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-boun...@zeus.theochem.tuwien.ac.at [wien-boun...@zeus.theochem.tuwien.ac.at] im Auftrag von huimei liu [wwillfore...@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 <pbl...@theochem.tuwien.ac.at<mailto:pbl...@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. _______________________________________________ Wien mailing list Wien@zeus.theochem.tuwien.ac.at<mailto:Wien@zeus.theochem.tuwien.ac.at> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html -- P.Blaha -------------------------------------------------------------------------- Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna Phone: +43-1-58801-165300 FAX: +43-1-58801-165982 Email: bl...@theochem.tuwien.ac.at<mailto:bl...@theochem.tuwien.ac.at> WIEN2k: http://www.wien2k.at WWW: http://www.imc.tuwien.ac.at/staff/tc_group_e.php -------------------------------------------------------------------------- _______________________________________________ Wien mailing list Wien@zeus.theochem.tuwien.ac.at<mailto:Wien@zeus.theochem.tuwien.ac.at> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html _______________________________________________ Wien mailing list Wien@zeus.theochem.tuwien.ac.at http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien SEARCH the MAILING-LIST at: http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html
