Dear Pavel,<br><br>Thank you for your reply！<br><br>You are definitely right. In general cases, the expression of the total energy should be modified. But in a uniaxial system, especially in cubic case, the torque method is correct and we can get the MAE from the expectation value of the derviative of the spin-orbit coupling Hamiltonian at the angle of 45. The author has calculated the magnetostriction in Fe-Ga alloy with variation of the c/c0 value in J. Phys.: Condens. Matter 15 S587. However, it's difficult for me to implement the torque method in Wien2K, since I am not familar with Fortran language. Would you like to tell me how to do the implement? for example, which part of the code do you need to change?<br>
<br>On the other hand, How many k-points do you need to get a precise using the ' force theorem' for fe monolayer?<br><br>Thank you!<br><br>Best regards,<br><br><br><div class="gmail_quote">On Tue, Sep 21, 2010 at 5:39 PM, Pavel Novak <span dir="ltr"><<a href="mailto:novakp@fzu.cz">novakp@fzu.cz</a>></span> wrote:<br>
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">Dear Bin Shao,<br>
<br>
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'<br>
(i) converge calculation without s-o<br>
(ii) using converged non s-o calculation run lapwso, lapw2up/dn for<br>
M along symmetry directions. Anisotropy is then given by differences<br>
of [:SUMup + :SUMdn] for M along say [001] and [100].<br>
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.<br>
<br>
Regards<br>
Pavel<div><div></div><div class="h5"><br>
<br>
<br>
On Mon, 20 Sep 2010, Bin Shao wrote:<br>
<br>
<blockquote class="gmail_quote" style="margin: 0pt 0pt 0pt 0.8ex; border-left: 1px solid rgb(204, 204, 204); padding-left: 1ex;">
Dear all,<br>
<br>
I intend to calculate magetocrystalline anisotropy (MCA) energy of the bcc<br>
Fe monolayer. Since the MCA energy usually has an order of magnitude about<br>
10^-6 eV, it's a tough work to get its calculated numerical value. The<br>
reference PRB. *54*. 61 proposes a torque method and the MCA energy can be<br>
easily evaluated through the expectation value of the angular derivative of<br>
the spin-orbit coupling Hamiltonian at an certain angle with this method.<br>
The paper gives an example of the free monolayer Fe using FLAPW method and<br>
mentioned that "one only needs the self-consistent scalar relativistic<br>
charge-spin density or potential and then performs one second-variational<br>
calculation with the SOC hamiltonian invoked."<br>
<br>
So, I want to know how to do this calculation, or to get the angular<br>
derivative of the derivative of the spin-orbit coupling Hamiltonian in<br>
Wien2K.<br>
<br>
Please give me some comments, thank you in advanced!<br>
<br>
Best regards,<br>
<br>
--<br>
Bin Shao, Ph.D. Candidate<br>
College of Information Technical Science, Nankai University<br>
94 Weijin Rd. Nankai Dist. Tianjin 300071, China<br>
Email: <a href="mailto:binshao1118@gmail.com" target="_blank">binshao1118@gmail.com</a><br>
<br>
</blockquote>
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</font></blockquote></div><br><br clear="all"><br>-- <br>Bin Shao, Ph.D. Candidate<br>College of Information Technical Science, Nankai University<br>94 Weijin Rd. Nankai Dist. Tianjin 300071, China<br>Email: <a href="mailto:binshao1118@gmail.com" target="_blank">binshao1118@gmail.com</a><br>