A piece of paper will be useful to discuss this point ;)
To my point of you, the picture is correct: Fe moment point inward and
outward. However, I think that for a given direction (c direction) the
001 and 00-1 orientation will lead to inward and outward respectively,
which will give the same spin moment and orbital moment. It is due to
the fact that the SO-effect will split the 3d orbitals similarly for the
001 and 00-1 orientations. Doing two calculations with 001 and 00-1
magnetization direction will lead to reverse the Fe moment for a given
surface, and thus you will have inward and outward, respectively.
In your calculations, you have both (inward and outward) for one
magnetization direction due to the surface termination.
The only limitation I see here is related to the definition of the Fermi
level which can lead to difficulties to properly distinguish the two
surfaces. Would it be possible that here is the problem? Are the partial
DOS exactly the same?
Best Regards
Xavier
Le 02/01/2018 à 16:08, Stefaan Cottenier a écrit :
Hello Xavier,
You touch some of the points I have been pondering, indeed.
For bulk bcc-Fe, there would be no problem. Having spin-orbit along
001 or along 00-1 must lead to the same result. In my naive picture,
this is equivalent to having the Fe-moment pointing along 001 or along
00-1, and for an infinite bulk lattice this is identical.
For a slab, the situation is slightly different. My expectation was
that all global properties (e.g. total energy) would not depend on the
choice between 001 or 00-1: there would be two inequivalent surfaces,
but taking the other orientation for the moment would just interchange
the two surfaces. The sum of both, would not change. What does
surprise me, however, is that the two surfaces are *not* inequivalent:
not only global properties yet also local properties (spin moment,
EFG,…) are identical for the two surfaces.
When I forget about the electric field of the initial question, and
use the unit cell suggested by sgroup, then the two surface layers
become equivalent. Even after ‘breaking’ the symmetry by initso_lapw.
That suggests it’s a general property, and not related to a particular
orbital occupation as you suggest in your second post.
I suspect my naive interpretation of the Fe moment pointing ‘inward’
for one surface layer and pointing ‘outward’ for the other layer, is
not correct. Yet I don’t see why.
Thanks!
Stefaan
*Van:*Wien [mailto:wien-boun...@zeus.theochem.tuwien.ac.at] *Namens
*Xavier Rocquefelte
*Verzonden:* dinsdag 2 januari 2018 15:38
*Aan:* wien@zeus.theochem.tuwien.ac.at
*Onderwerp:* Re: [Wien] zigzag potential interpretation
Dear Stefaan
As always it is very nice to read your posts :)
I will only react on your "Thought 3". What will happen if you do the
same calculation along 00-1? To my point of view, you will obtain the
same result. Indeed, the magnetic anisotropy (MAE) of bulk-Fe must be
symmetric. Here you break the symmetry, it could be seen considering 2
local pictures (for each slab surface):
- one experiencing a magnetization direction along 001
- one along 00-1.
These two directions must lead to the same SO effects and thus the
same spin moments, orbital moments and EFG.
Here is one plausible interpretation ;) I hope it will help you.
I wish you all the best and HAPPY NEW YEAR to you and your familly.
Xavier
Le 02/01/2018 à 14:33, Stefaan Cottenier a écrit :
Dear wien2k mailing list,
I know that the Berry phase approach is the recommended way
nowadays for applying an external electric field in wien2k.
However, for a quick test I resorted to the old zigzag potential
that is described in the usersguide, sec. 7.1.
It works, but I have some questions to convince me that I’m
interpreting it the right way.
The test situation I try to reproduce is from this paper
(https://doi.org/10.1103/PhysRevLett.101.137201), in particular
this picture
(https://journals.aps.org/prl/article/10.1103/PhysRevLett.101.137201/figures/1/medium).
It’s a free-standing slab of bcc-Fe layers, with an electric field
perpendicular to the slab. For convenience, I use only 7
Fe-monolayers (case.struct is pasted underneath). Spin orbit
coupling is used, and the Fe spin moments point in the positive
z-direction.
This is the input I used in case.in0 (the last line triggers the
electric field) :
TOT XC_PBE (XC_LDA,XC_PBESOL,XC_WC,XC_MBJ,XC_REVTPSS)
NR2V IFFT (R2V)
30 30 360 2.00 1 min IFFT-parameters, enhancement
factor, iprint
30 1.266176 1.
Question 1: The usersguide tells “The electric field (in Ry/bohr)
corresponds to EFIELD/c, where c is your c lattice parameter.” In
my example, EFIELD=1.266176 and c=65.082193 b, hence the electric
field should be 0.019455 Ry/bohr. That’s 0.5 V/Angstrom. However,
by comparing the dependence of the moment on the field with the
paper cited above, it looks like that value for field is just half
of what it should be (=the moment changed as if it were subject to
a field of 1.0 V/Angstrom). When looking at the definition of the
atomic unit of electric field
(https://physics.nist.gov/cgi-bin/cuu/Value?auefld), I see it is
defined with Hartree, not Rydberg. This factor 2 would explain it.
Does someone know whether 2*EFIELD/c is the proper way to get the
value of the applied electric field in WIEN2k?
Question 2: It is not clear from the userguide where the extrema
in the zigzagpotential are. Are they at z=0 and z=0.5, as in fig.
6 of http://dx.doi.org/10.1103/PhysRevB.63.165205 ? I assumed so,
that’s why the slab in my case struct is positioned around z=0.25.
Adding this information to the usersguide or to the documentation
in the code would be useful. (or alternatively, printing the
zigzag potential as function of z by default would help too)
Thought 3: This is not related to the electric field as such, but
when playing with the slab underneath, I notice that in the
absence of an electric field all properties of atoms 1 and 2 – the
‘left’ and ‘right’ terminating slab surfaces – are identical. Same
spin moment, same orbital moment, same EFG,… I didn’t expect this,
as with magnetism and spin-orbit coupling along 001, the magnetic
moments of the atoms are pointing in the positive z-direction.
That means ‘from the vacuum to the bulk’ for atom 1, and ‘from the
bulk to the vacuum’ for atom 2. That’s not the same situation, so
why does it lead to exactly the same properties? What do I miss
here? (The forces (:FGL) for atoms 1 and 2 are opposite, as
expected. And when the electric field is switched on, atoms 1 and
2 do become different, as expected.)
Thanks for your insight,
Stefaan
blebleble s-o calc. M|| 0.00 0.00 1.00
P 7 99 P
RELA
5.423516 5.423516 65.082193 90.000000 90.000000 90.000000
ATOM -1: X=0.00000000 Y=0.00000000 Z=0.12500000
MULT= 1 ISPLIT=-2
Fe1 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -2: X=0.00000000 Y=0.00000000 Z=0.37500000
MULT= 1 ISPLIT=-2
Fe2 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -3: X=0.00000000 Y=0.00000000 Z=0.20833333
MULT= 1 ISPLIT=-2
Fe3 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -4: X=0.00000000 Y=0.00000000 Z=0.29166667
MULT= 1 ISPLIT=-2
Fe4 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -5: X=0.50000000 Y=0.50000000 Z=0.16666667
MULT= 1 ISPLIT=-2
Fe5 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -6: X=0.50000000 Y=0.50000000 Z=0.33333333
MULT= 1 ISPLIT=-2
Fe6 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
ATOM -7: X=0.50000000 Y=0.50000000 Z=0.25000000
MULT= 1 ISPLIT=-2
Fe7 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000
LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000
0.0000000 1.0000000 0.0000000
0.0000000 0.0000000 1.0000000
8 NUMBER OF SYMMETRY OPERATIONS
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