# [Pw_forum] why are there two Fermi energies?

Gabriele Sclauzero sclauzer at sissa.it
Thu Apr 21 11:28:51 CEST 2011

```Hello,

I'm also interested in going deeper into this topic. I tell what (I think) I've understood, so maybe we can trigger a discussion with Paolo or Stefano ;)

Il giorno 21/apr/2011, alle ore 01.35, Eduardo Ariel Menendez Proupin ha scritto:

> Hi,
> Why are there two Fermi energies in certain spin-polarized calculations ?

It's just a practical way to deal with spin polarized calculations when you fix a net non-zero total magnetization in the unit cell. Since you know the total charge and the total magnetization, you can determine univocally the number of spin up and of spin down electrons. This in turns allows you to treat the up and down Fermi energies independently, using the same techniques for spin-unpolarized calculations to determine the two Fermi energies.

>
> input             starting_magnetization(1) = 0.0,
>                     starting_magnetization(2) = 0.5,
> output      the Fermi energy is     6.1598 ev
>                !    total energy              =    -502.92538790 Ry
>
> input           tot_magnetization = 1
> output     the spin up/dw Fermi energies are     6.3821    6.1598 ev
>               !    total energy              =    -502.92538790 Ry
>
> What is the meaning of the spin up Fermi level in the second case?

Did you get this with smearing? Otherwise the Fermi energy should not be printed.
Specifying starting_magnetization or tot_magnetization is not equivalent, the former is just used to break the symmetry. You might end with a different magnetization, if that set by
tot_magnetization does not correspond to the ground state. In your case it looks like the GS has M_tot=1, since you got exactly the same energy. What do you get as total magnetization in the first case?
At first glance I don't see why in the first case you get the lowest of the two Fermi energies, I would rather expect the other. What changes between the two calculations is how the occupations are computed (see PW/weights.f90). You can print them on output by specifying verbosity='high'.

>
> This numbers are for a 64 atoms Si unit cell with one Si replaced by Al, and only one k-point, but the same happens with more k-points. I also used Fermi smearing with a very low smearing.
>  There is a difference if I set the starting magnetization or the total magnetization, with pw.x version 4.2.1. However, despite reporting different Fermi levels, the total energy and magnetization are equal. Also are equal KS energies, at least around the Fermi levels.

Yes, I know there have been some changes in the last versions. I think Paolo can be more helpful here.

HTH

GS

>
> Thanks,
>
> Eduardo Menendez
> Departamento de Fisica
> Phone: (56)(2)9787439
> URL: http://fisica.ciencias.uchile.cl/~emenendez
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> Pw_forum at pwscf.org
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§ Gabriele Sclauzero, EPFL SB ITP CSEA
PH H2 462, Station 3, CH-1015 Lausanne

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