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{{TAGDEF|LSORBIT|.TRUE. {{!}} .FALSE.}}
{{TAGDEF|LSORBIT|.TRUE. {{!}} .FALSE.|.FALSE.}}


Description: {{TAG|LSORBIT}} specifies whether spin-orbit coupling is taken into account.
Description: {{TAG|LSORBIT}} specifies whether spin-orbit coupling is taken into account.
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Supported as of VASP.4.5.
Supported as of VASP.4.5.


{{TAG|LSORBIT}} = .TRUE. switches on spin-orbit coupling and automatically sets {{TAG|LNONCOLLINEAR}} = .TRUE.. This option works only for PAW potentials and is not supported by ultrasoft pseudopotentials. If spin-orbit coupling is not included, the energy does not depend on the direction of the magnetic moment, i.e. rotating all magnetic moments by the same angle results in principle exactly in the same energy. Hence there is no need to define the spin quantization axis, as long as spin-orbit coupling is not included. Spin-orbit coupling however couples the spin to the crystal structure. Spin-orbit coupling is switched on by selecting
{{TAG|LSORBIT}} = .TRUE. switches on spin-orbit coupling (automatically sets {{TAG|LNONCOLLINEAR}} = .TRUE.).{{cite|Steiner:2016}} This option works only for PAW potentials and is not supported by ultrasoft pseudopotentials. If spin-orbit coupling is not included, the energy does not depend on the direction of the magnetic moment, i.e. rotating all magnetic moments by the same angle results in principle exactly in the same energy. Hence there is no need to define the spin quantization axis, as long as spin-orbit coupling is not included. Spin-orbit coupling however couples the spin to the crystal structure. Spin-orbit coupling is switched on by selecting


   {{TAG|LSORBIT}} = .TRUE.
   {{TAG|LSORBIT}} = .TRUE.
  {{TAG|SAXIS}} =  <math>s_x s_y s_z</math> (quantisation axis for spin)


where the default for {{TAG|SAXIS}} = <math>(0+,0,1)</math> (the notation <math>0+</math> implies an infinitesimal small positive number in <math>\hat x</math> direction). All magnetic moments are now given with respect to the axis  
The spin quantization axis may be specified by means of the {{TAG|SAXIS}}-tag,
<math>(s_x,s_y,s_z)</math>, where we have adopted the convention '''that all magnetic moments and spinor-like quantities written or read by VASP are given with respect to this axis'''. This includes the {{TAG|MAGMOM}} line in the {{TAG|INCAR}} file, the total and local magnetizations in the {{TAG|OUTCAR}} and {{TAG|PROCAR}} file, the spinor-like orbitals in the {{TAG|WAVECAR}} file, and the magnetization density in the {{TAG|CHGCAR}} file. With respect to the Cartesian lattice vectors the components of the magnetization are (internally) given by


<span id="eqnarray">
  {{TAG|SAXIS}} =  s<sub>x</sub> s<sub>y</sub> s<sub>z</sub>    ! global spin quantisation axis
<math>
 
where the default for {{TAG|SAXIS}} = (0+,0,1) (the notation 0+ implies an infinitesimal small positive number in ''x''-direction). All magnetic moments are now given with respect to the axis
(s<sub>x</sub>,s<sub>y</sub>,s<sub>z</sub>), where we have adopted the convention '''that all magnetic moments and spinor-like quantities written or read by VASP are given with respect to this axis'''. This includes the {{TAG|MAGMOM}} line in the {{FILE|INCAR}} file, the total and local magnetizations in the {{FILE|OUTCAR}} and {{FILE|PROCAR}} file, the spinor-like orbitals in the {{TAG|WAVECAR}} file, and the magnetization density in the {{FILE|CHGCAR}} file. With respect to the Cartesian lattice vectors the components of the magnetization are (internally) given by
 
:<math>
\begin{align}
\begin{align}
m_x & = & \cos(\beta) \cos(\alpha) m^{\rm axis}_x - \sin(\alpha) m^{\rm axis}_y + \sin(\beta) \cos(\alpha) m^{\rm axis}_z \\  
m_x & = & \cos(\beta) \cos(\alpha) m^{\rm axis}_x - \sin(\alpha) m^{\rm axis}_y + \sin(\beta) \cos(\alpha) m^{\rm axis}_z \\  
Line 21: Line 23:
\end{align}
\end{align}
</math>
</math>
</span>




