Once more: A magnetic field influences the spin and orbital degrees of freedom.

The spin effects can approximately be taken care of as described in the UG for NMR in metals. It leads to a trivial (or non-trivial if there is screening) Zeeman splitting. Since even a large field of 100 T is only 1 mRy splitting, you get in first approximation 2 rigid band structures shifted by that value. In semiconductors, that shift is probably everything, however, in metals scf effects may affect this a little bit. You may get estimates of the induced magnetic moments, or the spin suszeptibility.

The magnetic field induces also an orbital current. This current is calculated in the NMR module (you can even plot it) and the orbital suszeptibility as well as the induced magnetic field is also calculated, however, only at the position of the nuclei, not in the whole crystal.

In addition, as I mentioned before, this magnetic field breaks translational symmetry and without that, the concept of "bandstructure" is in principle not valid anymore.

The "magnetic field effect" in case.inorb as described by Pavel Novak is a central field (single free atom) approximation and can be used to get the induced orbital magnetic moment for atoms with localized 4f (or maybe 3d) electrons. It cannot be used as a first principle method to obtain all magnetic field effects in every kind of solid.

I'm not an expert in in this kind of physics and thus cannot say much more about it, but eg. the anomalous Hall effect can be obtained from the off-diagonal epsilon in spin-orbit optics calculations (Jan Kunes) and the de Haas-van Alphen measurements give you effectively the ground state cross sections of the Fermi surface (one does not even need a magnetic field to calculate this, although experimentally you may even need very large fields to observe these oszillations).


Am 16.07.2017 um 10:40 schrieb Karel Vyborny:
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-boun...@zeus.theochem.tuwien.ac.at>
            on behalf of pieper
            <pie...@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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