[Wien] zigzag potential interpretation
Xavier Rocquefelte
xavier.rocquefelte at univ-rennes1.fr
Tue Jan 2 21:30:34 CET 2018
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-bounces at zeus.theochem.tuwien.ac.at] *Namens
> *Xavier Rocquefelte
> *Verzonden:* dinsdag 2 januari 2018 15:38
> *Aan:* wien at 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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