[Wien] spin polarization of valence states

Wed Dec 12 12:10:08 CET 2007

I still do not see why any band in W should be spin polarized (*).

Supposed you have at a certain point k of the Brillouin zone of W (**) a spin polarised state Psi_k
now apply the inversion operator (that leaves the spin unchanged) then the spinpolarisation
of the state Psi_-k at the point -k  will have the same sign.
What just means that one has a ferromagnet like bcc Fe.

However, I agree that the system W crystal plus incoming spinpolarized electron has a different symmetry,
but then you are not longer dealing with the band structure as ground state property. The result of the experiment
will, indeed, depend on that symmetry.

I also agree that the interaction of a spinpolarised electron with a band of d_5/2 character will be different
from one with a d_3/2 character and that one does not need ferromagnetism to have different inelastic scattering intensities
caused by exchange scattering.
However, besides the matrix elements for the exchange scattering one will need also to respect the Mott-type scattering and
effects of the surface potential, depending on the geometry of the experiment.

Ciao
Gerhard

* Assuming that spin polarisation means that the spin polarization vector P ={<s_x>,<s_y>, <s_z>} is not the Null-vector.
**Note: The lowering of the symmetry from O_h to C4_h by the SO Hamiltonian doesn't help you as it still contains the inversion operator
   and only those symmetry operations that leave the spin unchanged (S set along z).

________________________________________
Von: wien-bounces at zeus.theochem.tuwien.ac.at [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Pavel Novak [novakp at fzu.cz]
Gesendet: Mittwoch, 12. Dezember 2007 07:35
An: A Mailing list for WIEN2k users
Betreff: Re: [Wien] spin polarization of valence states

Dear Oleg,

in order to see the spin polarized bands the time inversion symmetry must
be broken. In your case time inversion is broken by the incoming spin
polarized electron. Consequently, if you wish to have spin polarized bands
the interaction of the spin of incoming electron with the spin and orbital
momenta of valence electrons must be included in calculation. Perhaps you
can approximate this interaction by an effective field - this possibility
is included in WIEN2k.

Pavel

_________________________________________________
Dr. Pavel Novak
Department of Magnetism and Superconductivity
Institute of Physics AS CR
Cukrovarnicka 10, 162 53 Praha 6, Czech Republic
tel: +420 2 20 318 532
e-mail: novakp at fzu.cz

On Tue, 11 Dec 2007, Oleg Artamonov wrote:

