Dear colleagues,
We have found non-physical asymmetry related with equivalent magnetization
directions, when calculating electronic structure for bcc Fe:
We want to calculate magnetic linear dichroism, MLD, defined as a
difference between diagonal permittivity element being parallel,
perpendicular to direction of magnetization, respectively.
MLD=epzz - (epxx+epyy)/2 for M001
MLD=epyy - (epxx+epzz)/2 for M010
MLD=epxx - (epyy+epzz)/2 for M100
Obviously, MLD calculated for different equivalent magnetization
directions should
be identical. But they are not, MLD calculated for 001 is different to
MLD calculated for 010 and 100 (MLD for 010 and 100 are identical).
In most cases, we used k-mesh 30x30x30, exgange LDA (choice 5), with
convergence criteria
runsp_lapw -so -cc 0.000001 -ec 0.0000001 -s lapw1
and the convergence was reached.
* We tested this asymmetry also for fcc structures (Ni, Co, Co2MnSi). We
also
tested simple cubic structure (bcc Fe, defined as a simple cubic
structure with two Fe atoms). In all those cases, the asymmetry
disappears. On the other hand, it also appeared also in bcc Ni.
Hence, the asymmetry seems to be specifically related with
bcc structure.
* this asymmetry can be observed already in energy levels (files
case.energysoup). Hence, we think, the asymmetry is not a feature of
optics.
Namely, there is a very good agreement for energies for M010 and M100
(in example below difference is below 2e-7Ry), but much bigger
difference between energies for M001 and (M010,M100) (in example below
max. difference is 18e-6 Ry for band 5). Therefore it seems
that this problem arises in either lapw0 or lapw1 for bcc structure.
To demonstrate the difference, we show energy levels for the first
k-point (in vicinity of the Gamma point shifted in 111 direction from
the Gamma point):
Fe30M001:
0.333333333333E-01 0.333333333333E-01 0.333333333333E-01 1 55
18 8.0
1 -3.4390104377017581
2 -3.4064979309023942
3 -3.3508627657180750
4 -3.2276472567243979
5 -3.1955089683446780
6 -3.1702455400854954
7 -7.1658179115217727E-002
8 -4.3723732810772589E-002
9 0.37296762299903474
10 0.37521967189559313
Fe30M010:
0.333333333333E-01 0.333333333333E-01 0.333333333333E-01 1 55
18 8.0
1 -3.4390110394480322
2 -3.4064968725403300
3 -3.3508644682352022
4 -3.2276486274720977
5 -3.1954902103327028
6 -3.1702472318057655
7 -7.1659013996950252E-002
8 -4.3723316415832839E-002
9 0.37296632778787425
10 0.37521816821120640
Fe30M100:
0.333333333333E-01 0.333333333333E-01 0.333333333333E-01 1 55
18 8.0
1 -3.4390109925234049
2 -3.4064968346346225
3 -3.3508643700301919
4 -3.2276485335559135
5 -3.1954901707639891
6 -3.1702471600962974
7 -7.1658839213425571E-002
8 -4.3723135315494835E-002
9 0.37296642179994044
10 0.37521826479385562
The difference in energy is (in micro-Ry):
left column E(001)-E(100), right column E(010)-E(100)
1 0.5548 -0.0469
2 -1.0963 -0.0379
3 1.6043 -0.0982
4 1.2768 -0.0939
5 -18.7976 -0.0396
6 1.6200 -0.0717
7 0.6601 -0.1748
8 -0.5975 -0.1811
9 1.2012 -0.0940
10 1.4071 -0.0966
clearly, energies for M001 are different from those for M010 and M100.
* We checked also similar calculation by elk code. Here the
asymmetry in optical spectra is not present.
On the other hand, it is presented and equals in all wien2k versions 14-17.
Similar asymmetry is also present when testing equivalent directions of
types 110 and 111 directions in bcc Fe.
* calculations were done for k-point mesh 30x30x30, but the same
symmetry/asymmetry appears from k-mesh 10x10x10 to mesh 40x40x40. With
increasing k-mesh density, the asymmetry somewhat decreases. All other
parameters to calculate bcc Fe were default parameters.
Any help how to remove this equivalent-magnetization-direction asymmetry
is very welcome.
With my best regards
Jaroslav Hamrle
Ondřej Stejskal
PS: We attach some spectral dependences of MLD on bcc Fe related to
previous text:
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/MLD_Fe30.pdf
MLD calculated for Fe30 (meaning bcc Fe with k-mesh 30x30x30), showing
unphysical optical anisotropy for equivalent magnetization direction.
Particularly notice peak around 4.8 eV, which looks artificial and has
opposite sign for M001 and (M010, M100).
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/MLD_Fe46.pdf
MLD on Fe46 (notice, peak at 4.8eV has smaller amplitude)
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/MLD_Fe30-as_simple_cubic.pdf
MLD on Fe30, where bcc Fe is calculated as simple cubic structure
containing two Fe
atoms. In this case, the asymmetry disappears.
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/MLD_Fe30-elk.pdf
To compare, MLD calculated by code elk does not provide previously
discussed
anisotropy.
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/MLD_Fe_compareall.pdf
Figure showing all previously mentioned MLD together.
details of calculations can be found:
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/Fe30M001
http://alma.karlov.mff.cuni.cz/hamrle/w2kfig/Fe30M100
PSS: there is a small bug in script 'x join_vectorfiles -so -up'
The script requires file case.in1c, which is not created and not needed for
all other calculations.
Anyway, 'cp case.in1 case.in1c' solves the problem.
--
------------------------------------------------------------------
Mgr. Jaroslav Hamrle, Ph.D.
Institute of Physics, room F232
Faculty of Mathematics and Physics
Charles University
Ke Karlovu 5
121 16 Prague
Czech Republic
tel: +420-95155 1340
email: ham...@karlov.mff.cuni.cz
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