[Wien] spin and orbital moments
Gavin Abo
gsabo at crimson.ua.edu
Sun Jul 1 23:55:04 CEST 2012
angle (M,z) and angle (M,x) deg are THETA and PHI, respectively.
Here is how the code calculates the Projection of M (for your crystal
system).
Your lattice constants a = b = c = 13.6697120 angstrom
Your crystal angles alpha = beta = gamma = 60 deg = 1.04719755119660 rad
M|| XMS1 = 1.000 XMS2 = 1.000 XMS3 = -1.000
XA=XMS1*a*sin(gamma)
XB=XMS1*a*cos(gamma)+b*XMS2
XC=c*XMS3
XX=sqrt(XA**2+XB**2+XC**2)
theta=acos(XC/XX)
XX=sqrt(XA^2+XB^2)
if XX < 1e-5
phi=0;
else
phi=acos(XA/XX)
if abs(XB) > 1e-5
phi=phi*XB/abs(XB)
end
end
M = sin(theta)*(cos(phi)*x+sin(phi)*y)+cos(theta)*z (equation from line
168 of code in $WIENROOT/SRC_lapwdm/output.f)
Example for
:ORB005: ORBITAL MOMENT: -0.03637 -0.06090 0.04160 PROJECTION ON M -0.08224
XA=1*13.6697120*sin(1.04719755119660) = 11.8383179
XB=1*13.6697120*cos(1.04719755119660)+13.6697120*1 = 20.504568
XC=13.6697120*-1 = -13.669712
XX=sqrt(11.8383179**2+20.504568**2+(-13.669712)**2) = 27.339424
theta=acos(-13.669712/27.339424) = 2.0943951 rad =*120 deg*
XX=sqrt(11.8383179**2+20.504568**2) = 23.6766357
phi=acos(XA/XX) = acos(11.8383179/23.6766357) = 1.04719755
phi=phi*XB/abs(XB) = 1.04719755*20.504568/abs(20.504568) = 1.04719755
rad = *60 deg*
M =
*sin(2.0943951)*(cos(1.04719755)*-0.03637+sin(1.04719755)*-0.06090)+cos(2.0943951)*0.04160*
= *-0.82223672* (has slight but acceptable round off error)
Now you can confirm for yourself that all ORBxxx and SPIxxx are satisfied.
On 7/1/2012 4:29 AM, foyevtsova at th.physik.uni-frankfurt.de wrote:
> Dear Gavin,
>
> in case.outputdmup, for instance, I find only this information on angles:
>
> 120.0 60.0 angle (M,z), angle (M,x) deg
>
> Here below is a passage where this line comes from:
>
> SUBSTANCE = blebleble
> s-o calc. M|| 1.00 1.00 -1.00
>
> LATTICE = P
> LATTICE CONSTANTS ARE = 13.6697120 13.6697120 13.6697120
> NUMBER OF ATOMS IN UNITCELL = 15
> MODE OF CALCULATION IS = RELA
> BR1, BR2
> 0.56295 -0.18765 -0.18765 0.56295 -0.18765 -0.18765
> 0.00000 0.53075 -0.26537 0.00000 0.53075 -0.26537
> 0.00000 0.00000 0.45964 0.00000 0.00000 0.45964
> alpha test 1.04719755119660 1.04719755119660
> 1.04719755119660
> SO= T
> Spin-polarized + s-o calculation, M|| 1.000 1.000 -1.000
> alpha test 1.04719755119660 1.04719755119660
> 1.04719755119660
> LATTICE:P
> alpha test 1.04719755119660 1.04719755119660
> 1.04719755119660
> 120.0 60.0 angle (M,z), angle (M,x) deg
> SYMMETRY OPERATIONS IN SPIN COORD. SYSTEM
>
> There is no information on THETA and PHI.
>
>> 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
> Sorry, this is my mistake: what you see is the last iteration. The true
> first iteration is
> :ORB005: ORBITAL MOMENT: -0.03637 -0.06090 0.04160 PROJECTION ON M -0.08224
>
> For these values, sqrt(x**2 + y**2 + z**2) indeed holds. Then, in the
> converged solution the orbital moment deviates from M.
>
> Could it be that something is wrong in the code?
>
>
>
>
>> 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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