[Wien] Qestion about DOS results

Wed Dec 12 14:12:18 CET 2018

My two cents on the FAQ of Shayam:

> Can I conclude FM for my system?

Recall what you may find in your favorite textbook on magnetism about 
the definitions of para-, dia, non-, ferro-, antiferro-, ferri-, heli-, 
and whatsoever-magnetic. I think the textbook will say something similar 
to

DM: When set into an inhomogeneous magnetic field the material 
experiences a force in the direction of LOWER field. As an alternative 
it might say that the average magnetic field flux density in the 
material is smaller than outside. (field is pushed out of a 
superconductor, frogs can levitate in inhomogeneous magnetic field).

PM: When set into an inhomogeneous magnetic field the material 
experiences a force in the direction of LARGER field. Alternaatively, 
the magnetic field flux density in the material is LARGER than outside 
(magnetic shield materials pull the magnetic field in, clearing some 
volume outside)

NM: A perfect balance of the two - EVERYWHERE in the material. Exists 
only in textbooks and in DFT-programs like Wien2k, where equal density 
of spin-up and -down electrons may be assumed to simplify calculations. 
The nearest thing nature provides are materials where a diamagnetic 
response of one part of the electrons cancels a paramagnetic response 
from another part. That occurs only at a certain temperature and applied 
field, and only for the overall response, not everyhwere on a local 
scale.

Note that these three are defined by (linear) response in some applied 
field - something you usually don't calculate in DFT! This NM-thing is 
just an abbreviation for 'I wanted to save computing time so I told the 
program to ignore spin'. This may or may not be a good idea - it depends 
on what property of which material one is interested in.

The other forms of magnetism may be defined by appearance of a 
spontaneous magnetization. The spin resolved electronic density breaks 
the symmetry between up and down spins somewhere, and WITHOUT a field 
being applied. This is much easier to do in (spin resolved) DFT.

The cases are distinguished by the distribution of the magnetic moments 
in real space:

FM: All spontaneous moments are parallel. Notice what Lyudmila pointed 
out: in both, DFT and real materials there will be local diamagnetic 
response of some electrons coupling to this spontaneous magnetization. 
The electrons are, after all, NOT independent. Strictly speaking this 
corresponds to (usually very small) moments pointing in the opposite 
direction. I am not aware of a rigorous procedure to distinguish small 
spontaneous moments from induced ones in DFT, but definitely would be 
interested.

AFM: For each spontaneous moment at point r in the structure pointing in 
one direction there is one at a symmetry related position with exactly 
the same size and pointing in the opposite direction.

FerriM: All spontaneous moments are collinear, but not of the same size. 
This is the most general case standard Wien2k can handle. Notice what 
Gerhard and Lyudmila pointed out: The structural basis used in the 
calculation must support the magnetic structure one wants to check. No 
DFT program will tell you anything about electronic structures not 
compatible with the symmtry of the structure file.

HeliM: Non-collinear arrangements of spontaneous moments, for example 
umbrella structures of 4f-moments in rare-earth insulators, or helical 
spin density waves in metals. The unsupported Wien-NCM might help with 
such a case.

Notice that the definitions refer to moemnts in real space while the 
valid quantum numbers of the electronic states are in k-space. There is 
usually considerable ambiguity in assigning an electron to some atom in 
the structure. Maybe this works for some 4f-moments with practically all 
their density within the RMT. For a metal such an assignement obviously 
can become problematic pretty fast.

To identify FM as the magnetic ground state in DFT you will have to 
compare calculated total energies of various magnetic structures. If in 
your case only one U-atom in the crystalografic unit cell of U3O8 
carries a sizeable spontaneous moment, then in a calculation based on a 
single unit cell only PM (no sizeable spontaneous moment in sight) or FM 
are possible.

Within a single unit cell you might try to find AFM solutions by 
following Lyudmilas advice: initialize with a sizeable moment in various 
orientations on all three U-atoms and look what the SCF-cycle does with 
them. They may all converge to solutions with just one sizeable moment 
remaining. I gather that this seems to be the case, but I am not sure if 
you really tried starting from different initial magnetic structures.

As Gerhard pointed out some favorable AFM (or FerriM) structure may be 
found when sticking with this single magnetic U, but doubling 
(multiplying) the unit cell and pointing the moment the opposite way in 
the second unit cell. However, this becomes computationaly expensive 
pretty fast ...

Good luck,

Martin Pieper

---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564

Am 11.12.2018 23:06, schrieb shaymlal dayananda:
> Dear all
> 
> Sorry, my reply to the original mail chain is waiting for the
> moderator approval! So I am sending this as a new email.
> 
> ............................................................
> 
> I have actually considered hubard-U (4.5 eV is included) and spin
> orbital coupling also added. My structure is U3O8,
> 
> case.indmc
>  -12.0000         Emin cutoff energy
>   2               number of atoms for which density matrix is
> calculated
>   1  1  3         index of 1st atom, number of L, L1
>   2  1  3         index of 1st atom, number of L, L1
>   0  0            krad, kls
> 
> case.inorb
> 
>   1  2  0                     nmod, natorb, ipr
>  PRATT  1.0                    BROYD/PRATT, mixing
>   1 1 3                          iatom nlorb, lorb
>   2 1 3                          iatom nlorb, lorb
>   1                              nsic 0..AMF, 1..SIC, 2..HFM
>    0.3307 0.00        U J (Ry)   Note: we recommend to use U_eff = U-J
> and J=0
>    0.3307 0.00        U J
> 
> I am having a followup question for your comments.
> 1. Can I conclude FM for my system?
> 
>   because: atom-1(uranium1) is non-magnetic, atom-2 uranium
> (multiplicity is 2 for this atom) has a magnetic moment  of 0.71935.
> These two  uranium has parallel magnetism.
> 
> 2. This system is U3O8, (not U2O5). It has only 11 atoms in the unit
> cell as 1 (U), 2(U), 2(U), 3(O), 4(O), 4(O), 5 (O), 6(O), 6(O), 7(O),
> 7(O).
> With this, is this possible to accept the obtained DOS?
> (And do we necessarily should get different DOS for FM/AFM cases for
> their spin UP/DN cases?
> 
> Thank you
> 
> Shayam
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