[Wien] spin and orbital moments

[Kateryna Foyevtsova]

Dear Gavin,

thanks a lot for your detailed answer and the very useful links!

If ORBxxx and SPIxxx are in CCS, how to explain the fact that for, eg,
SPI005 in the first iteration

sqrt(0.46560**2 + 0.80642**2 + 0.53749**2) = 1.075

ie, exactly the projection on the M axis. I would not expect that if
0.46560, 0.80642 and 0.53749 were projections on the non-orthogonal
axes. That is for me the hardest thing to understand.

Best regards,
Kateryna


On 29/06/12 04:49, Gavin Abo wrote:
> 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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>>
> 
> 
> 
> 
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