^{\uparrow} \\ \chi_{n
> \mathbf{k}}^{\downarrow}\end{array}\right)
>
> and the Pauli matrices:
>
>
> \sigma^{x}=\left(\begin{array}{cc}0 & 1 \\ 1 & 0\end{array}\right),
> \quad \sigma^{y}=\left(\begin{array}{cc}0 & -i \\ i &
> 0\end{array}\right), \quad \sigma^{z}=\left(\begin{array}{cc}1 & 0 \\
> 0 & -1\end{array}\right)
>
> The first set is the total (absolute) magnetization, while the
> remaining three sets of entries correspond to the three directions j =
> 1 , 2 , 3.
> ```
>
> [1] https://www.vasp.at/wiki/index.php/PROCAR

For clearer/readable information, see the attachment.

Yours,
Hongyi
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