<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=iso-8859-1">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Consolas;
panose-1:2 11 6 9 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
color:black;
mso-fareast-language:EN-US;}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:#0563C1;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:#954F72;
text-decoration:underline;}
pre
{mso-style-priority:99;
mso-style-link:"HTML - vooraf opgemaakt Char";
margin:0cm;
margin-bottom:.0001pt;
font-size:10.0pt;
font-family:"Courier New";
color:black;
mso-fareast-language:NL-BE;}
p.msonormal0, li.msonormal0, div.msonormal0
{mso-style-name:msonormal;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
font-size:11.0pt;
font-family:"Calibri",sans-serif;
color:black;
mso-fareast-language:NL-BE;}
span.E-mailStijl19
{mso-style-type:personal;
font-family:"Calibri",sans-serif;
color:windowtext;}
span.HTML-voorafopgemaaktChar
{mso-style-name:"HTML - vooraf opgemaakt Char";
mso-style-priority:99;
mso-style-link:"HTML - vooraf opgemaakt";
font-family:Consolas;
color:black;
mso-fareast-language:EN-US;}
span.E-mailStijl22
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 70.85pt 70.85pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body bgcolor="white" lang="NL-BE" link="#0563C1" vlink="#954F72">
<div class="WordSection1">
<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 lang="EN-US" style="color:windowtext">You touch some of the points I have been pondering, indeed.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext">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 lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext">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 lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext">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 lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext">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 lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext">Thanks!<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext">Stefaan<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="color:windowtext"><o:p> </o:p></span></p>
<p class="MsoNormal"><a name="_MailEndCompose"><span lang="EN-US" style="color:windowtext"><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 0cm 0cm 4.0pt">
<div>
<div style="border:none;border-top:solid #E1E1E1 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span lang="NL" style="color:windowtext;mso-fareast-language:NL-BE">Van:</span></b><span lang="NL" style="color:windowtext;mso-fareast-language:NL-BE"> Wien [mailto:wien-bounces@zeus.theochem.tuwien.ac.at]
<b>Namens </b>Xavier Rocquefelte<br>
<b>Verzonden:</b> dinsdag 2 januari 2018 15:38<br>
<b>Aan:</b> wien@zeus.theochem.tuwien.ac.at<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 lang="EN-US" style="font-size:10.5pt"><a 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 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 lang="EN-US" style="mso-fareast-language:NL-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 (<a 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 lang="EN-US" style="mso-fareast-language:NL-BE"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">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 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 lang="EN-US" style="mso-fareast-language:NL-BE"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">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 lang="EN-US" style="mso-fareast-language:NL-BE"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Thanks for your insight,</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Stefaan</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> </span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">blebleble s-o calc. M|| 0.00 0.00 1.00</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">P
</span><span lang="FR-BE" style="mso-fareast-language:NL-BE">7 99 P</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="FR-BE" style="mso-fareast-language:NL-BE"> RELA</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="FR-BE" style="mso-fareast-language:NL-BE"> 5.423516 5.423516 65.082193 90.000000 90.000000 90.000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="FR-BE" style="mso-fareast-language:NL-BE">ATOM -1: X=0.00000000 Y=0.00000000 Z=0.12500000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="FR-BE" style="mso-fareast-language:NL-BE">
</span><span lang="EN-US" style="mso-fareast-language:NL-BE">MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe1 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">ATOM -2: X=0.00000000 Y=0.00000000 Z=0.37500000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe2 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">ATOM -3: X=0.00000000 Y=0.00000000 Z=0.20833333</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe3 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">ATOM -4: X=0.00000000 Y=0.00000000 Z=0.29166667</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe4 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">ATOM -5: X=0.50000000 Y=0.50000000 Z=0.16666667</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe5 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">ATOM -6: X=0.50000000 Y=0.50000000 Z=0.33333333</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe6 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">ATOM -7: X=0.50000000 Y=0.50000000 Z=0.25000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> MULT= 1 ISPLIT=-2</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">Fe7 NPT= 781 R0=.000050000 RMT= 2.22000 Z: 26.00000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE">LOCAL ROT MATRIX: 1.0000000 0.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 1.0000000 0.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 0.0000000 0.0000000 1.0000000</span><o:p></o:p></p>
<p class="MsoNormal"><span lang="EN-US" style="mso-fareast-language:NL-BE"> 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>
<p class="MsoNormal"><span style="mso-fareast-language:NL-BE"><br>
<br>
<br>
<o:p></o:p></span></p>
<pre>_______________________________________________<o:p></o:p></pre>
<pre>Wien mailing list<o:p></o:p></pre>
<pre><a href="mailto:Wien@zeus.theochem.tuwien.ac.at">Wien@zeus.theochem.tuwien.ac.at</a><o:p></o:p></pre>
<pre><a href="http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien">http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien</a><o:p></o:p></pre>
<pre>SEARCH the MAILING-LIST at: <a 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><o:p></o:p></pre>
</blockquote>
<p class="MsoNormal"><span style="mso-fareast-language:NL-BE"><o:p> </o:p></span></p>
</div>
</div>
</body>
</html>