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<p>A piece of paper will be useful to discuss this point ;) <br>
</p>
<p>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. <br>
</p>
<p>In your calculations, you have both (inward and outward) for one
magnetization direction due to the surface termination. <br>
</p>
<p>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? <br>
</p>
<p>Best Regards</p>
<p>Xavier <br>
</p>
<p><br>
</p>
<p><br>
</p>
<p><br>
</p>
<br>
<div class="moz-cite-prefix">Le 02/01/2018 à 16:08, Stefaan
Cottenier a écrit :<br>
</div>
<blockquote
cite="mid:2df386a8adb640a98069e5d117febb8c@xmail403.UGent.be"
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<p class="MsoNormal"><span style="color:windowtext">Hello
Xavier,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">You
touch some of the points I have been pondering, indeed.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">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
<b>not</b> inequivalent: not only global properties yet also
local properties (spin moment, EFG,…) are identical for the
two surfaces.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">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.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">Thanks!<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US">Stefaan<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:windowtext" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><a moz-do-not-send="true"
name="_MailEndCompose"><span style="color:windowtext"
lang="EN-US"><o:p> </o:p></span></a></p>
<span style="mso-bookmark:_MailEndCompose"></span>
<div style="border:none;border-left:solid blue 1.5pt;padding:0cm
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<p class="MsoNormal"><b><span
style="color:windowtext;mso-fareast-language:NL-BE"
lang="NL">Van:</span></b><span
style="color:windowtext;mso-fareast-language:NL-BE"
lang="NL"> Wien
[<a class="moz-txt-link-freetext" href="mailto:wien-bounces@zeus.theochem.tuwien.ac.at">mailto:wien-bounces@zeus.theochem.tuwien.ac.at</a>]
<b>Namens </b>Xavier Rocquefelte<br>
<b>Verzonden:</b> dinsdag 2 januari 2018 15:38<br>
<b>Aan:</b> <a class="moz-txt-link-abbreviated" href="mailto:wien@zeus.theochem.tuwien.ac.at">wien@zeus.theochem.tuwien.ac.at</a><br>
<b>Onderwerp:</b> Re: [Wien] zigzag potential
interpretation<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p>Dear Stefaan <span style="mso-fareast-language:NL-BE"><o:p></o:p></span></p>
<p>As always it is very nice to read your posts :) <o:p></o:p></p>
<p class="MsoNormal" style="margin-bottom:12.0pt">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>
<o:p></o:p></p>
<div>
<p class="MsoNormal">Le 02/01/2018 à 14:33, Stefaan
Cottenier a écrit :<o:p></o:p></p>
</div>
<blockquote style="margin-top:5.0pt;margin-bottom:5.0pt">
<p class="MsoNormal"><span lang="EN-US">Dear wien2k mailing
list,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></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.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></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.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></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" 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.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">This is the input I
used in case.in0 (the last line triggers the electric
field) :</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">TOT XC_PBE
(XC_LDA,XC_PBESOL,XC_WC,XC_MBJ,XC_REVTPSS)</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">NR2V IFFT
(R2V)</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> 30 30 360
2.00 1 min IFFT-parameters, enhancement factor,
iprint</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US">30 1.266176 1.</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></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="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?</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span
style="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)</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span
style="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.)</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Thanks
for your insight,</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Stefaan</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">blebleble
s-o calc. M|| 0.00 0.00
1.00</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">P
</span><span style="mso-fareast-language:NL-BE"
lang="FR-BE">7 99 P</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="FR-BE">
RELA</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="FR-BE">
5.423516 5.423516 65.082193 90.000000 90.000000
90.000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="FR-BE">ATOM
-1: X=0.00000000 Y=0.00000000 Z=0.12500000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="FR-BE">
</span><span style="mso-fareast-language:NL-BE"
lang="EN-US">MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe1
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">ATOM
-2: X=0.00000000 Y=0.00000000 Z=0.37500000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe2
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">ATOM
-3: X=0.00000000 Y=0.00000000 Z=0.20833333</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe3
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">ATOM
-4: X=0.00000000 Y=0.00000000 Z=0.29166667</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe4
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">ATOM
-5: X=0.50000000 Y=0.50000000 Z=0.16666667</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe5
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">ATOM
-6: X=0.50000000 Y=0.50000000 Z=0.33333333</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe6
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">ATOM
-7: X=0.50000000 Y=0.50000000 Z=0.25000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">Fe7
NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">LOCAL
ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span
style="mso-fareast-language:NL-BE" lang="EN-US">
8 NUMBER OF SYMMETRY OPERATIONS</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US"> </span><o:p></o:p></p>
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style="mso-fareast-language:NL-BE"><br>
<br>
<br>
<o:p></o:p></span></p>
<pre>_______________________________________________<o:p></o:p></pre>
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<p class="MsoNormal"><span style="mso-fareast-language:NL-BE"><o:p> </o:p></span></p>
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<pre wrap="">_______________________________________________
Wien mailing list
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SEARCH the MAILING-LIST at: <a class="moz-txt-link-freetext" href="http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html">http://www.mail-archive.com/wien@zeus.theochem.tuwien.ac.at/index.html</a>
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