Where <math>m^{\rm axis}</math> is the externally visible magnetic moment. Here, <math>\alpha</math> is the angle between the {{TAG|SAXIS}} vector <math>(s_x,s_y,s_z)</math> and the Cartesian vector <math>\hat x</math>, and <math>\beta</math> is the angle between the vector {{TAG|SAXIS}} and the Cartesian vector <math>\hat z</math>:
Where ''m''<sup>axis</sup> is the externally visible magnetic moment. Here, <math>\alpha</math> is the angle between the {{TAG|SAXIS}} vector (s<sub>x</sub>,s<sub>y</sub>,s<sub>z</sub>) and the Cartesian vector <math>\hat x</math>, and <math>\beta</math> is the angle between the vector {{TAG|SAXIS}} and the Cartesian vector <math>\hat z</math>:


<span id="eqnarray">
:<math>
<math>
\begin{align}
\begin{align}
\alpha &=& {\rm atan} \frac{s_y}{s_x} \\  
\alpha &=& {\rm atan} \frac{s_y}{s_x} \\  
Line 33: Line 33:
\end{align}
\end{align}
</math>
</math>
</span>


The inverse transformation is given by
The inverse transformation is given by


<span id="eqnarray">
:<math>
<math>
\begin{align}
\begin{align}
m^{\rm axis}_x & = & \cos(\beta) \cos(\alpha) m_x + \cos(\beta) \sin(\alpha) m_y + \sin(\beta) m_z \\
m^{\rm axis}_x & = & \cos(\beta) \cos(\alpha) m_x + \cos(\beta) \sin(\alpha) m_y + \sin(\beta) m_z \\
Line 45: Line 43:
\end{align}
\end{align}
</math>
</math>
</span>


It is easy to see that for the default <math>(s_x, s_y, s_z)=(0+,0,1)</math>, both angles are zero, i.e. <math>\beta=0</math> and <math>\alpha=0</math>. In this case, the internal representation is simply equivalent to the external representation:
It is easy to see that for the default (s<sub>x</sub>,s<sub>y</sub>,s<sub>z</sub>)=(0+,0,1), both angles are zero, i.e. <math>\beta=0</math> and <math>\alpha=0</math>. In this case, the internal representation is simply equivalent to the external representation:


<span id="eqnarray">
:<math>
<math>
\begin{align}
\begin{align}
m_x & = & m^{\rm axis}_x \\  
m_x & = & m^{\rm axis}_x \\  
Line 57: Line 53:
\end{align}
\end{align}
</math>
</math>
</span>


The second important case, is <math>m^{\rm axis}_x=0</math> and <math>m^{\rm axis}_y=0</math>. In this case
The second important case, is ''m''<sup>axis</sup>=(0,0,''m''). In this case


<span id="eqnarray">
:<math>
<math>
\begin{align}
\begin{align}
m_x & = & \sin(\beta)*\cos(\alpha) m^{\rm axis}_z = m^{\rm axis}_z s_x / \sqrt{s_x^2+s_y^2+s_z^2} \\
m_x & = & \sin(\beta)*\cos(\alpha) m = m s_x / \sqrt{s_x^2+s_y^2+s_z^2} \\
m_y & = & \sin(\beta)*\sin(\alpha) m^{\rm axis}_z = m^{\rm axis}_z s_y / \sqrt{s_x^2+s_y^2+s_z^2} \\
m_y & = & \sin(\beta)*\sin(\alpha) m = m s_y / \sqrt{s_x^2+s_y^2+s_z^2} \\
m_z & = & \cos(\beta) m^{\rm axis}_z = m^{\rm axis}_z s_z / \sqrt{s_x^2+s_y^2+s_z^2}
m_z & = & \cos(\beta) m = m s_z / \sqrt{s_x^2+s_y^2+s_z^2}
\end{align}
\end{align}
</math>
</math>
</span>


Hence now the magnetic moment is parallel to the vector {{TAG}|SAXIS}}. Thus there are two ways to rotate the spins in an arbitrary direction, either by changing the initial magnetic moments {{TAG|MAGMOM}} or by changing {{TAG}|SAXIS}}.


