[Wien] Questions about imposing external magnetic field on no-magnetic system
Peter Blaha
pblaha at theochem.tuwien.ac.at
Sun Jul 16 21:25:22 CEST 2017
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-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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