[Pw_forum] questions about the initio magnetization of ion

[Dr. Shu-jun Hu]

Dear Prof. Stefano de Gironcoli,
Thank you for your detailed reply.
After posting my question, I perform the projwfc calculation.
I found a puzzling relation between the starting magnetization and the resulting polarization (magnetic moment).
I setup the input file as: starting_magnetization(3) = -0.8, and a large value for lambda. In the last iteration pw.x output the following information:
 ==============================================================================
     atom number   20 relative position :    1.4040   4.1784   9.7071
     charge :     7.067449
     magnetization :         -0.801893
     magnetization/charge:   -0.113463
     constrained moment :    -0.800000
 ==============================================================================

Now, it was noted that the magnetization is constrained at -0.801893. However, the projwfc calculation gave the results:
     Atom #  20: total charge =  16.3788, s =  2.3540, p =  7.1679, d =  6.8569, 
                 spin up      =   7.2902, s =  1.1726, p =  3.5766, d =  2.5410, 
                 spin down    =   9.0886, s =  1.1814, p =  3.5913, d =  4.3159, 
                 polarization =  -1.7983, s = -0.0088, p = -0.0147, d = -1.7748, 
                                  ______________

Actually the magnetic moment is -1.7983 (muB?).
I tried the different value of starting_magnetization, and found that the polarization is always about the double of starting_magnetization. So I think the output "magnetization" duing the pw calculation is not the magnetic moment. If the polarized rho is defined as: rho(r)*(1/2+sigma*starting_magnetization), rather than rho(r)*(1+sigma*starting_magnetization)/2, the above relation is reasonable.Am I right?

Best regards
Shujun Hu


>Dr. Shu-jun Hu wrote:
>>
>> Dear all,
>>
>> I have some qustions about the initio magnetization of ion for LSDA
>> calculation.
>>
>> In the input file the "starting_magnetization" is used to break the
>> spin symmetry of magnetic system. By specifying such parameters, how
>> does pw.x initio the magnetic moment of certain ions?
>> Taking transition metal ion Fe for example, if the
>> starting_magnetizaton(Fe)=0.4, how many electrons occupy the spin-up
>> and spin-down channels respectively for the initio wfc? Only the
>> symmetry breaking of 3d electrons are considered in LSDA calculation,
>> or all the valence electrons (both 3d and 4s)?
>>
>the starting magnetization variables define the way the initial initial
>charge density, that is used to generate the initial potential, is
>built. The initial density is obtained from the superposition of atomic
>charges, read from the pseudopotential file, and in the case of a spin
>polarized calculation the initial charge density is defined as
>rho(r,sigma) = sum_s=1,Nat rho_at_type(r-Rs) * (1 + sigma*
>starting_magnetization_type)/2
>where sigma is +/- 1 for up/down spin components
>
>the atomic charge density is the total one (including the 4s in case of Fe).
>
>occupation of the initial wfs is NOT imposed and is the result of the
>first diagomalization + smearing + fermi energy...
>
>> Such a question concerns about the output information of calculation
>> with constrained magnetization.
>>
>> During the calculation, I got the output information as:
>>
>> atom number 14 relative position : 1.4040 4.1784 3.2357
>> charge : 7.082847
>> magnetization : 0.239576
>> magnetization/charge: 0.033825
>> constrained moment : 0.200000
>>
>> Does the value of "magnetization" (0.239576) represent the magnetic
>> moment of ion, or the polarization? If the latter case, how to derive
>> the magnetic moment in unit of Bohr?
>>
>I may be wrong (I'm not usign this feature often) but inspecting the
>code the meaning of the following output is:
>there are 7.08... electrons in the chosen sphere around the atom # 14
>there are 0.2395... more up electrons than down ones in the sphere...
>this is more the local moment than the local magnetization
>0.033 is the ratio of the two numbers above
>0.20 is the target value of the magnetic moment (the actual value is as
>said 0.2395...). the fact that the actual moment does not agree with the
>target one is due to the fact that the constraint is impose via a
>penalty function. the larger the value of lambda the closer should be
>the computed value to its target.
>
>> -------
>>
>> Another question is about the total energy given by constrained
>> calculations.
>> I want to compare the total energy of a system with different magnetic
>> moment for certain ions, and find the ground state.
>> In order to fix magnetic moment at the starting value, lambda = 1000
>> is setup. That's a large value.
>> As described in INPUT_PW.html, the penalty energy is introduced at
>> this time. I wonder if the comparison make any sense?
>>
>what the code minimizes is the energy including the penalty cost... This
>penalty cost is reported in the output.... I'm not sure however whether
>the printed value of the total energy includes or not this term...
>I hope someone else can comment on that...
>
>stefano de Gironcoli
>
>
>> Any reply to any question is appreciated. If you can also guide me to
>> the position of source code refering to the question, that's great!
>>
>> Best regards
>>
>> Shujun Hu
>>
>> ------------------------------------------------------------------------
>>
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