To initialize calculations with the magnetic moment parallel to a chosen vector <math>(x,y,z)</math>, it is therefore possible to either specify (assuming a single atom in the cell)
Hence now the magnetic moment is parallel to the vector {{TAG|SAXIS}}. Thus there are two ways to rotate the spins in an arbitrary direction, either by changing the initial magnetic moments {{TAG|MAGMOM}} or by changing {{TAG|SAXIS}}.
 
To initialize calculations with the magnetic moment parallel to a chosen vector (''x'',''y'',''z''), it is therefore possible to either specify (assuming a single atom in the cell)


  {{TAG|MAGMOM}} = x y z  ! local magnetic moment in x,y,z
  {{TAG|MAGMOM}} = x y z  ! local magnetic moment in x,y,z
Line 81: Line 75:


  {{TAG|MAGMOM}} = 0 0 total_magnetic_moment  ! local magnetic moment parallel to {{TAG|SAXIS}}
  {{TAG|MAGMOM}} = 0 0 total_magnetic_moment  ! local magnetic moment parallel to {{TAG|SAXIS}}
  {{TAG|SAXIS}} =  x y z  ! quantization axis parallel to vector <math>(x,y,z)</math>
  {{TAG|SAXIS}} =  x y z  ! quantization axis parallel to vector (''x'',''y'',''z'')


Both setups should in principle yield exactly the same energy, but for implementation reasons the second method is usually more precise. The second method also allows to read a preexisting {{TAG|WAVECAR}} file (from a collinear or non collinear run), and to continue the calculation with a different spin orientation. When a non collinear {{TAG|WAVECAR}} file is read, the spin is assumed to be parallel to {{TAG|SAXIS}} (hence VASP will initially report a magnetic moment in the <math>z</math>-direction only).
Both setups should in principle yield exactly the same energy, but for implementation reasons the second method is usually more precise. The second method also allows to read a preexisting {{FILE|WAVECAR}} file (from a collinear or non collinear run), and to continue the calculation with a different spin orientation. When a non collinear {{FILE|WAVECAR}} file is read, the spin is assumed to be parallel to {{TAG|SAXIS}} (hence VASP will initially report a magnetic moment in the ''z''-direction only).


The recommended procedure for the calculation of magnetic anisotropies is therefore (please check the section on {{TAG|LMAXMIX}}):
The recommended procedure for the calculation of magnetic anisotropies is therefore (please check the section on {{TAG|LMAXMIX}}):


*Start with a collinear calculation and calculate a {{TAG|WAVECAR}} and {{TAG|CHGCAR}} file.
*Start with a collinear calculation and calculate a {{FILE|WAVECAR}} and {{FILE|CHGCAR}} file.
*Add the tags
*Add the tags


   {{TAG|LSORBIT}} = .TRUE.
   {{TAG|LSORBIT}} = .TRUE.
   {{TAG|ICHARG}} = 11      ! non selfconsistent run, read {{TAG|CHGCAR}}
   {{TAG|ICHARG}} = 11      ! non selfconsistent run, read {{FILE|CHGCAR}}
   {{TAG|LMAXMIX}} = 4      ! for d-elements increase {{TAG|LMAXMIX}} to 4, f-elements: {{TAG|LMAXMIX}} = 6
   {{TAG|LMAXMIX}} = 4      ! for d-elements increase {{TAG|LMAXMIX}} to 4, f-elements: {{TAG|LMAXMIX}} = 6
                             ! you need to set {{TAG|LMAXMIX}} already in the collinear calculation
                             ! you need to set {{TAG|LMAXMIX}} already in the collinear calculation
Line 97: Line 91:
   {{TAG|NBANDS}} = 2 * number of bands of collinear run
   {{TAG|NBANDS}} = 2 * number of bands of collinear run


