[Wien] spin and orbital moments

Fri Jun 29 14:49:48 CEST 2012

That should be because the equation is not sqrt(x**2 + y**2 + z**2).

The equation that it seems to use is 
sin(theta)*(cos(phi)*x+sin(phi)*y)+cos(theta)*z for both ORBxxx and SPIxxx.

So, sin(theta)*(cos(phi)*0.46560+sin(phi)*0.80642)+cos(theta)*0.53749 = 
1.075 (projection on the M axis).

What are the values of phi and theta?  I believe they are given in 
case.outputdm(up/dn).  Hopefully the values satisfy the equation, else I 
must have overlooked something.

On 6/29/2012 1:54 AM, Kateryna Foyevtsova wrote:
> 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.
>>> _______________________________________________
>>> Wien mailing list
>>> Wien at zeus.theochem.tuwien.ac.at
>>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>>>
>>
>>
>>
>> _______________________________________________
>> Wien mailing list
>> Wien at zeus.theochem.tuwien.ac.at
>> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
> _______________________________________________
> Wien mailing list
> Wien at zeus.theochem.tuwien.ac.at
> http://zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>