# [Pw_forum] PDOS in the presence of spin-orbit coupling

Mohsen Modaresi modaresi.mohsen at gmail.com
Sat Sep 20 16:51:41 CEST 2014

```Dear Dr. Sclauzero Gabriele,

Best,

On Fri, Sep 19, 2014 at 12:25 PM, Sclauzero Gabriele <
gabriele.sclauzero at mat.ethz.ch> wrote:

>
> In general, you cannot, because in presence of spin-orbit coupling the
> spherical harmonics are not eigenstates of the atomic Hamiltonian.
> Therefore the code projects onto spin-angle functions (see PRB 71, 115106),
> which are eigenstates of total angular momentum J=L+S, and of its
> projections along z.
> As you can see from eqs. 3 and 4 of that paper, spin-angle functions of,
> say, j=1/2 and m_j=1/2 contains contributions from both m=0 and m=1, while
> the one with  j=1/2,m_j=-1/2 from both m=0 and m=-1.
> The only spin-angle functions that have contributions from a unique
> spherical harmonic are the j=3/2,m_j=3/2 (only m=1 contributions), and the
> j=3/2,m_j=-3/2 (only m=-1).
>
> HTH
>
> GS
>
> Dear all,
>
> I face with a problem in the pdos calculations. In the absence of
> spin-orbit coupling the for pdos has a form like this
> "X.pdos_atm#1(Y)_wfc#2(p)" in the data file one can find the Pz, Py and Px
> contribution.
> But by inclusion of SOC the I have "X.pdos_atm#1(Y)_wfc#2(p_j0.5)" and
> "X.pdos_atm#1(Y)_wfc#3(p_j1.5)". The first one has 2 column (2*0.5+1) and
> the second one has 4 column (2*1.5+1).
> How can I recognize the contribution from different component of P (Px, Py
> and Pz)?
>
> Best,
>
> --
> Mohsen Modarresi,
> PhD student of Solid State Physics, Ferdowsi University of Mashhad, Iran.
> Phone +98-9133452131
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>
> Dr. Gabriele Sclauzero
> Materials Theory (D_MATL)
> ETH Zurich, HIT G 43.2
> Wolfgang-Pauli-Str. 27
> 8093 Zürich, Switzerland
>
> Phone +41 44 633 94 10
> Fax +41 44 633 14 59
> gabriele.sclauzero at mat.ethz.ch<mailto:gabriele.sclauzero at mat.ethz.ch>
> www.theory.mat.ethz.ch/people/postdocs/gsclauze<
> http://www.theory.mat.ethz.ch/people/postdocs/gsclauze>
>
>
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--
Mohsen Modarresi,
PhD student of Solid State Physics, Ferdowsi University of Mashhad, Iran.
Phone +98-9133452131
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