[Wien] f orbital under an external magnetic field

[pieper]

Dear Bin Shao,

unfortunately I am travelling and won't be able to contribute during the 
next days. I am looking forward to comments from people with experience 
in calculations with rare earths.

May I just ask why you go for the energy and not for the magnetization 
or the susceptibility? If there is some change of the crystal field 
ground state this should show. From your calculation you get the size of 
the magnetic moments for a given field, from that you get a 
susceptibility. From what you say something happens around 4 T. I cannot 
guess from the information I have what, but I would expect it to show in 
the susceptibility as well.

Good luck with this interesting problem

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 15:47, schrieb Bin Shao:
> Dear Martin Pieper，
> 
> Thank you for your comments!
> 
> Actually, I intend to demonstrate that the energy difference between
> the ground state of Er^3+ (S=3/2; L=6; J=15/2) and the excited state
> (S=3/2; L=0; J=3/2) can be tuned by the external magnetic field, With
> the magnetic filed and the crystal field, the excited state splits
> into four states, |+3/2>, |+1/2>, |-1/2>, and |-3/2>. For the 45 Tesla
> magnetic field, the delta energy between the |+3/2> and |-3/2> is over
> 10 meV. Since we can not directly get the excited state in wien2k,
> even by forcing the occupation number, the calculation will still be
> trick. 
> 
> However, because the spin quantum number of the two states is the same
> (S=3/2), there is no spin flip from the ground state to the excited
> state. In this case, we can estimate the energy difference between the
> ground state and the excited state by calculating the energy
> difference between the occupied states of f electron in minority spin
> of the ground state and the unoccupied counterparts in minority spin
> of the ground state. The energy difference should become smaller with
> increasing the magnetic field, which can be attributed to the lower in
> energy of the |-3/2> state relative to the |+/-3/2> state with no
> magnetic field.
> 
> Since the energy shift is in the magnitude of meV, we can not seen
> this shift from the dos calculation due to the smear of the dos. Since
> the f band is usually very local and the band is very flat, so I
> checked the eigenvalues of the 7 f-electron at the Gamma point and try
> to show the energy shift from the variations of the eigenvalues.
> However, the results show that there is only an energy shift from the
> 0 T to 4 T. When the magnetic filed is increasing, the eigenvalues are
> almost the same as that of 4 T.
> 
>> This most probably is the old problem of the energy zero in
>> disguise.
> 
> This may be the problem. But I have calculated all the energy
> differences between the 3 unoccupied and 4 occupied states of f
> electron in minority spin, the 12 (3*4) values are keep the same trend
> while the magnetic filed is varied and they are all flat. For the
> different f states, they get different J and the energy shifts
> (g_J*mu_B*J*B) induced by the magnetic filed should be also different.
> So I am confused. It should be noted that the energy difference is
> independent to the energy zero. 
> 
> Best,
> 
> Bin
> 
> On Thu, Aug 6, 2015 at 7:23 PM, pieper <pieper at ifp.tuwien.ac.at>
> wrote:
> 
>> As an afterthought:
>> 
>> This most probably is the old problem of the energy zero in
>> disguise. The Zeeman interaction you estimated and as accounted for
>> in Wien2k is basically g*mu_B*S*B. It gives you the energy
>> difference between a moment pointing up and one pointing down.
>> However, it has a vanishing trace, the zero is at B=0 and the center
>> stays there.
>> 
>> Best regards,
>> 
>> Martin Pieper
>> 
>> ---
>> Dr. Martin Pieper
>> Karl-Franzens University
>> Institute of Physics
>> Universitätsplatz 5
>> A-8010 Graz
>> Austria
>> Tel.: +43-(0)316-380-8564 [3]
>> 
>> 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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> 
> --
> 
> Bin Shao
> Postdoc
> Department of Physics, Tsinghua University
> Beijing 100084, P. R. China
> Email: binshao1118 at gmail.com
> 
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