Determining the Magnetic Anisotropy

Description: Magnetocrystalline Anisotropy Energy

The Magnetocrystalline Anisotropy Energy is determined by rotating all spins according to different directions. First of all, an accurate (PREC = Accurate, LREAL = .False.) collinear calculation (using the vasp-std script) in the ground state has to be done because of the very low changes in measured energies (sometimes, it could be about the micro-eV). Next, the Spin-Orbit Coupling (LSORBIT = .True. ; using the vasp-ncl script) is took into account non-self-consistently (ICHARG = 11) for several spin orientations. The number of bands has to be twice compared to a collinear run).

To modify the orientation of the spins in the crystal, we consider the second approach describes here. 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 Magnetocrystalline Anisotropy Energy of NiO by orientating the spins along the following path : (1,0,0) --> (7,1,1) --> (6,2,2) --> ... --> (1,1,1) ou (4,4,4) --> ... --> (1,7,7) --> (0,1,1). Verify that the NiO possesses an easy (magnetic) axis according to the [111] direction. You can can also determine the orbital moment and its variation according to this path.

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• INCAR

NiO MAE
  SYSTEM    = "NiO"

Electronic minimization
  PREC = Accurate
  ENCUT         = 450
  EDIFF         = 1E-7
  LORBIT        = 11
  LREAL         = .False.
  ISYM          = -1
  NELMIN        = 6
  #  ICHARG = 11
  #  LCHARG = .FALSE.
  #  LWAVE = .FALSE.
  #  NBANDS = 52
  #  GGA_COMPAT = .FALSE.

DOS
  ISMEAR    = -5

Magnetism
  ISPIN     = 2
  MAGMOM = 2.0 -2.0 2*0.0
  # MAGMOM    = 0 0 2 0 0 -2 6*0 # Including Spin-orbit
  # LSORBIT       = .True.
  # SAXIS = 1 0 0 # Quantization axis used to rotate all spins in a direction defined in the (O,x,y,z) Cartesian frame

Orbital mom.
  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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Firstly, a collinear calculation has to be done. The magnetic anisotropy is determined non-self-consistently by rotating all spins according to a defined direction [uvw].

Download

4_3_NiO_LSDA+U.tgz

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