[Wien] zigzag potential interpretation

Wed Jan 3 14:24:31 CET 2018

Dear Stefaan,
I am not realy sure what difference you expect,
I do not see why at two seemingly same surfaces the size of the magnetic moment (orbital or spin) should depend on their orientation in the sense that it is parallel or antiparallel to the surface normal.

I wonder about the interpretation where the magnetic moment points to (in an absolute sense), if you change from 001 to 00-1 then the sign of the magnetic moment does not change,
however, if you change the sign of the magnetisation from m to -m  (instgen) then the quantisation axis and the magnetisation may not longer be parallel 
(the different situations are found in case.scfdmup).
The same might happen when applying an external magnetic field, it seems that it is never checked that all quantisation axes are consistent, 
that means it is not checked  whether m or H parallel or antiparallel to the SO quantisation axes,
without SO it seems that H doesn't change the symmetry at all (!?).

If there is a difference in the wave functions it may be only in the sign of the phase such that it is lost in all cases where you use the absolute square.

Such differences in the phase enter effects that depend on the interferrence of waves as appear in all kinds of circular dichroism, you will not see them in pure intenities (square of wave functions but only in differences, what reminds me on Jaroslavs recent questions before X-mas).

Analysing the wave functions one needs to have a look on the spinors.
Note that only s up, s down correspond to |1/2,1/2>, |1/2, -1/2> ==> mj = ml + ms is either 0+1/2 or 0-1/2 because of ml=0 if l=0
for all higher angular momenta (l>0) mj = ml + ms may be reached by differen spin orientation e.g. mj = 3/2 = 1+1/2 = 2-1/2  (here you may have ml=0, 1, 2 for l=2)

The situation becomes worth if the quantisation axis is not along z (001, 00-1) but along x or y,
in the latter case one either needs to rotate the wave functions (leading to numerical issues) or one has additional off-diaogonal terms in the coupling matrices.
(note that the treatment in the ncm version of Wien2k differs from the regular one) 

Coming back to my starting point, just something that will be different: If you think about XMCD then you have to change the direction of photons to hit the two different surfaces. 
(and this might reverse the circular polarisation and thus the XMCD)

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 [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Stefaan Cottenier [Stefaan.Cottenier at UGent.be]
Gesendet: Mittwoch, 3. Januar 2018 12:26
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] zigzag potential interpretation

> Provide a indmc file as for lda+u (d-states and 0 0 at the end)

OK, done that, and now I see the vectorial information. Which confirms the same picture as ever before: these two surfaces are fully equivalent. The question remains: why...?

:ORB001:  ORBITAL MOMENT:  0.00000  0.00000  0.09334 PROJECTION ON M  0.09334
:SPI001:  SPIN MOMENT:   0.00000   0.00000   3.00530 PROJECTION ON M  3.00530

:ORB002:  ORBITAL MOMENT:  0.00000  0.00000  0.09334 PROJECTION ON M  0.09334
:SPI002:  SPIN MOMENT:   0.00000   0.00000   3.00531 PROJECTION ON M  3.00531

Stefaan

> On 01/03/2018 12:02 PM, Stefaan Cottenier wrote:
> >> Run    x lapwdm -so -up
> >>
> >> and look at the spin and orbital moments (vectorial) of the atoms there.
> >
> > Hello Peter,
> >
> > See underneath. I don't see vectorial information in there. The two atoms
> shown are the 'left' and 'right' surface (i.e. with moments pointing into the
> bulk and into the vacuum), and the two orbital moments are exactly identical
> (consistent with sgroup/initso, which would have made these two surfaces
> equivalent right away). Which is what I don't understand.
> >
> > Stefaan
> >
> >
> > Spin-polarized + s-o calculation, M||  0.000  0.000  1.000
> >    Calculation of <X>, X=c*Xr(r)*Xls(l,s)
> >    Xr(r)    =           I
> >    Xls(l,s) = L(dzeta)
> >    c=  1.00000
> >    atom   L        up          dn         total
> >   irtest           1           1   2.2199999999999989
> > :XOP001  0    0.000000    0.000000    0.000000    0.000000
> > :XOP001  1   -0.001531    0.001217   -0.000313    0.000000
> > :XOP001  2   -0.010694    0.104042    0.093349    0.000000
> > :XOP001  3   -0.000044   -0.000228   -0.000274    0.000000
> > :XOP001  4    0.092763   total
> >   irtest           1           2   2.2199999999999989
> > :XOP002  0    0.000000    0.000000    0.000000    0.000000
> > :XOP002  1   -0.001531    0.001217   -0.000313    0.000000
> > :XOP002  2   -0.010694    0.104043    0.093349    0.000000
> > :XOP002  3   -0.000044   -0.000228   -0.000274    0.000000
> > :XOP002  4    0.092763   total
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>
> --
>
>                                        P.Blaha
> --------------------------------------------------------------------------
> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
> Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
> Email: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
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