VASP reads in the {{TAG|WAVECAR}} and {{TAG|CHGCAR}} files, aligns the spin quantization axis parallel to {{TAG|SAXIS}}, which implies that the magnetic field is now parallel to {{TAG|SAXIS}}, and performs a non selfconsistent calculation. By comparing the energies for different orientations the magnetic anisotropy can be determined. Please mind, that a completely selfconsistent calculation ({{TAG|ICHARG}} = 1) is in principle also possible with VASP, but this would allow the spinor wavefunctions to rotate from their initial orientation parallel to {{TAG|SAXIS}} until the correct groundstate is obtained, i.e. until the magnetic moment is parallel to the easy axis. In practice this rotation will be slow, however, since reorientation of the spin gains little energy. Therefore if the convergence criterion is not too tight, sensible results might be obtained even for fully selfconsistent calculations (in the few cases we have tried this worked beautifully).
VASP reads in the {{FILE|WAVECAR}} and {{FILE|CHGCAR}} files, aligns the spin quantization axis parallel to {{TAG|SAXIS}}, which implies that the magnetic field is now parallel to {{TAG|SAXIS}}, and performs a non selfconsistent calculation. By comparing the energies for different orientations the magnetic anisotropy can be determined. Please mind, that a completely selfconsistent calculation ({{TAG|ICHARG}} = 1) is in principle also possible with VASP, but this would allow the spinor wavefunctions to rotate from their initial orientation parallel to {{TAG|SAXIS}} until the correct groundstate is obtained, i.e. until the magnetic moment is parallel to the easy axis. In practice this rotation will be slow, however, since reorientation of the spin gains little energy. Therefore if the convergence criterion is not too tight, sensible results might be obtained even for fully selfconsistent calculations (in the few cases we have tried this worked beautifully).
      
      
*Be very careful with symmetry. We recommend to switch off symmetry ({{TAG|ISYM}} = 0) altogether, when spin-orbit coupling is selected. Often the k-point set changes from one to the other spin orientation, worsening the transferability of the results (also the {{TAG|WAVECAR}} file can not be reread properly if the number of k-points changes). Additionally VASP.4.6 (and all older versions) had a bug in the symmetrization of magnetic fields (fixed only VASP.4.6.23).
*Be very careful with symmetry. We recommend to switch off symmetry altogether ({{TAG|ISYM}}=-1), when spin-orbit coupling is selected. Often the k-point set changes from one to the other spin orientation, worsening the transferability of the results (also the {{FILE|WAVECAR}} file can not be reread properly if the number of k-points changes). Additionally VASP.4.6 (and all older versions) had a bug in the symmetrization of magnetic fields (fixed only VASP.4.6.23).
 
*Generally be extremely careful, when using spin-orbit coupling: energy differences are tiny, k-point convergence is tedious and slow, and the computer time you require might be infinite.
 
*It is recommended to set {{TAG|GGA_COMPAT}} = .FALSE. for non collinear calculations in VASP.4.6, since this improves the numerical precision of GGA calculations.
 
== Assumptions and output ==
Switching on spin-orbit coupling (SOC) in a conventional DFT calculation adds an additional term <math>H^{\alpha\beta}_{soc}\propto\vec{\sigma}\cdot\vec{L}</math> to the Hamiltonian that couples the Pauli-spin operator <math>\vec{\sigma}</math> with the angular momentum operator <math>\vec{L}=\vec{r}\times \vec{p}</math>.{{cite|Steiner:2016}}
As an relativistic correction SOC acts predominantly in the immediate vicinity of the nuclei, such that it is assumed that contributions of <math>H_{soc}</math> outside the PAW spheres are negligible. VASP, therefore, calculates the matrix elements of <math>H_{soc}</math> only for the all-electron one-center contributions
 
