[Wien] spin texture?
Gerhard Fecher
fecher at uni-mainz.de
Tue Oct 4 22:08:42 CEST 2011
I do not calculate spinorientation with Wien2k as I am usually interested in the spin of photoemitted electrons
and for that I use my own program (because the polarization of the emitted electrons will also depend on the photon polarisation and not just on the polarisation
of the initial (ground) state wave function)
I can give only a short general answer (you find more details in the Kessler book, and more correct as its hard to distinguish here row and column and matrices)
Lets assume only the large component and a wave function given as (a, b) (just the up and down components)
that is normalized such that aa* + bb* = 1
then the 3 components of the polarisation vector are (note, here * is the Hermetian and not just the conjugate and, indeed not a multiplication)
Px = a* b + b* a = Re(a* b)
Py = i(b* a - a* b) = Im(a* b)
Pz = a a* - b b* = |a|^2 - |b|^2
Oftenly, the spin polarisation is assigned to Pz only, but you can easily find examples that this is not true.
Note also the nice example in Kesslers book that the coherent superposition (1 0) + (0 1) = (1 1) of pure up and down spinor (should be columns not rows) wave functions
does not lead to an unpolarized wave function (just put it into the definition given above), now you should know how to build
a s wave function with polarization along x or y from s1/2,1/2 and s1/2,-1/2.
There are also two other good (but old) books on spin polarized electrons at surfaces
one by Kirschner and one by Feder (I don't remember the complete titles).
Ciao
Gerhard
====================================
Dr. Gerhard H. Fecher
Institut of Inorganic and Analytical Chemistry
Johannes Gutenberg - University
55099 Mainz
________________________________________
Von: wien-bounces at zeus.theochem.tuwien.ac.at [wien-bounces at zeus.theochem.tuwien.ac.at]" im Auftrag von "Ruben Weht [ruweht at cnea.gov.ar]
Gesendet: Dienstag, 4. Oktober 2011 19:33
Bis: A Mailing list for WIEN2k users
Betreff: Re: [Wien] spin texture?
Dear Gerhard,
Thanks a lot for your answer.
I think you are absolutely right about
my misconception.
I guess what I wrongly called "non-collinear spin
in reciprocal space" was that, the spin polarization.
With your advice I re-read some of the papers and
found that is it what people show.
Sorry for my ignorance.
I would try to figure out how to calculate P
using Wien2k.
I will also read that book. It seems interesting.
Thanks again for all,
Ruben
> I guess you have some misconcept about spin, spin magnetic moments,
> magnetic moments, spin polarisation etc..
>
> There is no non-colinear magnetic moment in topological insulators
>
> What you have to calculate is the expectation value
> P=<Psi|Sigma|Psi*>/<Psi|Psi*> the for the Px, Py, Pz components of
> the spinpolarisation vector
> where Sigma are the Pauli spin matrices
> (consult the textbook "Polarized Electrons" by J. Kessler, Springer)
>
> Ciao
> Gerhard
>
> ====================================
> Dr. Gerhard H. Fecher
> Institut of Inorganic and Analytical Chemistry
> Johannes Gutenberg - University
> 55099 Mainz
> ________________________________________
> Von: wien-bounces at zeus.theochem.tuwien.ac.at
> [wien-bounces at zeus.theochem.tuwien.ac.at]" im Auftrag von
> "Ruben Weht [ruweht at cnea.gov.ar]
> Gesendet: Freitag, 30. September 2011 23:49
> Bis: A Mailing list for WIEN2k users
> Betreff: Re: [Wien] spin texture?
>
> Dear Yundi,
>
> Thanks for your reply.
>
> Well, really I do not know, that is part of
> my doubts....
>
> The spin texture is in reciprocal space.
> How can I manage that in real space?
>
> Ruben
>
>> Since the spin of the system changes like a spiral. The magnetic
>> moment is
>> non-collinear. The quantization axis changes. So it is necessary
>> to
>> do a
>> non-collinear calculation.
>>
>> Yundi
>>
>> On Fri, Sep 30, 2011 at 1:24 PM, Ruben Weht <ruweht at cnea.gov.ar>
>> wrote:
>>
>>> Dear Wien users,
>>>
>>> I am trying to reproduce some papers regarding the
>>> electronic structure of topological insulators
>>> and system with an important Rashba interaction
>>> (for instance BiTeI, Bi2Se3, etc).
>>>
>>> On many of them people calculate the electronic band
>>> structure (on a slab for a topological insulator
>>> or in bulk for a Rashba system) and showed what
>>> is called "spin texture", a non-collinear spin
>>> arrangement along the resulting Fermi surface
>>> (most of the time near a Dirac cone).
>>> Almost all of those papers said that the electronic
>>> structure was calculated using Wien2k.
>>>
>>> In general those system have a very strong
>>> spin-orbit coupling so, naively, I thought that
>>> spins up and down were completely mixed.
>>>
>>> Does anyone know how to calculate/plot that
>>> property?
>>> Do I have to use the non-collinear code, Wienncm?.
>>>
>>> Thanks a lot for your help,
>>>
>>> Ruben
>>>
>>> *===============================================*
>>> | Ruben Weht |
>>> | Departmento de Fisica - CNEA |
>>> | Avda. General Paz y Constituyentes |
>>> | 1650 - San Martin - ARGENTINA |
>>> | Email: ruweht at cnea.gov.ar |
>>> | Tel: (54-11) 6772-7104 |
>>> | Fax: (54-11) 6772-7121 |
>>> *===============================================*
>>>
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>
>
> *===============================================*
> | Ruben Weht |
> | Departmento de Fisica - CNEA |
> | Avda. General Paz y Constituyentes |
> | 1650 - San Martin - ARGENTINA |
> | Email: ruweht at cnea.gov.ar |
> | Tel: (54-11) 6772-7104 |
> | Fax: (54-11) 6772-7121 |
> *===============================================*
>
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*===============================================*
| Ruben Weht |
| Departmento de Fisica - CNEA |
| Avda. General Paz y Constituyentes |
| 1650 - San Martin - ARGENTINA |
| Email: ruweht at cnea.gov.ar |
| Tel: (54-11) 6772-7104 |
| Fax: (54-11) 6772-7121 |
*===============================================*
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