Including the Spin-Orbit Coupling

Description: Spin-Orbit Coupling (SOC) included self-consistently

The Magnetocrystalline Anisotropy Energy is determined by rotating all spins according to different directions. To modify the orientation of the spins in the crystal, we consider the second approach describes in the SAXIS page. For the MAGMOM-tag, the total local magnetic moment is written according to the z direction (necessarily, the x and y-directions are equal to 0). The spin orientation [uvw] is defined by the SAXIS-tag in the Cartesian frame. The Magnetocrystalline Anisotropy Energy is calculated by orientating the spins in different directions and the following equation : E_MAE = E_[uvw] - E_min, with E_min the energy of the most stable spin orientation.

More details are available in the SAXIS and LSORBIT pages.

Exercise : Determine the total magnetic moment by adding the orbital moment of the Ni atoms. Calculate the Magnetocrystalline Anisotropy Energy of NiO by orientating the spins along the following path : (2,2,2) --> (2,2,1) --> (2,2,0) --> ... --> (2,2,-6). Identify the most stable spin orientation according to this path.

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• INCAR

NiO GGA+U SOC
  SYSTEM    = "NiO"

Electronic minimization
  ENCUT     = 450
  EDIFF     = 1E-5
  LORBIT    = 11
  LREAL     = .False.
  ISTART    = 0
  ISYM      = -1
  NELMIN    = 6
  LSORBIT   = .True.
  LWAVE     = .False.
  LCHARG    = .False.

DOS
  ISMEAR    = -5

Magnetism
  ISPIN     = 2
  MAGMOM    = 0 0 2 0 0 -2 6*0
  SAXIS     = 2 2 2

Orbital Moment
  LORBMOM   = T 

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

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