How to calculate the magnetic exchange parameter of Nickel Oxide NiO

We will calculate the J2 parameter which represents the superexchange coupling between the next nearest neighbors (d_Ni-Ni = 4.17 A)using the GGA+U method.

We need to do a ferromagnetic and antiferromagnetic calculations and calculate the J2 parameter through a formula.

Ferromagnetic calculation

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

  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*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

 

POTCAR

Download the pseudopotential file from this link nio_Jcoupl.tgz

/NiO_fm> vasp_std

The output for the OUTCAR file

 

1 F= -.19296856E+02 E0= -.19296856E+02  d E =0.000000E+00  mag=     4.0000

 

Antiferromagnetic calculation

We need to replace only line in the INCAR file

MAGMOM    = 2*2.0 2*0  # FM conf

  by 

MAGMOM    = 2.0 -2.0 2*0  # AFM conf.

 

/NiO_afm> vasp_std

The output for the OUTCAR file

1 F= -.19537598E+02 E0= -.19537598E+02  d E =0.000000E+00  mag=     0.0000

 

Calculation of J2

 E_FM = -.19296856E+02 eV  = -19.296856 eV

E_AFM = -.19537598E+02 eV = -19.537598 eV

J₂ = (E_FM - E_AFM) / 12 = (  -19.296856 + ( -19.537598  ) )/12 

J2 =  0.02006183 eV = 20.06183 meV

The experimental value : J₂ = 19.01 meV (Hutchings M. T., Samuelsen E. J., Phys. Rev. B 6, 9, 1972, 3447)