[Wien] different MLD for bcc structure for magnetic equivalent directions M001, M010 and M100

Jaroslav Hamrle hamrle at karlov.mff.cuni.cz
Fri Nov 24 16:36:49 CET 2017


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: hamrle at karlov.mff.cuni.cz
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