<math>
E_{soc}^{ij} = \delta_{{\bf R}_i{\bf R}_j}\delta_{l_il_j} \sum_{n \bf k} w_{\bf k} f_{n\bf k} \sum_{\alpha\beta} \langle \tilde{\psi}^\alpha_{n\bf k} |\tilde{p}_i \rangle \langle \phi_i | H^{\alpha\beta}_{soc} | \phi_j \rangle \langle \tilde{p}_j | \tilde{\psi}^\beta_{n\bf k} \rangle
</math>
 
where <math> \phi_i({\bf r}) = R_i(|{\bf r}-{\bf R}_i|) Y_{l_im_i}(\hat{ \bf r-\bf R}_i) </math> are the partial waves of an atom centered at <math>{\bf R}_i</math>, <math>\tilde{\psi}^\alpha_{n\bf k}</math> is the spinor-component &alpha; of the pseudo-orbital with band-index ''n'' and Bloch-vector '''k''', and <math>f_{n\bf k}</math> and <math>w_{\bf k}</math> are the Fermi- and '''k'''-point weights, respectively.{{cite|Steiner:2016}}
After a successful calculation with inclusion of spin-orbit coupling, VASP writes following results to the {{TAG|OUTCAR}}:


*Generally be extremely careful, when using spin-orbit coupling: energy differences are tiny, k-point convergence is tedious and slow, and the computer time you require might be infinite. Additionally, this feature-- although long implemented in VASP-- is still in a late beta stage, as you might deduce from the frequent updates. No promise, that your results will be useful!!!
Spin-Orbit-Coupling matrix elements
      Here a small summary from the README file:
          *20.11.2003: The present {{TAG|GGA}} routine breaks the symmetry slightly for non orthorhombic cells. A spherical cutoff is now imposed on the gradients and all intermediate results in reciprocal space. This changes the {{TAG|GGA}}
Ion:    1  E_soc:     -0.0984080
                      results slightly (usually by 0.1 meV per atom), but is important for magnetic anisotropies.
l=  1
          *05.12.2003: continue... Now VASP.4.6 defaults to the old behavior {{TAG|GGA_COMPAT}} = .TRUE., the new behavior can be obtained by setting {{TAG|GGA_COMPAT}} = .FALSE. in the {{TAG|INCAR}} file.
    0.0000000    -0.0134381    -0.0134381
          *12.08.2003: MAJOR BUG FIX in symmetry.F and paw.F: for non-collinear calculations the symmetry routines did not work properly.
    -0.0134381    0.0000000    -0.0134381
*If you have read the previous lines, you will realize that it is recommended to set {{TAG|GGA_COMPAT}} = .FALSE. for non collinear calculations in VASP.4.6, since this improves the numerical precision of {{TAG|GGA}} calculations.
    -0.0134381    -0.0134381    0.0000000
l=  2
    0.0000000    -0.0005072    0.0000000    -0.0005072    -0.0024560
    -0.0005072    0.0000000    -0.0018420    -0.0005072    -0.0006140
    0.0000000    -0.0018420    0.0000000    -0.0018420    0.0000000
    -0.0005072    -0.0005072    -0.0018420    0.0000000    -0.0006140
    -0.0024560    -0.0006140    0.0000000    -0.0006140    0.0000000
l=   3
    0.0000000    -0.0000000    0.0000000    0.0000000    0.0000000    -0.0000000    -0.0000000
    -0.0000000    0.0000000    -0.0000000    0.0000000    -0.0000000    -0.0000000    -0.0000000
    0.0000000    -0.0000000    0.0000000    -0.0000000    -0.0000000    -0.0000000    0.0000000
    0.0000000    0.0000000    -0.0000000    0.0000000    -0.0000000    0.0000000    0.0000000
    0.0000000    -0.0000000    -0.0000000    -0.0000000    0.0000000    -0.0000000    0.0000000
    -0.0000000    -0.0000000    -0.0000000    0.0000000    -0.0000000    0.0000000    -0.0000000
    -0.0000000    -0.0000000    0.0000000    0.0000000    0.0000000    -0.0000000    0.0000000
Here "E_soc" represents the accumulated energy <math>E_{soc}=\sum_{ij} E_{soc}^{ij}</math> contribution inside the augmentation sphere that is centered at <math>{\bf R}_1</math> (position of ion 1), while the following entries correspond to the matrix elements
<math>E_{soc}^{ij}</math>
for the angular momentum <math>l</math>.


