[Wien] f orbital under an external magnetic field

Fri Aug 7 00:56:32 CEST 2015

Dear Martin Pieper,

Thank you for your reply.

Actually, the energy difference can be observed by the photoluminescence
experiment. I want to make a demonstration for the experiment from
first-principles calculation.

May I just ask why you go for the energy and not for the magnetization or
> the susceptibility?

I don't know how to calculate the susceptibility of a material from
first-principles calculation. According to the definition, it is a constant
indicates the response of a material to an external magnetic field. I have
got the magnetic moments for a give field, then how to get the
susceptibility? Besides, I think the magnetic moments are almost the same
as 4T when I changed the magnitude of the magnetic field.

  If there is some change of the crystal field ground state this should
> show.

Do you mean that the magnetic filed may be change the crystal field? I am
not quite sure how to connect these two things, the magnetic field and
crystal field.

Best,

Bin

On Fri, Aug 7, 2015 at 6:35 AM, pieper <pieper at ifp.tuwien.ac.at> wrote:

> 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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-- 
Bin Shao
Postdoc
Department of Physics, Tsinghua University
Beijing 100084, P. R. China
Email: binshao1118 at gmail.com
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