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 (d_Ni-Ni = 4.17 A) by varying the U_eff value. The following equation J₂ = (E_FM - E_AFM) / 12 expresses the super exchange coupling as a function of the energy difference of the antiferromagnetic (AFM) and ferromagnetic (FM) 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)

INCAR

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

KPOINTS

k-points
 0
gamma
 4  4  4 
 0  0  0

POSCAR

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 U_eff value. To assess the obtain value, similar calculations could be done using a hybrid functional.

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