[Wien] zigzag potential interpretation
Stefaan Cottenier
Stefaan.Cottenier at UGent.be
Fri Jan 5 09:49:29 CET 2018
Dear Laurence, Xavier, Gerhard,
Thanks for your answers. After having digested everything, I can understand the problem described in 'Thought 3' of my initial post now. I'll summarize the answer underneath. The two other questions about the implementation of the zigzag potential are still open. For clarity, I'll repost them after this mail.
This was the initial question:
Thought 3: This is not related to the electric field as such, but when playing with the slab underneath, I notice that in the absence of an electric field all properties of atoms 1 and 2 - the 'left' and 'right' terminating slab surfaces - are identical. Same spin moment, same orbital moment, same EFG,. I didn't expect this, as with magnetism and spin-orbit coupling along 001, the magnetic moments of the atoms are pointing in the positive z-direction. That means 'from the vacuum to the bulk' for atom 1, and 'from the bulk to the vacuum' for atom 2. That's not the same situation, so why does it lead to exactly the same properties? What do I miss here? (The forces (:FGL) for atoms 1 and 2 are opposite, as expected. And when the electric field is switched on, atoms 1 and 2 do become different, as expected.)
And this is a summary of the answer:
WIEN2k did everything correctly. The root cause of my misunderstanding was that I treated the magnetic moments as vectors, instead of pseudovectors (axial vectors). Without caring about the electric field yet, and including magnetism as well as spin orbit coupling (along 001), my slab has space group 123. The two surfaces are equivalent in this space group. I did not understand this, as for one surface the magnetic moment in the surface layer is pointing away from the vacuum, for the other surface layer the moment is pointing towards the vacuum. That looked inconsistent with the mirror plane perpendicular to the slab axis, going through the center of the slab. However, that's exactly how a pseudovector should behave (see this Wikipedia picture, and mentally rotate the ring current until it lies in the vertical plane, parallel to the mirror: https://en.wikipedia.org/wiki/File:BIsAPseudovector.svg). The mirror plane in the slab correctly mirrors the ring currents. That's the fundamental quantity.
In order to put the slab at the region in the unit cell where it would feel a constant electric field, I had to break the space group to nr. 99. This makes the two surfaces inequivalent. Which is even necessary, because the applied electric field is a vector (not a pseudovector), hence it makes a difference whether it is pointing away or towards the vacuum. And that's indeed what is shown in the calculations, for instance: the EFG is different in both surfaces when there is an electric field. My mistake was to expect a similar difference in the absence of the electric field, having only spin polarization and spin-orbit coupling. WIEN2k did not show that difference, and it was right.
Thanks!
Stefaan
> -----Oorspronkelijk bericht-----
> Van: Wien [mailto:wien-bounces at zeus.theochem.tuwien.ac.at] Namens
> Fecher, Gerhard
> Verzonden: woensdag 3 januari 2018 18:04
> Aan: A Mailing list for WIEN2k users <wien at zeus.theochem.tuwien.ac.at>
> Onderwerp: Re: [Wien] zigzag potential interpretation
>
> Dear Xavier
> In case you apply (in addition) a electric field the symmetry will change one
> more time, because a "h" type mirror plane (as wll as C2 rotations with axis
> perpendicular to E) would change the sign of the electric field.
> (see Koster et al , the complete reference is in irrep )
>
> Say we start with Oh
> then applying a magnetic field, or setting the SO axis to 001 (along z) the
> point group will change to C4h: Oh + Hz => C4h instead applying a electric
> field (or a current) along 001 (z) the point group will change to C4v: Oh + Ez
> => C4v
>
> The difference arises from the fact that E is a real and H is a pseudo vector.
>
> Let's go ahead:
> a slab from 001 planes should already have C4h for example, then C4h + Hz
> => C4h and nothing has to be changed with the symmetry (concerns also SO)
>
> now apply Ez to C4h then you end up at C4 that is C4h + Ez => C4 (As
> example, for a 3 layer Fe slab, you have that when you make the upper and
> lower atom in the slab not equivalent I assume the center atom to be still at
> 1/2, 1/2, 1/2 and space group P 4/mm (99) before initialising SO)
>
> If I understand, then SOINIT finds C4h (where the upper and lower atoms are
> equal) and not C4, therefore one has to set the appropriate symmetry
> operations somehow by hand, e.g. as just suggested.
>
> (Note: indeed, C4v + Hz => C4, too)
>
> This are just some short thoughts about things with the point groups
> (probably one has to use the full coloured groups, depending on the
> complete problem)
>
> The overall problem is the same, however, independent whether you apply E
> or H, you have to check for the correct symmetry.
>
>
>
>
>
> 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
> Xavier Rocquefelte [xavier.rocquefelte at univ-rennes1.fr]
> Gesendet: Mittwoch, 3. Januar 2018 15:41
> An: wien at zeus.theochem.tuwien.ac.at
> Betreff: Re: [Wien] zigzag potential interpretation
>
> Dear Gerhard
>
> One clarification is needed I think. The discussion was about applying an
> external ELECTRIC field (not a magnetic one).
>
> Thus one part of your answer concerns something else which is also
> interesting :) Indeed, my PhD student has written a modification of WIEN2k
> to take into account the effect of an external magnetic field and we are
> testing this new version with Peter and Pavel at this moment.
>
> Happy new year to you Gerhard
>
> Xavier
>
>
>
> Le 03/01/2018 à 14:24, Fecher, Gerhard a écrit :
> > 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
> >>> _______________________________________________
> >>> Wien mailing list
> >>> Wien at 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 at 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: blaha at theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at
> >> WWW: http://www.imc.tuwien.ac.at/TC_Blaha
> >> ---------------------------------------------------------------------
> >> ----- _______________________________________________
> >> Wien mailing list
> >> Wien at 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 at zeus.theochem.tuwien.ac.at/index.html
> > _______________________________________________
> > Wien mailing list
> > Wien at 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 at zeus.theochem.tuwien.ac.at/index.html
> > _______________________________________________
> > Wien mailing list
> > Wien at 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 at zeus.theochem.tuwien.ac.at/index.html
>
> _______________________________________________
> Wien mailing list
> Wien at 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 at zeus.theochem.tuwien.ac.at/index.html
> _______________________________________________
> Wien mailing list
> Wien at 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 at zeus.theochem.tuwien.ac.at/index.html
More information about the Wien
mailing list