[Wien] f orbital under an external magnetic field

[pieper]

Dear Bin Shao,

I never tried that one, and I am admittedly unsure about what the 
'eigenvalues at Gamma point of the Er' actually contain (density, 
multiplicity,...). So this will be a comment not a solution to your 
problem. My first suspect for something to go wrong would be this 
'simple estimate'. Do you estimate the thing you want to estimate?

 From the info you give I take it you estimated

\mu(Er) * \mu_B * 45 T / e \approx 10 meV

as the energy per Er in a field of 45 T, where \mu(Er) is the Er moment 
from your scf? Since you study Er-doping you presumably have one Er per 
unit cell? In a rigid band model one would expect a difference of 1 
\mu_B * 45 T between up and down channel at all k-points. The shift 
shows in the field induced magnetic moment, in a metal reshuffling 
electrons at the Fermi surface. You don't have rigid bands and you have 
SO mixing the spin channels, so why does one expect the 10 meV to show 
up at the Gamma point of Er?

I hope this helps a little,

Martin Pieper


---
Dr. Martin Pieper
Karl-Franzens University
Institute of Physics
Universitätsplatz 5
A-8010 Graz
Austria
Tel.: +43-(0)316-380-8564


Am 06.08.2015 04:55, schrieb Bin Shao:
> Dear all,
> 
> I made calculations of a compound with Er^3+(4f^11 5d^0 6s^0, ground
> state S=3/2, L=6, J=15/2) doping under an external magnetic field. I
> got the corresponding occupation of Er^3+ with 7 electrons in majority
> spin and 4 electrons in minority spin. With soc including, I got
> eigenvalues at Gamma point of the Er^3+ under the magnetic field from
> 4 Tesla to 45 Tesla. However, the picture indicates that the
> eigenvalues with the different magnetic fields almost keep the same as
> that of 4 T. Why? According to a simple estimation, the magnetic field
> of 45 T will introduce an energy shift about 10 meV, that would
> definitely be seen from the figure.
> 
> Any comments will be appreciated. Thank you in advance!
> 
> Best regards,
> 
> Bin
> 
> 
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