[Pw_forum] Sign of magnetization

[Paolo Giannozzi]

On Nov 12, 2007, at 20:59 , Ivo Souza wrote:

> I am trying to understand whether there is a sign error in the  
> definition
> of the total magnetization in pwscf. In other words, when the code  
> tells
> us that, e.g., the magnetic moment of bcc iron points along +z, is  
> it really
> pointing along minus z?

short answer: yes, or at least, this is what I understood after the  
exchange
of several e-mails with several other developers ...

>    The spin magnetic moment of a state is (n units of the Bohr  
> magneton)
>
> <\mu_z> = -<sigma_z>

or, equivalently,
  <\mu_z> = -\mu_B <sigma_z>
where \mu_B = |e|\hbar/(2mc) is the Bohr magneton (a positive number).

For historical reasons, going back to the first implementations of  
colinear
and noncolinear magnetism in PWscf, the Bohr magneton is instead
implicitly defined as
   \mu_B = e\hbar/(2mc)
with e = true (negative) electron charge, so :
  <\mu_z> = \mu_B <sigma_z>
This convention is used in Andrea's papers and in other papers on
noncolinear magnetism as well. There is nothing wrong in this  
convention,
but its usage in PWscf is a little bit at odds with the rest of the  
code, where
'e', the electron charge, is actually |e| and is positive (as all the  
other physical
constants are).

Since the exchange-correlation energy depends on the modulus of the
magnetization, the theory is invariant with respect to its sign. Of  
course
this is no longer true when one introduces an external magnetic field
and one has to take care to use a consistent convention.

Paolo
---
Paolo Giannozzi, Dept of Physics, University of Udine
via delle Scienze 208, 33100 Udine, Italy
Phone +39-0432-558216, fax +39-0432-558222