Query Regarding Local Spin Density and Magnetic Moment

[alok_shukla1]

Dear Experts,

I have a question regarding the relationship between the local spin density and the magnetic moment obtained from VASP calculations.
Suppose an atom has a very small local magnetic moment, for example, on the order of 0.001 μB. In such a case, is it still possible to observe a finite spin density around that atom in the spin-density distribution?

More specifically, can a non-zero local spin polarization exist in the spatial spin-density distribution even when the integrated magnetic moment associated with the atom is essentially negligible? How should one interpret such a situation physically?

I would appreciate any clarification on this point. Thank you very much for your time and help.

[zahedzx]

Hi,

Yes. The local magnetic moment is the integral of the spin density over the chosen atomic region, whereas the spin density itself is a spatially resolved quantity.
An atom can therefore exhibit finite positive and negative spin-polarized regions in ρ↑(r)−ρ↓(r), while these contributions nearly cancel upon integration, resulting in a very small net moment (e.g., ∼10-3μB).

In practice, such a situation often indicates induced spin polarization due to hybridization with neighboring atoms rather than a significant intrinsic local moment.

I hope answered your question, otherwise please le me know.
Best regards,
Zahed

[alok_shukla1]

Dear Expert,
Indeed, it is a very helpful explanation. Thank you for resolving my query and for such a clear explanation.