[Wien] Questions about imposing external magnetic field on no-magnetic system
Karel Vyborny
vybornyk at fzu.cz
Sun Jul 16 10:40:43 CEST 2017
As for NMR in not-too-strong B-field, it may indeed not be necessary to
consider the orbital effects of B. I am not an expert in NMR. What I had
in mind is related to my quantum Hall effect background and could be
explained e.g. with bulk GaAs as an example.
For B=0, the conduction band of this semiconductor is (to a good
approximation) parabolic and centered around Gamma. The corresponding DOS
is ~\sqrt{E-Eg} (when Ef is at the top of the valence band and Eg is the
gap). With magnetic field switched on, two things happen. First, spin up
and spin down bands get split by the Zeeman energy. The less trivial
effect is the Landau quantisation (which is what I mean by "orbital
effects"). In principle for any finite B, the smooth DOS breaks up into a
comb of van Hove singularities ~1/\sqrt{E-Eg-Eorb*(n+1/2)}, n=0,1,2 (Eorb
is the cyclotron energy). In reality (for a real sample), any disorder
will smear out this structure and DOS~\sqrt{E-Eg} is recovered unless B is
really strong. Condition for "strong" is something like Eorb>>Gamma
(disoreder broadening).
The fact that Shubnikov-de Haas and de Haas-van Alphen oscillations can be
observed in some bulk solids shows that "strong B" is indeed achievable.
Those 1728 T mentioned below would certainly be strong enough for many
real systems. However, fields of max. several tesla would not - unless we
deal with a very clean system (like 2DEGs needed for QHE). Nevertheless,
I'd think twice before showing any "band structure with B switched on" as
calculated by WIEN.
KV
--- x ---
dr. Karel Vyborny
Fyzikalni ustav AV CR, v.v.i.
Cukrovarnicka 10
Praha 6, CZ-16253
tel: +420220318459
On Sat, 15 Jul 2017, Gavin Abo wrote:
>
> I looked at the Landau quantization Wikipedia entry [1]. However, it was
> not clear to me whether this was needed to describe a system with moving
> spin (e.g., oscillating spins).
>
> If so, I think the answer to your question it that your not missing anything
> and WIEN2k does not have an external magnetic field implementation for
> Landau quantization.
>
> In Chapter 10 Landau Quantization on page 182 of the book titled "Quantum
> Hall Effects: Recent Theoretical and Experimental Developments" by Zyun F.
> Ezawa, it mentions that spinless theory is frequently considered when the
> spin degree of freedom can be ignored, such that a spin frozen system
> becomes a good approximation under the condition that the Zeeman energy is
> large.
>
> Previously, I didn't understand Dr. Novak's reference to the frozen spin
> method [2], but it seems now that might be why he mentioned it.
>
> The NMR slides [3,4] do show B_ext in the H_NMR equation, but I don't see it
> described in which input file it is to be included (or if just part of a
> result in an output file). There is the external magnetic field value that
> can be entered in case.inorb [5]. Perhaps, the NMR program also uses that
> too.
>
> Of note, it was estimated before that a Bext value of a least 1728 T may be
> needed to see any noticeable effect in the plots (if the default
> autoscale-like settings are used) [6].
>
> [1] https://en.wikipedia.org/wiki/Landau_quantization
> [2]
> http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg01508.html
> [3] http://susi.theochem.tuwien.ac.at/events/ws2015/rolask_nmr.pdf
> [4]http://susi.theochem.tuwien.ac.at/reg_user/textbooks/WIEN2k_lecture-notes_2
> 013/nmr-chemical-shift.pdf
> [5]
> http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg12904.html
> [6]
> https://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/msg11093.html
>
> On 7/15/2017 4:56 AM, Karel Vyborny wrote:
> Interesting, I didn't know that WIEN2k can figure out what "band
> structure with B>0" is... I thought there ought to be some
> Landau quantisation which is hard to do except for idealised
> systems. Am I missing something here?
>
> KV
>
>
> --- x ---
> dr. Karel Vyborny
> Fyzikalni ustav AV CR, v.v.i.
> Cukrovarnicka 10
> Praha 6, CZ-16253
> tel: +420220318459
>
>
> On Sat, 15 Jul 2017, Peng Bingrui wrote:
>
> Dear professor Blaha
>
> Thank you very much for your suggestions. However,
> I'm still kind of
> confused, because my purpose is to see the change of
> band structure under
> external magnetic field, and l'm wondering whether
> NMR calculation can do
> this ? I'm sorry for my limited knowledge as an
> undergraduate student.
>
> Sincerely yours,
> Bingrui Peng
> from the Department of Physics, Nanjing University,
> China
>
> ___________________________________________________________________________
> _
> From: Wien <wien-bounces at zeus.theochem.tuwien.ac.at>
> on behalf of pieper
> <pieper at ifp.tuwien.ac.at>
> Sent: Wednesday, July 12, 2017 1:15:41 AM
> To: A Mailing list for WIEN2k users
> Subject: Re: [Wien] Questions about imposing
> external magnetic field on
> no-magnetic system
> In case no one has answered this up to now:
>
> ad 1) The procedure itself is ok. You might want
> switch on SO first and
> converge that without the orbital potential to
> establish a zero-field
> base line. Remember to put in LARGE fields - your
> off-the-shelf lab
> field of 10 T will not show up at any energy
> precision you can achieve.
> Estimate the energy of 1 mu_B in 10 T field in Ry
> units to see that.
>
> Note that your not-so-recent version of Wien2k is
> not the best for the
> task. The latest version is 17.1. With 16.1 came the
> NMR package which
> should be much better suited to calculate the
> effects of a magnetic
> field.
>
> ad 2) If you apply a magnetic field experimentally
> in the lab you do it
> at all atoms. I suppose you want to model that
> situation. imho it makes
> little sense to exempt one or two of your atoms from
> the field.
>
> Good luck
>
> ---
> Dr. Martin Pieper
> Karl-Franzens University
> Institute of Physics
> Universitätsplatz 5
> A-8010 Graz
> Austria
> Tel.: +43-(0)316-380-8564
>
>
> Am 10.07.2017 12:20, schrieb Peng Bingrui:
> > Dear professor Blaha and WIEN2K users
> >
> > I'm running WIEN2K of 14 version on Linux system.
> I'm going to impose
> > external magnetic field on LaPtBi, a no-magnetic
> material. The
> > procedure that I'm going to use is :
> >
> > 1、Do a no-SO calculation : runsp_c_lapw.
> >
> > 2、Do a SO calculation : runsp_c_lapw -so -orb,
> while including
> > external magnetic field as orbital potential in
> the same time.
> >
> > My questions are:
> >
> > 1、Whether this procedure is OK ? If it is not OK,
> what is the right
> > one ?
> >
> > 2、Which atoms and which orbitals should I treat
> with orbital
> > potential ? The electron configurations of these 3
> atoms are: La (5d1
> > 6s2) ; Pt (4f14 5d9 6s1); Bi (4f14 5d10 6s2
> 6p3).
> >
> > Thanks very much for your attention.
> >
> > Sincerely yours,
> >
> > Bingrui Peng
> >
> > from the Department of Physics, Nanjing
> University, China
>
>
>
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