Spin-orbit coupling in a Ni monolayer

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Task

Spin-orbit coupling (SOC) in a freestanding Ni monolayer.

Input

POSCAR

fcc Ni 100 surface
 3.53
   .50000   .50000   .00000
  -.50000   .50000   .00000
   .00000   .00000  5.00000
  1
Cartesian
   .00000   .00000   .00000

INCAR

SYSTEM        = Ni (100) monolayer
ISTART        = 0
ENCUT         = 270.00
LNONCOLLINEAR = .TRUE.
MAGMOM        = 0.0 0.0 1.0
VOSKOWN       = 1
LSORBIT       = .TRUE.
    
LMAXMIX       = 4

• Initialization of moment along z-direction (out of plane) (MAGMOM = 0.0 0.0 1.0).
• Spin-orbit interaction switched on (LSORBIT=.TRUE.).
• For the second calculation, switch to in-plane magnetization by setting MAGMOM = 1.0 0.0 0.0 in the INCAR file.

KPOINTS

k-points
 0
Monkhorst-Pack
9 9 1
0 0 0

Calculation

• The sample output for the total energy using out of plane magnetization is given in the OSZICAR file:

...
DAV:  20    -0.371322930070E+01    0.15852E-03   -0.11632E-03   636   0.235E-01    0.225E-02
DAV:  21    -0.371323204989E+01   -0.27492E-05   -0.13047E-05   500   0.184E-02
   1 F= -.37132320E+01 E0= -.37139803E+01  d E =0.224478E-02  mag=  0.0000  0.0000  0.9035

• The sample output for the total energy using in plane magnetization looks like the following:

...
DAV:  19    -0.371443443024E+01   -0.80757E-04   -0.35822E-03  1084   0.323E-01    0.119E-02
DAV:  20    -0.371446032472E+01   -0.25894E-04   -0.42423E-05   916   0.263E-02
   1 F= -.37144603E+01 E0= -.37150300E+01  d E =0.170900E-02  mag=  0.9049  0.0000  0.0000

• From the energy difference of these calculations we see that the easy axis lies in plane:

$E_{\textrm{MAE}}=E(m_{\perp})-E(m_{\parallel})=1.2 \, \textrm{meV}$

Download

4_4_SOI_Ni.tgz

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