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# Estimation of J magnetic coupling

Description: Estimation of the J magnetic exchange coupling using the GGA+U method.

Switching off the symmetry (ISYM = 0) is often necessary to generate different magnetic configurations.

Exercise : Study the change of the 180° superexchange coupling J2 between the next nearest neighbors (dNi-Ni = 4.17 A) by varying the Ueff value. The following equation J2 = (EFM - EAFM) / 12 expresses the super exchange Ni-O-Ni coupling as a function of the energy difference of the ferromagnetic (FM) and antiferromagnetic (AFM) configurations. In this case, the superexchange coupling J1 between the nearest neighbors is neglected. The theoretical results can be compared to the experimental one : J2 = 19.01 meV (Hutchings M. T., Samuelsen E. J., Phys. Rev. B 6, 9, 1972, 3447)

```NiO GGA+U AFM
SYSTEM    = "NiO"

Electronic minimization
ENCUT     = 450
EDIFF     = 1E-4
LORBIT    = 11
LREAL     = .False.
ISTART    = 0
ISYM      = 0
NELMIN    = 6

DOS
ISMEAR    = -5

Magnetism
ISPIN     = 2
MAGMOM    = 2.0 -2.0 2*0  # AFM conf.
# MAGMOM    = 2*2.0 2*0  # FM conf.
```
```Mixer
AMIX      = 0.2
BMIX      = 0.00001
AMIX_MAG  = 0.8
BMIX_MAG  = 0.00001

GGA+U
LDAU      = .TRUE.
LDAUTYPE  = 2
LDAUL     = 2 -1
LDAUU     = 5.00 0.00
LDAUJ     = 0.00 0.00
LDAUPRINT = 2
LMAXMIX   = 4
```

```k-points
0
gamma
4  4  4
0  0  0
```
```NiO
4.17
1.0 0.5 0.5
0.5 1.0 0.5
0.5 0.5 1.0
2 2
Cartesian
0.0 0.0 0.0
1.0 1.0 1.0
0.5 0.5 0.5
1.5 1.5 1.5
```

Necessarely, the J magnetic coupling decreases with the increasing of the Ueff value. To assess the obtained value, similar calculations could be done using a hybrid functional.