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


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


{{TAG|LSORBIT}} = .TRUE. switches on spin-orbit coupling (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 (SOC){{cite|Steiner:2016}} and automatically sets {{TAG|LNONCOLLINEAR}} = True. It requires using <code>vasp_ncl</code>. SOC couples the spin degrees of freedom with the lattice degrees of freedom. We recommend carefully checking the symmetry and convergence of your results when using SOC; see below.


  {{TAG|LSORBIT}} = .TRUE.
{{TAG|LSORBIT}} only works for PAW potentials and is not supported by ultrasoft pseudopotentials. It is supported as of VASP.4.5.  
  {{TAG|SAXIS}} =  s<sub>x</sub> s<sub>y</sub> s<sub>z</sub>    ! global spin quantisation axis


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
== Assumptions and output ==
(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
* Switching on spin-orbit coupling (SOC) adds an additional term <math>H^{\alpha\beta}_{soc}\propto\mathbf{\sigma}\cdot\mathbf{L}</math> to the Hamiltonian that couples the Pauli-spin operator <math>\mathbf{\sigma}</math> with the angular momentum operator <math>\mathbf{L}</math>.{{cite|Steiner:2016}} As a relativistic correction, SOC acts predominantly in the immediate vicinity of the nuclei. Therefore, it is assumed that contributions of <math>H_{soc}</math> outside the PAW spheres are negligible. Hence, VASP calculates the matrix elements of <math>H_{soc}</math> only for the all-electron one-center contributions


:<math>
::<math>
\begin{align}
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
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_y & = & \cos(\beta) \sin(\alpha) m^{\rm axis}_x + \cos(\alpha) m^{\rm axis}_y + \sin(\beta) \sin(\alpha) m^{\rm axis}_z \\  
m_z & = & -\sin(\beta) m^{\rm axis}_x+ \cos(\beta) m^{\rm axis}_z
\end{align}
</math>
</math>


:where <math> \phi_i({\bf r}) = R_i(|{\bf r}-{\bf R}_i|) Y_{l_im_i}(\theta,\varphi) </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 <math>\alpha=\uparrow,\downarrow</math> 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}}


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>:
* It is possible to write the partial magnetization by setting {{TAG|LORBIT}}, i.e., the site- and orbital-resolved expectation value of the Pauli-spin operator <math>\mathbf{\sigma}</math>. And the partial orbital angular momentum by setting {{TAG|LORBMOM}}, i.e., the site- and orbital-resolved expectation value of the orbital angular momentum operator <math>\mathbf{L}</math>.
{{NB|mind|The orbital angular momentum (vector-like quantity) is written to the {{FILE|OUTCAR}} file in Cartesian coordinates, while the magnetic moments (spinor-like quantity) are read and written in the basis specified by {{TAG|SAXIS}} (spinor space).|:}}
:The default orientation of spinor space is <math>\sigma_1=\hat x</math>, <math>\sigma_2 =\hat y</math>, <math>\sigma_3 = \hat z</math>. Hence, the bases agree by default, and no transformation is required.


:<math>
* After a successful calculation including SOC, VASP writes the following results to the {{TAG|OUTCAR}} file:  
\begin{align}
\alpha &=& {\rm atan} \frac{s_y}{s_x} \\
\beta &=& {\rm atan} \frac{\vert s_x^2+s_y^2\vert}{s_z}
\end{align}
</math>
 
The inverse transformation is given by
 
:<math>
\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}_y & = & -\sin(\alpha) m_z + \cos(\alpha) m_y \\
m^{\rm axis}_z & = & \sin(\beta) \cos(\alpha) m_x + \sin(\beta) \sin(\alpha) m_y + \cos(\beta) m_z
\end{align}
</math>
 
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:


:<math>
Spin-Orbit-Coupling matrix elements
\begin{align}
m_x & = & m^{\rm axis}_x \\
Ion:    1  E_soc:    -0.0984080
m_y & = & m^{\rm axis}_y \\
l=  1
m_z & = & m^{\rm axis}_z
    0.0000000    -0.0134381    -0.0134381
\end{align}
    -0.0134381    0.0000000    -0.0134381
</math>
    -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, <code>1  E_soc</code> represents the accumulated energy contribution <math>E_{soc}=\sum_{ij} E_{soc}^{ij}</math> 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>.


The second important case, is ''m''<sup>axis</sup>=(0,0,''m''). In this case
== Symmetry and convergence ==


:<math>
In any spin-polarized ({{TAG|ISPIN}}=2) or noncollinear ({{TAG|LNONCOLLINEAR}}=T) calculation, even without SOC, the total energy depends on the relative orientation of magnetic moments. For instance, two magnetic sites may couple ferromagnetically or antiferromagnetically. On the other hand, the total energy is independent of the orientation of the magnetic moments with respect to the lattice without SOC. For instance, in-plane and out-of-plane moments on a surface would yield the same energy in the absence of SOC.
\begin{align}
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 = m s_y / \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}
</math>


Switching on SOC couples the spin degrees of freedom that live in spinor space and the lattice degrees of freedom that live in real space, see {{TAG|SAXIS}}. Therefore, the in-plane and out-of-plane magnetic moments on a surface would yield different energies, when including SOC. Similarly, the ferromagnetically or antiferromagnetically ordered magnetic moments may additionally align with, e.g., the third lattice vector by setting {{TAG|LSORBIT}} = True.


