[Wien] Problems of HCP (the fourth time)

[Stefaan Cottenier]

>     I think there was a misunderstanding about my first question:
> case.scfdmup
>  *************************************************************
>  Spin-polarized + s-o calculation, M||  0.000  0.000  1.000
>    Calculation of <X>, X=c*Xr(r)*Xls(l,s)
>    Xr(r)    =           I
>    Xls(l,s) = L(dzeta)
>    c=  1.00000
>    atom   L        up          dn         total
>  :XOP  1  3     0.00332     1.25294     1.25626
>  *************************************************************
>  
>     (1)My question is that* why* the direction of orbital moment* is 
> oppsite to* the spin moment ? (spin moment is up, orbital moment is 
> down, and I know the third rules of Hund's rules)

This file tells you that the orbital moment is +1.25626 (and not
-1.25626), and that the dn-electrons are responsible for this orbital
moment. That "+" means that it is parallel to the spin moment (which is
positive as well). You probably confuse "dn electrons" with "positive or
negative moment".

>     (2)Is setting or changing the occupational numbers of electrons in 
> case.dmatdn reasonable ? ( I mean we are try to simulate the microscopic 
> behavior by First principles, we should not change or set any parameters 
> in order to get the result we want.)  I don't know why my understanding 
> is right or not ,please correct it if I am wrong, thank you.

In an ideal world, you would get the correct answer, whatever your
starting input is. We don't live in this ideal world, however. If you
start from nonmagnetic atoms (by the case.inst file), you get a
nonmagnetic result, even if your material is a ferromagnet. Similarly
here, if you start from some specific distribution of electrons over the
m-orbitals, you will end up in a particular result with one orbital
moment. But no guarantee that no other starting distribution would lead
to another solution with a different orbital moment and a lower total
energy.

This problem is already there for simple magnetic calculations, where
you have some freedom how to distribute electrons over up and dn. With
orbital potentials (where you have even much more freedom how to
distribute electrons over many m-orbitals), it just gets worse.

>     (3)I checked the DOS by GGA or GGA+SO, the f_up states are always 
> localized with or without plus U. So my understanding is that plus U can 
> only redistribute the electrons of f_dn states, or localize the f_dn 
> states electrons ? Am I right ?

Correct. The f-up shell is filled, well-localized, and therefore inert.
All action happens in the dn-shell.

>     (4)I have read a book "Condensed Matter Physics" before, it said 
> spin_orbit spliting energy is about 300 meV, so what the effect of SO on 
> DOS ?

Schematically, it will split the single LDA-peak into two peaks,
according to the relativistic quantum number kappa (you'll probably see
that if you compare the f-dn DOS for GGA and GGA+SO). Adding U will
introduce even more structure in the DOS.

Stefaan