[Wien] Magnetocrystalline anisotropy energy

[Pavel Novak]

Dear Bin Shao,

we did implement the torque method in WIEN2k some years ago, but after 
gaining some experience we stopped using it. The problem is that the 
conception is not quite correct: when s-o coupling is strong and 
magnetization is in a general direction, spin is not along the 
quantization axis as we input it in .inso, exception being symmetrical 
directions, where Etot(M) has extrema - in case of (001) Fe film these are 
e.g. [001], [100], [110]. Then, however torque is zero by definition. 
It is thus more reliable to use the 'force theorem'
(i) converge calculation without s-o
(ii) using converged non s-o calculation run lapwso, lapw2up/dn for
     M along symmetry directions. Anisotropy is then given by differences
    of [:SUMup + :SUMdn] for M along say [001] and [100].
To get reliable results for Fe film is not too difficult, as the symmetry 
is axial. For bulk Fe it does not work - cubic anisotropy is too small.

Regards
Pavel


  On Mon, 20 Sep 2010, Bin Shao wrote:

> Dear all,
>
> I intend to calculate magetocrystalline anisotropy (MCA) energy of the bcc
> Fe monolayer. Since the MCA energy usually has an order of magnitude about
> 10^-6 eV, it's a tough work to get its calculated numerical value. The
> reference PRB. *54*. 61 proposes a torque method and the MCA energy can be
> easily evaluated through the expectation value of the angular derivative of
> the spin-orbit coupling Hamiltonian at an certain angle with this method.
> The paper gives an example of the free monolayer Fe using FLAPW method and
> mentioned that "one only needs the self-consistent scalar relativistic
> charge-spin density or potential and then performs one second-variational
> calculation with the SOC hamiltonian invoked."
>
> So, I want to know how to do this calculation, or to get the angular
> derivative of the derivative of the spin-orbit coupling Hamiltonian  in
> Wien2K.
>
> Please give me some comments, thank you in advanced!
>
> Best regards,
>
> --
> Bin Shao, Ph.D. Candidate
> College of Information Technical Science, Nankai University
> 94 Weijin Rd. Nankai Dist. Tianjin 300071, China
> Email: binshao1118 at gmail.com
>

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