[Wien] Fwd:

[Fecher, Gerhard]

I guess you are searching for the x and y components of the spin polarisation because usually only the z-component
Pz = alpha alpha* - beta beta*  
is given (alpha, beta being the "up" and "down" components of a 2 component spinor, * means conjugate complex)
the remaining two components (x and y-component) are
Px =  2 Re(alpha beta*)   (Re = real part)
Py = -2 Im(alpha beta*)   (Im =imaginary part)

it assumed that alpha beta are normalized to alpha alpha* + beta beta* = 1, otherwise you need to divide for normalization.

For wave functions that arise from a coherent superposition of spinors you should have Px^2 + Py^2 + Pz^2 = P = 1 
but not for an incoherent superposition of spinors (e.g. two spaghetti are crossing), then P may be lower than 1.

if Pz is calculated somewhere in a subroutine, then it should be possible to calculate Px and Py

maybe this helps you or Peter to localize the place (subroutine) to look for to answer your request.

Problems will appear with the above definition if the "small" coponent of a 4 component Dirac spinor is large compared to the "large component"

An old but still very good source about spin polarization is the book of J. Kessler "Polarized Electrons" (1976) from Springer  (may be it is sold out but still available online).

Ciao
Gerhard

DEEP THOUGHT in D. Adams; Hitchhikers Guide to the Galaxy:
"I think the problem, to be quite honest with you,
is that you have never actually known what the question is."

====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
and
Max Planck Institute for Chemical Physics of Solids
01187 Dresden
________________________________________
Von: wien-bounces at zeus.theochem.tuwien.ac.at [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von huimei liu [wwillforever at gmail.com]
Gesendet: Montag, 24. November 2014 13:18
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] Fwd:

If so, where can I get ul(r,E2,l) file?
Is there any output files that can directily tell me <ψ|σ|ψ> ?
Thank you very much!

2014-11-24 17:20 GMT+08:00 Peter Blaha <pblaha at theochem.tuwien.ac.at<mailto:pblaha at theochem.tuwien.ac.at>>:
The error depends on how large the Blm component is. Usually it should be SMALL and therefore for an qualitative analysis negligible.

However, there could be local orbitals and "Clm"s in certain cases, which could lead to errors of 100 %.


On 11/24/2014 10:00 AM, huimei liu wrote:

Dear Wien2k designers and users:
It seems I want more than  the spin-up and dn contribution for a state.
I 'd like to draw the spin texture.

I want to calculate the spin direction for a state (k-point +
band-index)  using the formalism <ψ|σ|ψ> to evaluate the x,y and z
component of spin. Since I can get the Alm and Blm of the Wave function
:ψ can be written as the sum of [Alm*ul(r)+Blm*ul'(r)]Ylm. Here is the
question, if I use Alm only to calculate  <ψ|σ|ψ>, can I get the  close
answer?  Or can anyone tell me the margin of error of using Alm only
compared with using Alm and Blm toghther.



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