How can we predict the magnetic state of the materials from density of states (DOS) that is either the material is ferromagnetic, antiferromagnetic, ferrimagnetic or paramagnetic?
There is a way to calculate the magnetic moment from a spin polarised DOS calculation. The equation for the magnetic moment, μ from such a calculation is μ = (Nup- Ndown)μB, where Nup and Ndown are the number of spin-up and spin-down valence electrons, respectively. The Nup/down are related to the spin-up or spin-down density of states, n±(E) ('+' for spin-up and '-' for spin-down) via the relation
Nup = ∫ n+(E) dE and a corresponding equation for Ndown, where the integral goes on the domain (-∞,0) for a DOS with its origin shifted on to the Fermi level. Hence the magnetic moment is
μ = μB ∫ [n+(E) - n-(E)] dE.
You can approximate the integral via the trapezium rule. To work this out for specific orbital contributions for specific atoms, you can calculate the partial/projected DOS (PDOS) and apply the same equation. If you are working out the average magnetic moment for a particular layer (assuming a surface), you can straightforwardly average the PDOS for each atom in a layer, and work out the integral in the same manner as above. The proof is simple, and you can find it attached.
If you need any further assistance in the matter, please do feel free to contact me.
Is it possible to calculate magnetic moment from splitting of sub-bands in DOS?
Yes, but I am curious about the behavior of DOS across the Fermi level in different states of magnetic materials.
There is a way to calculate the magnetic moment from a spin polarised DOS calculation. The equation for the magnetic moment, μ from such a calculation is μ = (Nup- Ndown)μB, where Nup and Ndown are the number of spin-up and spin-down valence electrons, respectively. The Nup/down are related to the spin-up or spin-down density of states, n±(E) ('+' for spin-up and '-' for spin-down) via the relation
Nup = ∫ n+(E) dE and a corresponding equation for Ndown, where the integral goes on the domain (-∞,0) for a DOS with its origin shifted on to the Fermi level. Hence the magnetic moment is
μ = μB ∫ [n+(E) - n-(E)] dE.
You can approximate the integral via the trapezium rule. To work this out for specific orbital contributions for specific atoms, you can calculate the partial/projected DOS (PDOS) and apply the same equation. If you are working out the average magnetic moment for a particular layer (assuming a surface), you can straightforwardly average the PDOS for each atom in a layer, and work out the integral in the same manner as above. The proof is simple, and you can find it attached.
If you need any further assistance in the matter, please do feel free to contact me.
To distinguish between ferro and antiferro (or generally ferri-) you need to compare total energies of these states. Your elementary cell of course has to be big enough for the AFM order. For example for FeRh you would have a cell with 2 Fe atoms (together with Rh basis is 4). Then you simple do one calculation with Fe magnetizations parallel, second one antiparallel, and compare. A more complex way is to look at exchange integrals.
Thank you for your comments. I know on the basis of ground state we can also differentiate between anti and ferromagnetic states. But as I have mentioned in my question that I am interested to know the behavior of DOS in ferri, ferro, antiferro and paramagnetic states. Is it possible to predict paramagnetic and ferri-magnetic states by DFT? If yes, then how?
I am interested to predict magnetic states through DOS because we can also predict half metallic materials through DOS then why not magnetic materials.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Condensed Matter Physics
- Solid State Physics