== Related Tags and Sections ==
== Related Tags and Sections ==
{{TAG|MAGMOM}},
{{TAG|MAGMOM}},
{{TAG|SAXIS}},
{{TAG|SAXIS}},
{{TAG|LNONCOLLINEAR}}, {{TAG|LORBIT}}
{{TAG|LNONCOLLINEAR}}
 
{{sc|LSORBIT|Examples|Examples that use this tag}}


== References ==
<references/>
----
----
[[The_VASP_Manual|Contents]]


[[Category:INCAR]][[Category:Magnetism]][[Category:Spin-orbit coupling]]
[[Category:INCAR]][[Category:Magnetism]][[Category:Spin-orbit coupling]][[Category:Noncollinear magnetism]]

Revision as of 19:18, 12 November 2020

LSORBIT = .TRUE. | .FALSE.
Default: LSORBIT = .FALSE. 

Description: LSORBIT specifies whether spin-orbit coupling is taken into account.


Supported as of VASP.4.5.

LSORBIT = .TRUE. switches on spin-orbit coupling (automatically sets LNONCOLLINEAR = .TRUE.).[1] This option works only for PAW potentials and is not supported by ultrasoft pseudopotentials. If spin-orbit coupling is not included, the energy does not depend on the direction of the magnetic moment, i.e. rotating all magnetic moments by the same angle results in principle exactly in the same energy. Hence there is no need to define the spin quantization axis, as long as spin-orbit coupling is not included. Spin-orbit coupling however couples the spin to the crystal structure. Spin-orbit coupling is switched on by selecting

 LSORBIT = .TRUE.

The spin quantization axis may be specified by means of the SAXIS-tag,

 SAXIS =   sx sy sz    ! global spin quantisation axis

where the default for SAXIS = (0+,0,1) (the notation 0+ implies an infinitesimal small positive number in x-direction). All magnetic moments are now given with respect to the axis (sx,sy,sz), where we have adopted the convention that all magnetic moments and spinor-like quantities written or read by VASP are given with respect to this axis. This includes the MAGMOM line in the INCAR file, the total and local magnetizations in the OUTCAR and PROCAR file, the spinor-like orbitals in the WAVECAR file, and the magnetization density in the CHGCAR file. With respect to the Cartesian lattice vectors the components of the magnetization are (internally) given by


Where maxis is the externally visible magnetic moment. Here, is the angle between the SAXIS vector (sx,sy,sz) and the Cartesian vector , and is the angle between the vector SAXIS and the Cartesian vector :

The inverse transformation is given by

It is easy to see that for the default (sx,sy,sz)=(0+,0,1), both angles are zero, i.e. and . In this case, the internal representation is simply equivalent to the external representation:

The second important case, is maxis=(0,0,m). In this case


Hence now the magnetic moment is parallel to the vector SAXIS. Thus there are two ways to rotate the spins in an arbitrary direction, either by changing the initial magnetic moments MAGMOM or by changing SAXIS.

To initialize calculations with the magnetic moment parallel to a chosen vector (x,y,z), it is therefore possible to either specify (assuming a single atom in the cell)

MAGMOM = x y z   ! local magnetic moment in x,y,z
SAXIS =  0 0 1   ! quantisation axis parallel to z

or

MAGMOM = 0 0 total_magnetic_moment   ! local magnetic moment parallel to SAXIS
SAXIS =  x y z   ! quantization axis parallel to vector (x,y,z)

Both setups should in principle yield exactly the same energy, but for implementation reasons the second method is usually more precise. The second method also allows to read a preexisting WAVECAR file (from a collinear or non collinear run), and to continue the calculation with a different spin orientation. When a non collinear WAVECAR file is read, the spin is assumed to be parallel to SAXIS (hence VASP will initially report a magnetic moment in the z-direction only).

