Magnetic dipole-dipole interaction and crystal field splitting

[hongyang_ma]

Dear VASP users,

I was wondering if VASP has the capability to compute the magnetic dipole-dipole interaction and crystal field splitting energy of a solid system?

Regards,
Hongyang

[merzuk.kaltak]

Dear Hongyang,

yes VASP can calculate the crystal field splitting energy in solids.
This energy is typically estimated from the density of states of the system with the broken symmetry.
For instance following example is taken from a study on silver doped hollandite
For convenience, here is Fig. 6 from the paper:

pDosAg2Mn8O16.png

The blue and green lines show the dx2-y2 and dz2 states of the Mn in the purple octahedra.
In the high-symmetry case these two states represent the e_g states of Mn in the purple octahedra, see Fig. (c), where both peaks are very close to each other.
To good approximation, there is no crystal field splitting present.
Fig. (d) shows the DOS after doping the material with Ag and applying a specific U-value.
The symmetry of the e_g states is now broken, dz2 and d_x2-y2 peaks are now well separated.
The energy difference of the corresponding blue and green peak in Fig. (d) is the crystal field splitting after the Jahn-Teller distortion and is roughly 2 eV.

[hongyang_ma]

Dear Merzuk,

Thank you for your response. It has been quite helpful.

Regarding the computation of magnetic dipole-dipole interaction energy, does VASP have the capability to handle this task? If not, could you recommend a post-processing code or method that can perform this calculation?

Regards,
Hongyang

[merzuk.kaltak]

Dear Hongyang,

here is a study on magnetic dipole-dipole interaction using magnetic density from first principles.
Looking at Eq. (1) the atomic spin moment model (AMM) gives an estimate for the magnetic dipole-dipole interaction via

AMM.png

To evaluate this expression, you require the positions of the atoms R_j from the POSCAR and their magnetic moments m_i.
The magnetic moments can be found in the OUTCAR after an ISPIN=2 calculation.
Look for following lines.

Code: Select all

 magnetization (x)                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                                                                                                                                        
# of ion       s       p       d       tot                                                                                                                                                                                                                                                                              
------------------------------------------                                                                                                                                                                                                                                                                              
    1        0.006  -0.003   1.702   1.705                                                                                                                                                                                                                                                                              
    2       -0.006   0.003  -1.702  -1.705                                                                                                                                                                                                                                                                              
    3        0.000   0.000   0.000   0.000                                                                                                                                                                                                                                                                              
    4        0.000   0.000   0.000   0.000             

Be aware that the energies in vasp in eV.

[hongyang_ma]

Dear Merzuk,

Great! Thanks a lot!

Regards,
Hongyang

[hongyang_ma]

Dear Merzuk,

I'm curious if this method also applies to rare earth elements like Er for investigating the crystal field splitting energy of its 4f orbitals.

Regards,
Hongyang

Dear Hongyang,

yes VASP can calculate the crystal field splitting energy in solids.
This energy is typically estimated from the density of states of the system with the broken symmetry.
For instance following example is taken from a study on silver doped hollandite
For convenience, here is Fig. 6 from the paper:
pDosAg2Mn8O16.png
The blue and green lines show the dx2-y2 and dz2 states of the Mn in the purple octahedra.
In the high-symmetry case these two states represent the e_g states of Mn in the purple octahedra, see Fig. (c), where both peaks are very close to each other.
To good approximation, there is no crystal field splitting present.
Fig. (d) shows the DOS after doping the material with Ag and applying a specific U-value.
The symmetry of the e_g states is now broken, dz2 and d_x2-y2 peaks are now well separated.
The energy difference of the corresponding blue and green peak in Fig. (d) is the crystal field splitting after the Jahn-Teller distortion and is roughly 2 eV.