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# Difference between revisions of "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 described 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 ${\displaystyle (u,v,w)}$ 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

${\displaystyle E_{\text{MAE}}=E_{(u,v,w)}-E_{0}}$

with ${\displaystyle E_{0}}$ 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.

NiO GGA+U SOC
SYSTEM    = "NiO"

Electronic minimization
ENCUT     = 450
EDIFF     = 1E-7
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

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