The recommended procedure for the calculation of magnetic anisotropies is therefore (please check the section on LMAXMIX):

  • Start with a collinear calculation and calculate a WAVECAR and CHGCAR file.
  • Add the tags
  LSORBIT = .TRUE.
  ICHARG = 11      ! non selfconsistent run, read CHGCAR
  LMAXMIX = 4      ! for d-elements increase LMAXMIX to 4, f-elements: LMAXMIX = 6
                           ! you need to set LMAXMIX already in the collinear calculation
  SAXIS =  x y z   ! direction of the magnetic field
  NBANDS = 2 * number of bands of collinear run

VASP reads in the WAVECAR and CHGCAR files, aligns the spin quantization axis parallel to SAXIS, which implies that the magnetic field is now parallel to SAXIS, and performs a non selfconsistent calculation. By comparing the energies for different orientations the magnetic anisotropy can be determined. Please mind, that a completely selfconsistent calculation (ICHARG = 1) is in principle also possible with VASP, but this would allow the spinor wavefunctions to rotate from their initial orientation parallel to SAXIS until the correct groundstate is obtained, i.e. until the magnetic moment is parallel to the easy axis. In practice this rotation will be slow, however, since reorientation of the spin gains little energy. Therefore if the convergence criterion is not too tight, sensible results might be obtained even for fully selfconsistent calculations (in the few cases we have tried this worked beautifully).

  • Be very careful with symmetry. We recommend to switch off symmetry altogether (ISYM=-1), when spin-orbit coupling is selected. Often the k-point set changes from one to the other spin orientation, worsening the transferability of the results (also the WAVECAR file can not be reread properly if the number of k-points changes). Additionally VASP.4.6 (and all older versions) had a bug in the symmetrization of magnetic fields (fixed only VASP.4.6.23).
  • Generally be extremely careful, when using spin-orbit coupling: energy differences are tiny, k-point convergence is tedious and slow, and the computer time you require might be infinite.
  • It is recommended to set GGA_COMPAT = .FALSE. for non collinear calculations in VASP.4.6, since this improves the numerical precision of GGA calculations.

Assumptions and output

Switching on spin-orbit coupling (SOC) in a conventional DFT calculation adds an additional term to the Hamiltonian that couples the Pauli-spin operator with the angular momentum operator .[1] As an relativistic correction SOC acts predominantly in the immediate vicinity of the nuclei, such that it is assumed that contributions of outside the PAW spheres are negligible. VASP, therefore, calculates the matrix elements of only for the all-electron one-center contributions

where are the partial waves of an atom centered at , is the spinor-component α of the pseudo-orbital with band-index n and Bloch-vector k, and and are the Fermi- and k-point weights, respectively.[1] After a successful calculation with inclusion of spin-orbit coupling, VASP writes following results to the OUTCAR:

Spin-Orbit-Coupling matrix elements

Ion:    1  E_soc:     -0.0984080
l=   1
    0.0000000    -0.0134381    -0.0134381
   -0.0134381     0.0000000    -0.0134381
   -0.0134381    -0.0134381     0.0000000
l=   2
    0.0000000    -0.0005072     0.0000000    -0.0005072    -0.0024560
   -0.0005072     0.0000000    -0.0018420    -0.0005072    -0.0006140
    0.0000000    -0.0018420     0.0000000    -0.0018420     0.0000000
   -0.0005072    -0.0005072    -0.0018420     0.0000000    -0.0006140
   -0.0024560    -0.0006140     0.0000000    -0.0006140     0.0000000
l=   3
    0.0000000    -0.0000000     0.0000000     0.0000000     0.0000000    -0.0000000    -0.0000000
   -0.0000000     0.0000000    -0.0000000     0.0000000    -0.0000000    -0.0000000    -0.0000000
    0.0000000    -0.0000000     0.0000000    -0.0000000    -0.0000000    -0.0000000     0.0000000
    0.0000000     0.0000000    -0.0000000     0.0000000    -0.0000000     0.0000000     0.0000000
    0.0000000    -0.0000000    -0.0000000    -0.0000000     0.0000000    -0.0000000     0.0000000
   -0.0000000    -0.0000000    -0.0000000     0.0000000    -0.0000000     0.0000000    -0.0000000
   -0.0000000    -0.0000000     0.0000000     0.0000000     0.0000000    -0.0000000     0.0000000

Here "E_soc" represents the accumulated energy contribution inside the augmentation sphere that is centered at (position of ion 1), while the following entries correspond to the matrix elements for the angular momentum .

Related Tags and Sections

MAGMOM, SAXIS, LNONCOLLINEAR

Examples that use this tag

References