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# Spin-orbit coupling in a Ni monolayer

## Contents

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:

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