[Wien] spin and orbital moments

Gavin Abo gsabo at crimson.ua.edu
Fri Jun 29 16:12:31 CEST 2012 

Do you have a case.outputdm, case.outputdmup, or case.outputdmdn file?  
Can you see if the THETA and PHI is different from that in case.outsymso?

How to explain the 1st iteration ORB005, since sqrt((-0.08361)**2 + 
(-0.01872)**2 + (0.02851)**2) = +0.0903 != -0.06454

For those angles, I also get 0.927 for SPI005 and -0.06356 for ORB005.  
If THETA and PHI in case.outputdm are slightly different, then both 
calculations could work out.

Kind Regards

On 6/29/2012 7:36 AM, Kateryna Foyevtsova wrote:
> Dear Gavin,
>
> that's the point: sqrt(x**2 + y**2 + z**2) works! I indeed get 1.075
> when I insert my x, y and z into this equation!
>
> >From case.outsymso:
>
> THETA, PHI   1.57079632679490       0.955316618124509
>
> and using your formula I get 0.927.
>
> Bests
>
> On 29/06/12 14:49, Gavin Abo wrote:
>> 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
>>>>>
>>>>
>>>>
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>>
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