## Electric Fields in FLEUR

Here, we describe how to put a metallic system in an electric field. For the actual application you might want to jump to see the [[#file_settings | input file settings ]]. In case of nonmetallic systems, you might be interested to find the description [[#asymmetricfield | how to place an asymmetric field]] or in an electric field with [[#Dirichlet|Dirichlet boundary conditions]].

### The screening charge

The ability to include applied electric fields in our electronic structure calculations is a very powerful tool. We can then begin to study magnetic tunnel junctions as these systems are a junction under the influence of an applied E-field or we can study field induced reconstructions at surfaces. It opens the door for us to a whole new class of systems and effects.

OK so how do we do it then?

In the FLEUR code we have a film, so the simplest method of introducing a field is to place a sheet of charge on either side of the film in the vacuum, this then provides an electric field perpendicular to the surface of the film. We need to ensure charge neutrality of the system so we must subtract the same amount of charge from the slab as we have placed on the charged sheets; that's where our screening charge comes from! The figure below shows schematically our film, the charge sheet and the induced screening charge. To answer the question that everyone asks, yes we could just put equal and opposite charges on either side of the film and then not have to subtract any charge from the film, we just have not implemented it yet! [Note: That has changed meanwhile, see below.] Can we test that it works OK? Yes, we can test it. We can show that there is a relationship between the change in electronic occupation and the the chemical potential: Remembering that applying an electric field corresponds to changing the occupancy we now have a test. We have two ways of calculating the change in total energy as a function of the change in occupancy (which corresponds to the change in field). We can calculate it directly from the total energy of two calculations (one with an applied field, one without) and we can calculate it by integrating the curve that represents the chemical potential as a function of applied field. The results of the test are shown below. We see from the above figures that the open squares that represent the results obtained from integrating the chemical potential curve sit almost perfectly centered upon the results calculated directly from the total energy calculations, so we can be confident that the method works well.

#### Example results

The first results show the screening charge induced in the Ag(001)c(2x2)-Xe structure when a field is applied. We can see that the screening still occurs at the metal surface and not where the adsorbate sits and that the adsorbate atom becomes polarised. The second example shows the spin-resolved screening charge in Fe(001). Here we see that even though the screening charge in the separate spin channels penetrates right to the center of the slab, the total screening charge only penetrates as deep as the first layer - the field is screened out. ### Schematic representation of a two-dimensional film in Fleur

---------------------------------           -.
\
================================= -.           \ delz*nmz  = 25 a.u.
\          /
.................................    > zsigma /       -.
/        /          \
********************************* \          \           \
*********************************  > z1 = D/2 \           \
********************************* /            > D = Dvac  > Dtilde
*********************************             /           /
*********************************            /           /
/
................................                      -'

================================

--------------------------------
• *** denotes the film (= interstitial + muffin tins); the width D'vac' (or short: D) is given in "inp.xml"
• ... denotes a slightly larger region of space to allow for more variational freedom and prevents nodes in the wavefunction at z = z1 (== D'vac'/2), where Psi'interstitial' and Psi'vacuum' are matched. Dtilde is also specified in "inp.xml"
• === denotes in electric-field calculations the position of charged plates. Default width of z'sigma' (= z'sheet' - z1) is 10 a.u. (= 5.291772 Å)
• --- denotes the end of the vacuum; an exponential decay to zero is assumed in the integrals when going from z = z1 + delznmz to infinity. The value delznmz is hard-wired to 25 a.u. (= 13.229430 Å); the number of steps 'nmz' to 250, i.e. 0.1 a.u. steps. Up to "nmzxy" g'||' =/= are taken into account; this zone extends to delz*nmzxy, which is set to 10 a.u. (nmzxy = 100).

### Placing asymmetric fields

Sometimes, it might be useful to place a thin film in an antisymmetrc or even asymmetric field. Since this requires to place charges of opposite sign on both sides of the film, it is necessary to provide additional input in the tag as mentioned above. It allows to place the film into a condenser that creates the electric field like that: In the image above, we omitted the film for clarity and just show the effect of the plates put at +/-10 a.u. in the vacuum. For polar films this is the correct setup, since it allows to have a flat potential in the vacuum and a vanishing electric field inside the film. Notice, however, that for large applied fields the potential in the vacuum can drop below the Fermi-level and you can get field-emission (i.e. the program stops with a message like vacuz).

### Using Dirichlet boundary conditions

In the scheme above, a (locally) constant surface charge density has been assumed, which matches a Neumann boundary condition. Another common boundary condition is a constant potential (Dirichlet boundary condition) -- such as provides by a metal plate, which can be either grounded or kept at a certain potential. In order to use Dirichlet boundary condition, add 'dirichlet="T" ' to the tag, which has been introduced above. The value given for 'sig_b_1/2' and in the different shapes are regarded as potential in Hartree or, if 'eV="T"' is set, as potential in (electron) volts.