Query related with MAE calculations

[alok_shukla1]

Dear Experts,
I have performed DFT+U calculations in VASP for a bulk heterostructure (ISIF=3). After optimization, I performed magnetic anisotropy calculations with SOC included in SCF runs for spin orientations along different crystallographic directions. I used a high-k mesh of 15×15×1 k-points to calculate the magnetic anisotropy energies. I obtained the following results:
100 = -270.34617219 eV (ΔE = 0.1251 meV)
010 =-270.34615575 eV (ΔE = 0.14155 meV)
001 = -270.34624761 eV (ΔE = 0.04969 meV)
110 = -270.34629730 eV (ΔE = 0 meV, lowest)

Now, I have some confusion regarding the obtained results:
1. Which direction should be considered the easy axis?
2. Since the differences are extremely small (<0.15 meV), should I simply take 110 as the easy axis (lowest energy), or treat 001 as nearly degenerate? The model Hamiltonian construction and the rest of the things depend on the easy axis in my system.
3. More generally, how should such small anisotropy energies be interpreted in practice? Are they meaningful, or within the numerical noise of DFT+U calculations?

I would be really thankful for suggestions and for clarifying my doubts.

[zahedzx]

Hi,

Based on the energies you report, the formal interpretation is that 110 is the easy axis, since it corresponds to the lowest total energy.

However, the energy difference between 110 and 001 is only about 0.05 meV, which is very small. Therefore, before concluding that 110 is unambiguously the easy axis, it is important to verify that the MAE is well converged with respect to parameters such as the k-point mesh, ENCUT, and electronic convergence criteria.

If the ordering of the energies remains unchanged upon further convergence tests, then 110 can be considered the easy axis with confidence. If the energy difference between 110 and 001 is comparable to the numerical uncertainty of the calculation, then the more appropriate conclusion would be that these directions are effectively degenerate and that the system has a very weak magnetic anisotropy.

In summary:

1. Formally, 110 is the easy axis.
2. The small energy difference to 001 suggests a weak preference for 110.
3. The physical significance of this difference depends on demonstrating that it is larger than the numerical uncertainty of the MAE calculation.

Best regards,
Zahed