Atomic Units in INFO.OUT

[zhangyg]

Dear Kay:

I am making a bfinite=.true. calculation. I plan to increase bfieldc successively to see the change in "total moment". So I would like to know the units printed out in INFO.OUT for the "total moment" at the end and "global magnetic field" at the beginning (actually an input parameter). When I tried to figure them out by timing these two parameters to get the "external B-field" energy, also printed in INFO.OUT, I can not get correct results even using the ga4 factor. Maybe I cann't do that because E_Bext is an integration of m times Bext.

Atomic Units for magnetism is still confusing me. We have magnetic dipole moment versus magnetic moment, magnetic flux density versus magnetic field strength. Hopefully the units concerning the bfieldc, "total moment" can be given in the user's guide sometime in the future.

with best wishes!

zhangyg

[exciting]

Dear zhangyg,

Magnetic units are somewhat confusing. The rules used in EXCITING are as follows:

1. Magnetic moment is defined to be the integral of the magnetisation vector field (WITHOUT the prefactor of mu_B).

2. The magnetisation vector field is defined to be

    m(r) = sum_i psi_i*(r)(sigma)psi_i(r)

where psi is a spinor wavefunction, sigma is the vector of Pauli matrices,, the sum is over occupied states and the spinor degrees of freedom are summed over (note this is also without the mu_B factor).

3. The units of magnetic field are defined by how the external B-field appears in the Hamiltonian:

   H_Bext = ge*alpha/4 (sigma.B_ext)

where ge is the electron g-factor (2.00231...).

4. The external magnetic field energy is thus

   E_Bext = int (ge*alpha/4) m(r).B_ext(r)

The external magnetic field in EXCITING was originally intended to be infinitesimal i.e. just to break spin symmetry, so units didn't matter much (even though they were always treated correctly). The variable bfinite has been added only recently, so proceed with caution.

Let me know how it goes.

All the best,
Kay.

[zhangyg]

Dear Kay:

Thanks for you explanation. So the units follow strictly the atomic units. Thus:

1 bfieldc = 2.350517 x 10^5 Tesla

1 total moment = 1 mu_B

Am I correct?

I will keep you informed about my progress.

Thanks again and

with best regards!

zhangyg

[zhangyg]

Dear Kay:

Would you kindly tell me straightly the unit for bfieldc. My understanding as 2.35 x 10^5 Tesla seems too large. The calculated susceptibility, as a consequence, is too small.

Thanks a lot.

zhangyg

[exciting]

Dear zhangyg,

Here's what I get for conversion of the EXCITING magnetic field units to Tesla:

1. Suppose we have a constant magnetisation in the unit cell pointing in the z-direction and which integrates to 1 (one), i.e. one fully polarised electron.

2. Let bfieldc=1.0 in the z-direction in exciting.in

3. Therefore the total energy in Hartree must be (from the coupling constant in the routine seceqnsv)

     g_e alpha/4 = 0.003652907479 Hartree
                 = 1.59257420868e-20 Joules

4. The total energy of one electron in a field of 1 Tesla is (from the Bohr magneton)

     mu_B*1 Tesla = 927.400949e-26 Joules

5. Thus the EXCITING units of magnetic field must be

     1 bfieldc = 1717.244532037614 Tesla

I think this factor differs from yours by alpha (1/137.03599...).

Does this correct the susceptibility value?

Regards,
Kay.

[zhangyg]

Dear Kay:

Thanks greatly for your response. Just to make sure, I have one more question: for a fixed spin calculation, the input parameter "momfix" is in the unit of "mu_B". Is this correct?

Really appreciate all your helps and the beautiful program. It is really EXCITING.

best wishes.

zhangyg

[exciting]

Dear zhangyg,

For a FSM calculation the input "momfix" is, like the output magnetisation, in units of mu_B.

Glad you like the code. Thanks for all the very useful feedback, I'll add it to the documentation/FAQ.

Best wishes,
Kay.