> Dear Gerhard,
>
> I work in the cooperation with J. Kirshner and R. Feder. But, please come
> back to my primary question. Let's suppose that due to SO coupling we see
> band splitting in the paramagnetic crystal. Is it possible using Wien2k to
> distinguish which sing of the spin is predominant in each of the bands?
> Regards,
>         Oleg.
>
>
>
> ----- Original Message -----
> From: "Gerhard Fecher" <fecher at uni-mainz.de>
> To: "A Mailing list for WIEN2k users" <wien at zeus.theochem.tuwien.ac.at>
> Sent: Tuesday, December 11, 2007 8:37 PM
> Subject: Re: [Wien] spin polarization of valence states
>
>
> > In that case you should consult some basic works:
> > Joachim Kessler "Polarized electrons" (this group did a lot of work on
> > scattering of spin polarized electrons)
> > J¨šrgen Kirschner "Polarized electrons at surfaces" (who invented the spin
> > detector based on scattering of low energy electrons at tungsten)
> > both published by Springer
> > or
> > R. Feder (ed.) Polarized Electron in Surface Physics, World Scientific
> > Singapore
> >
> > Ciao
> > Gerhard
> >
> > ________________________________________
> > Von: wien-bounces at zeus.theochem.tuwien.ac.at
> > [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Oleg Artamonov
> > [arto at mail.nnz.ru]
> > Gesendet: Dienstag, 11. Dezember 2007 13:42
> > An: A Mailing list for WIEN2k users
> > Betreff: Re: [Wien] spin polarization of valence states
> >
> > Dear Gerhard,
> >
> > We measure the spin-asymmetry of the inelastic scattering of the
> > spin-polarized low energy electron from the valence electron on W single
> > crystal. The more probable origin of the measured spin-asymmetry is the
> > exchange interaction between primary and valence electrons. The SO in the
> > valence states may give the energy splitting in some points of the BZ. For
> > this reason we expect the asymmetry of the spin density of the valence
> > electron in
> > thisi points. To conform this explanation I would like to get from the
> > calculations the SPIN ORIENTATION of the
> > valence electrons in the chosen point of the BZ.
> > For the normal incidence the measured spin-asymmetry changes the sign for
> > symmetry points in the BZ (relative to §¤ point) and that confirms the
> > idea
> > of the SO origin of the spin-asymmetry in the initial state.
> >
> > Best regards,
> >                           Oleg.
> >
> >
> > ----- Original Message -----
> > From: "Gerhard Fecher" <fecher at uni-mainz.de>
> > To: "A Mailing list for WIEN2k users" <wien at zeus.theochem.tuwien.ac.at>
> > Sent: Tuesday, December 11, 2007 1:12 PM
> > Subject: Re: [Wien] spin polarization of valence states
> >
> >
> > If you are talking about photoemission experiments, the question is more
> > complicated.
> >
> > You will detect spin polarized electrons even from non polarized initial
> > states, what is basically known as Fano-effect (and its later refinements
> > by
> > Cherepkov).
> > This are truely relativistic effects that are not implemented in Wien2k.
> > Anyway, the spin polarization is in the final state and not in the initial
> > state, it emerges from the optical selection rules (note the photons do
> > not
> > act on the spin but
> > on the total angular momentum). This means you populate the final states
> > with different m_j projection numbers  differently even if the initial
> > states had an equal occupation
> > of the m_j quantum numbers.
> > As an example, assume circularly polarised light (The details will become
> > more complicated for linearly polarized ligh (see the work of Heinzmann et
> > al.).
> > This will imply the selection rule Delta m_j=+1 for sigma^+ polarization.
> > If youre initial state is s_1/2,1/2 the final states is p_3/2,3/2 and for
> > s_1/2,-1/2 you have p_1/2,1/2 and p_3/2,1/2
> > immidiately, you see that the final state has not longer an equal
> > distribution of the m_j states.
> > The result is that you have spin polarized electrons, even so the initial
> > state was not polarized at all and had no SO-splitting (|0+1/2| =
> > |0-1/2|).
> > In the same way you will find in emission from the tungsten d-bands
> > polarised electrons, what does NOT mean that the bands are spin polarized
> > anywhere in the BZ.
> > (Following Cherepkov you will find that the effect is even larger due to
> > the
> > SO-splitting of the d-states (indeed not possible for s-states).
> > However, if you calculate the cross section in detail, you find that you
> > need the difference in the final state radial wave functions for p_1/2 and
> > p_3/2,
> > otherwise the effect will vanish.
> >
> > You may ask J¨šrgen Braun (braun at cs.uni-hildesheim.de) he did calculations
> > for W or N.A. Cherepkov (State University of Aerospace Instrumentation,
> > St.
> > Petersburg, Russia)
> > that will give you much more details than I can give here in short. Both
> > will be happy to help you with such questions, just remark that I did send
> > you.
> >
> > Ciao
> > Gerhard
> >
> >
> >
> > ________________________________________
> > Von: wien-bounces at zeus.theochem.tuwien.ac.at
> > [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Oleg Artamonov
> > [arto at mail.nnz.ru]
> > Gesendet: Dienstag, 11. Dezember 2007 09:42
> > An: A Mailing list for WIEN2k users
> > Betreff: Re: [Wien] spin polarization of valence states
> >
> > Dear Gerhard,
> >
> > Perhaps, I ask my question not completely correct. Of course, the net spin
> > polarization  is absent in tungsten.
> > We measure in the experiment the asymmetry of the spin-up and spin-down
> > valence electron density in the chosen point of the BZ. This local
> > difference of the spin density is due to the SO interaction.
> > I would like to get from the calculations the SPIN ORIENTATION of the
> > valence electrons in the chosen point of the BZ. How is it possible to
> > extract this information (including the sign of the spin)?
> > Thanks,
> >                Oleg Artamonov.
> >
> > ----- Original Message -----
> > From: "Gerhard Fecher" <fecher at uni-mainz.de>
> > To: "A Mailing list for WIEN2k users" <wien at zeus.theochem.tuwien.ac.at>
> > Sent: Monday, December 10, 2007 11:18 AM
> > Subject: Re: [Wien] spin polarization of valence states
> >
> >
> > The SO interaction will split states according to their total angular
> > momentum into such with
> > j=|l+s| and j=|l-s|
> > this does NOT mean that those states are spin polarised.
> > To have a net spin polarisation of the density of states one needs an
> > unequal occupation of states with different projection quantum number m_s
> > or
> > say better m_j=m_l+m_s.
> > In paramagnetic materials one has no magnetic exchange interaction.
> > Without exchange interaction - this is the case in W - all states with the
> > same absolut value of m_j are equally occupied
> > (for example the |l,j,m_j> state with |2,5/2,5/2> has always the same
> > occupation like the state with |2,5/2,-5/2>)
> > and therefore one has no spin polarisation anywhere in the BZ of a
> > paramagnetic material.
> >
> > If the question was related to photoemission then check J. Braun, Rep.
> > Prog.
> > Phys. 59 (1996) 1267¨C1338 (and references there) to see how it is still
> > possible to detect spin polarised "photo"electrons through the selection
> > rules.
> >
> > Ciao
> > Gerhard
> >
> >
> > ________________________________________
> > Von: wien-bounces at zeus.theochem.tuwien.ac.at
> > [wien-bounces at zeus.theochem.tuwien.ac.at] im Auftrag von Peter Blaha
> > [pblaha at theochem.tuwien.ac.at]
> > Gesendet: Sonntag, 9. Dezember 2007 15:57
> > An: A Mailing list for WIEN2k users
> > Betreff: Re: [Wien] spin polarization of valence states
> >
> > Of course in tungsgten even with SO included, the net magnetic moment is
> > zero and there is no difference between spin-up and dn densities
> > (integrated over all states of the BZ).
> > You are also right, SO could give you some splitting of a state at a
> > certain k-point (leading to possible spin-polarization), but there will
> > be an equivalent k-point in the BZ where this SO effect is just the
> > opposite, so in summary the effect is zero.
> >
> > Oleg Artamonov schrieb:
> >> Dear Wien users,
> >>
> >> Can anybody answer my question. I want to get information about the
> >> spin-polarization of the valence states. One can expect in the case of
> >> tungsten the significant energy shift between spin-up and spin-down
> >> particular states. How is it possible to extract the spin polarization
> >> state from the result of calculations with the spin-orbit interaction
> >> taken into account?. I use Wien2k_7.
> >> Thanks,
> >>             Oleg Artamonov.
> >>
> >>
> >> ------------------------------------------------------------------------
> >>
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