# Re: [Wien] f orbital under an external magnetic field

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 <pie...@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
>
>
> 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.
>>
>>
>> Best regards,
>>
>> Bin
>>
>>
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--
Bin Shao
Postdoc
Department of Physics, Tsinghua University
Beijing 100084, P. R. China
Email: binshao1...@gmail.com

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