Clarification on Calculating E_MAE Using the Formula E_{uvw} - E_0

[farah_shahzadi]

Dear VASP Community,

I am seeking clarification regarding the formula for calculating the magnetic anisotropy energy (E_MAE) as mentioned on the VASP Wiki, which states that E_MAE can be determined using the equation E(uvw)​−E0​.

Could you please provide guidance on how to accurately identify which energy corresponds to E0​, the most stable energy, and which corresponds to E(uvw)​? Specifically, I would like to understand the criteria or steps to determine E0​ and E(uvw)​ in the context of my calculations.

Thank you for your assistance.

Best regards,
Farah Shehzadi

[marie-therese.huebsch]

Hi,

It is basically a matter of definition. You choose some reference magnetic state, e.g., the most stable magnetic configuration or the in-plane ferromagnetic state or the one you are most interested in. Then you vary the direction of the magnetic moment. This could be written in terms of a vector (u,v,w) or an angle, etc. It is just a matter of notation. The magnetic anisotropy energy is the energy difference between the total energy of the reference magnetic state and the state with a different direction of the magnetic moments. Only the energy difference is meaningful. For the total energy there is no experimental quantity you could compare to.
When the reference magnetic state is not the magnetic ground state, the MAE could be negative. That's for instance the case in this example of an Fe monolayer: https://www.vasp.at/wiki/index.php/Spin ... _monolayer

Best,
Marie-Therese

[farah_shahzadi]

Thank you for your response. For the link you sent about spin-orbit coupling in a Fe monolayer, as I am doing test calculations, should I run those calculations using vasp_std or vasp_ncl?

[marie-therese.huebsch]

Hi,

Good question, because the magnetic moments are aligned collinear, nevertheless you need vasp_ncl!

For any noncollinear calculation you need vasp_ncl and SOC can only be included in a noncollinear framework. As MAE is due to SOC, you need to use vasp_ncl for the tutorial I linked before.

Best regards,
Marie-Therese

[farah_shahzadi]

Upon reviewing the link you provided on MAE calculations for Fe, I used the same POSCAR, INCAR, and KPOINTS files and performed VASP non-collinear calculations as mentioned on the VASP wiki. I obtained the following results for energies (I am only mentioning the last line from OSZICAR):
FOR IN-PLANE:
1 F= -.63126220E+01 E0= -.63121865E+01 d E =-.130647E-02 mag= 2.8462 -0.0000 0.0000
For OUT-OF-PLANE:
1 F= -.63122803E+01 E0= -.63116247E+01 d E =-.196664E-02 mag= -0.0000 -0.0000 2.8493

If I calculate EMAE=E⊥−E∥ , I get 0.3 meV, whereas the VASP wiki states -0.2 meV. Can you help clarify this discrepancy?