[Wien] zigzag potential interpretation

Tue Jan 2 14:33:47 CET 2018

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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