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<p>Dear Stefaan <br>
</p>
<p>As always it is very nice to read your posts :) <br>
</p>
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):<br>
- one experiencing a magnetization direction along 001<br>
- one along 00-1. <br>
These two directions must lead to the same SO effects and thus the
same spin moments, orbital moments and EFG. <br>
<br>
Here is one plausible interpretation ;) I hope it will help you. <br>
<br>
I wish you all the best and HAPPY NEW YEAR to you and your familly.
<br>
Xavier <br>
<br>
<br>
<br>
<br>
<div class="moz-cite-prefix">Le 02/01/2018 à 14:33, Stefaan
Cottenier a écrit :<br>
</div>
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<p class="MsoNormal"><span lang="EN-US">Dear wien2k mailing
list,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">It works, but I have
some questions to convince me that I’m interpreting it the
right way.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The test situation I try
to reproduce is from this paper (</span><span
style="font-size:10.5pt;font-family:"Helvetica
Neue";color:#222222;background:white" lang="EN-US"><a
moz-do-not-send="true"
href="https://doi.org/10.1103/PhysRevLett.101.137201">https://doi.org/10.1103/PhysRevLett.101.137201</a></span><span
lang="EN-US">), in particular this picture (<a
moz-do-not-send="true"
href="https://journals.aps.org/prl/article/10.1103/PhysRevLett.101.137201/figures/1/medium">https://journals.aps.org/prl/article/10.1103/PhysRevLett.101.137201/figures/1/medium</a>).
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.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">This is the input I used
in case.in0 (the last line triggers the electric field) :<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">TOT XC_PBE
(XC_LDA,XC_PBESOL,XC_WC,XC_MBJ,XC_REVTPSS)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">NR2V IFFT
(R2V)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> 30 30 360 2.00
1 min IFFT-parameters, enhancement factor, iprint<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">30 1.266176 1.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">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
</span><span style="color:black;mso-fareast-language:NL-BE"
lang="EN-US">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 (<a moz-do-not-send="true"
href="https://physics.nist.gov/cgi-bin/cuu/Value?auefld">https://physics.nist.gov/cgi-bin/cuu/Value?auefld</a>),
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?<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">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
<a moz-do-not-send="true"
href="http://dx.doi.org/10.1103/PhysRevB.63.165205">http://dx.doi.org/10.1103/PhysRevB.63.165205</a>
? 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)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">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.)<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Thanks
for your insight,<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Stefaan<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">blebleble
s-o calc. M|| 0.00 0.00
1.00<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">P
</span><span style="color:black;mso-fareast-language:NL-BE"
lang="FR-BE">7 99 P<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="FR-BE">
RELA<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="FR-BE">
5.423516 5.423516 65.082193 90.000000 90.000000 90.000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="FR-BE">ATOM
-1: X=0.00000000 Y=0.00000000 Z=0.12500000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="FR-BE">
</span><span style="color:black;mso-fareast-language:NL-BE"
lang="EN-US">MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe1
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">ATOM
-2: X=0.00000000 Y=0.00000000 Z=0.37500000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe2
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">ATOM
-3: X=0.00000000 Y=0.00000000 Z=0.20833333<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe3
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">ATOM
-4: X=0.00000000 Y=0.00000000 Z=0.29166667<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe4
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">ATOM
-5: X=0.50000000 Y=0.50000000 Z=0.16666667<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe5
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">ATOM
-6: X=0.50000000 Y=0.50000000 Z=0.33333333<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe6
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">ATOM
-7: X=0.50000000 Y=0.50000000 Z=0.25000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">Fe7
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000<o:p></o:p></span></p>
<p class="MsoNormal"><span
style="color:black;mso-fareast-language:NL-BE" lang="EN-US">
8 NUMBER OF SYMMETRY OPERATIONS<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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