Orbital resolved MAE from the SOC matrix element

[fahmida_fakhera]

Hi,
I am trying to understand how the orbital-resolved magnetic anisotropy energy (as shown in Fig. 4) can be extracted from VASP, following the methodology of Peng et al. ["Origin of interfacial perpendicular magnetic anisotropy in MgO/CoFe/metallic capping layer structures," Scientific Reports 5, 18173 (2015)]. When performing a non-collinear calculation with SOC included, VASP provides spin-orbit coupling matrix elements for 𝑙=0,1,2,3. Are these matrix elements directly useful for plotting the orbital-resolved MAE?

Thank you for your assistance.
Fahmida

[pedro_melo]

Dear Fahmida,

I am not familiar with orbital-resolved MAE. Do you have a reference with its definition and some equation that tells you how to compute it? The one you mentioned does not specify how it is done. That way I might be able to associate it with what VASP outputs.

Kind regards,
Pedro

[fahmida_fakhera]

Hi,
Here is a reference : Pan, W. (2022). Tuning the magnetic anisotropy and topological phase with electronic correlation in single-layer H-FeBr 2. Physical Review B, 106(12), 125122. Please find 4 (a, d). I have added the equations for obtaining MAE and an example in .png format. My question is: are the “Spin–Orbit Coupling Matrix elements” (3×3 for p-orbitals, 5×5 for d-orbitals, etc.) provided in the OUTCAR for noncollinear calculations—where the magnetic moments are oriented along the xy and z directions—useful for this purpose?

Many thanks for your response.

Regards,
Fahmida

[pedro_melo]

Dear Fahmida,

My apologies for the delayed response. Unfortunately the answer is no, the numbers reported in the file do not match what the equations you posted seem to require.

Kind regards,
Pedro