[Wien] spin and orbital moments

[Gavin Abo]

1) In which coordinate system are SPI005 and ORB005 given?

In Appendix C (http://www.wien2k.at/reg_user/textbooks/) of "New notes 
about Hyperfinefield calculations (ps)", it mentions that the subroutine 
/couplx/ (of lapwdm) now calculates matrices of all components of spin 
and orbital momentum in the "crystal coordinate system 
(sx,sy,sz,lx,ly,lz)". Therefore, *I believe the x, y, and z values of 
SPIxxx and ORBxxx are also in the crystal coordinate system (CCS), while 
the M values ("PROJECTION ON M" values) are parallel to the 
magnetization. *

If your good with reading fortan, you can look into the code. I don't 
full understand what is going on in the code, but I believe the 
"direction to M" (in your case: 1 1 -1) specified in case.inso is read 
in SRC_lapwdm/lapwdm.f. Then, the angles theta and phi between the 
"direction to M" and CCS are calculated in SRC_lapwdm/angle.f. Next, the 
x, y, and z values of SPIxxx and ORBxxx are calculated in the CCS. The 
x, y, and z values are written to case.outputdm(up/dn) and 
case.scfdm(up/dn), while a Cartesian to spherical equation [r = 
sin(theta)*(cos(phi)*x+sin(phi)y)+cos(theta)*z] is used to calculate the 
radius (M) using the x, y, and z, theta, and phi values before writing 
to the same output files as performed by SRC_lapwdm/output.f.

2) Why for the first iteration MMI005 is not even roughly equal to 
SPI005 + ORB005?

SPIxxx is the spin moment calculated from selected electrons only 
(usually d or f).

MMIxxx is the sum from all electrons (s, p, d and f states) inside the 
atomic sphere xxx.

ORBxxx is the orbital magnetic moment.

So*MMIxxx = SPIxxx + ORBxxx is not necessarily true.*

See the reference links below for more information:

http://zeus.theochem.tuwien.ac.at/pipermail/wien/2011-September/015296.html
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2008-April/010820.html
http://zeus.theochem.tuwien.ac.at/pipermail/wien/2005-January/004399.html

On 6/28/2012 9:18 AM, Kateryna Foyevtsova wrote:
> Dear Wien2k developers,
>
> I use wien2k version 11.1 to run spin-polarized GGA+U calculations with
> SO coupling for a molibdenum oxide.
> The symmetry of the system is the following
>
> blebleble                                s-o calc. M||  1.00  1.00 -1.00
> P                           15 2 P-
>               RELA
>   13.669712 13.669712 13.669712 60.000000 60.000000 60.000000
>
> As you see, I set magnetization axis to 1 1 -1, which should be in terms
> of (non-orthogonal) lattice vectors.
> With the help of xcrysden and case.outsymso, I can deduce that this
> direction corresponds to the 0.577350, 0.816497, 0 direction in terms of
> the cartesian global coordinate system.
>
> When I converge the electron density with (without using any previously
> converged non-relativistic calculation)
>
> runsp_lapw -p -orb -so -dm
>
> I get the following data for the first and the last iteration on one of
> the Mo atoms:
>
> 1. iteration:
> :SPI005:  SPIN MOMENT:   0.46560   0.80642  -0.53749 PROJECTION ON M
> 1.07518
> :ORB005:  ORBITAL MOMENT: -0.08361 -0.01872  0.02851 PROJECTION ON M
> -0.06454
> :MMI005: MAGNETIC MOMENT IN SPHERE   5    =    1.86180
>
> last iteration (converged solution):
> :SPI005:  SPIN MOMENT:   0.61653   1.06239  -0.70860 PROJECTION ON M
> 1.41804
> :ORB005:  ORBITAL MOMENT: -0.08361 -0.01872  0.02851 PROJECTION ON M
> -0.06454
> :MMI005: MAGNETIC MOMENT IN SPHERE   5    =    1.43149
>
> Now, I am struggling to understand two things:
> 1) In which coordinate system are SPI005 and ORB005 given?
> If they were given in the global cartesian coordinate system, they would
> be parallel to 0.577350, 0.816497, 0, but they are not.
>
> 2) Why for the first iteration MMI005 is not even roughly equal to
> SPI005 + ORB005?
>
> Thank you very much!
> Kateryna Foyevtsova
>
> P.S. When I perform relativistic calculations starting with a
> preconverged electron density of the non-relativistic solution I get the
> same final result.
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