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}}.
Generally, be extremely diligent when using SOC: The energy differences can be of the order of few <math>\mu</math>eV/atom, k-point convergence is tedious and slow, and the required compute time might be huge, even for small cells.
{{NB|warning| When SOC is included, we recommend testing whether switching off symmetry ({{TAG|ISYM}}{{=}}-1) changes the results.|}} Often, the k-point set changes from one to the other spin orientation, thus worsening the transferability of the results. Note that the {{FILE|WAVECAR}} file cannot be reread properly if the number of k-points changes. Hence, restart the calculation without symmetry from a converged charge density by setting {{TAG|ICHARG}}=1! Also, consider the setting of {{TAG|LMAXMIX}}.


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)
We recommend setting {{TAG|GGA_COMPAT}} = False for noncollinear calculations since this improves the numerical precision of GGA calculations.


{{TAG|MAGMOM}} = x y z  ! local magnetic moment in x,y,z
Please check the sections on {{TAG|LNONCOLLINEAR}}, {{TAG|SAXIS}}, {{TAG|LMAXMIX}}, and {{TAG|GGA_COMPAT}}.
{{TAG|SAXIS}} =  0 0 1  ! quantisation axis parallel to z
<!---


or
Known issue: Additionally, VASP.4.6 (and all older versions) had a bug in symmetrizing magnetic fields (fixed only VASP.4.6.23). Although we are confident that the present code base is free of errors in the symmetrization, it is recommended to double-check the results without symmetry.


{{TAG|MAGMOM}} = 0 0 total_magnetic_moment  ! local magnetic moment parallel to {{TAG|SAXIS}}
It is recommended to set {{TAG|GGA_COMPAT}} = False for noncollinear calculations since this improves the numerical precision of GGA calculations.
{{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 {{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}}):
Line 90: Line 78:
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).
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 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).
*Be very careful with symmetry. When spin-orbit coupling is selected, we recommend to test whether switching off symmetry altogether ({{TAG|ISYM}}=-1) changes the results. 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). Although we are confident that the present code base is free of errors in the symmetrization, it is recommended to double check the results without symmetry.


*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.
*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 huge even for small cells.


*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.
*It is recommended to set {{TAG|GGA_COMPAT}} = .FALSE. for non-collinear calculations, since this improves the numerical precision of GGA calculations.-->
 
== Related tags and articles ==
== Related Tags and Sections ==
{{TAG|LNONCOLLINEAR}},
{{TAG|MAGMOM}},
{{TAG|MAGMOM}},
{{TAG|SAXIS}},
{{TAG|SAXIS}},
{{TAG|LNONCOLLINEAR}}, {{TAG|LORBIT}}
{{TAG|LORBMOM}},
{{TAG|LORBIT}},
{{TAG|LMAXMIX}},
{{TAG|GGA_COMPAT}}
 
{{sc|LSORBIT|Examples|Examples that use this tag}}


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


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

Latest revision as of 12:10, 25 September 2023

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

Description: Switch on spin-orbit coupling.


LSORBIT = True switches on spin-orbit coupling (SOC)[1] and automatically sets LNONCOLLINEAR = True. It requires using vasp_ncl. SOC couples the spin degrees of freedom with the lattice degrees of freedom. We recommend carefully checking the symmetry and convergence of your results when using SOC; see below.

LSORBIT only works for PAW potentials and is not supported by ultrasoft pseudopotentials. It is supported as of VASP.4.5.

Assumptions and output

  • Switching on spin-orbit coupling (SOC) adds an additional term to the Hamiltonian that couples the Pauli-spin operator with the angular momentum operator .[1] As a relativistic correction, SOC acts predominantly in the immediate vicinity of the nuclei. Therefore, it is assumed that contributions of outside the PAW spheres are negligible. Hence, VASP 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 of the pseudo-orbital with band-index n and Bloch vector k, and and are the Fermi- and k-point weights, respectively.[1]
  • It is possible to write the partial magnetization by setting LORBIT, i.e., the site- and orbital-resolved expectation value of the Pauli-spin operator . And the partial orbital angular momentum by setting LORBMOM, i.e., the site- and orbital-resolved expectation value of the orbital angular momentum operator .
Mind: The orbital angular momentum (vector-like quantity) is written to the OUTCAR file in Cartesian coordinates, while the magnetic moments (spinor-like quantity) are read and written in the basis specified by SAXIS (spinor space).
The default orientation of spinor space is , , . Hence, the bases agree by default, and no transformation is required.
  • After a successful calculation including SOC, VASP writes the following results to the OUTCAR file:
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, 1 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 .

Symmetry and convergence

In any spin-polarized (ISPIN=2) or noncollinear (LNONCOLLINEAR=T) calculation, even without SOC, the total energy depends on the relative orientation of magnetic moments. For instance, two magnetic sites may couple ferromagnetically or antiferromagnetically. On the other hand, the total energy is independent of the orientation of the magnetic moments with respect to the lattice without SOC. For instance, in-plane and out-of-plane moments on a surface would yield the same energy in the absence of SOC.

Switching on SOC couples the spin degrees of freedom that live in spinor space and the lattice degrees of freedom that live in real space, see SAXIS. Therefore, the in-plane and out-of-plane magnetic moments on a surface would yield different energies, when including SOC. Similarly, the ferromagnetically or antiferromagnetically ordered magnetic moments may additionally align with, e.g., the third lattice vector by setting LSORBIT = True.

Generally, be extremely diligent when using SOC: The energy differences can be of the order of few eV/atom, k-point convergence is tedious and slow, and the required compute time might be huge, even for small cells.

Warning: When SOC is included, we recommend testing whether switching off symmetry (ISYM=-1) changes the results.

Often, the k-point set changes from one to the other spin orientation, thus worsening the transferability of the results. Note that the WAVECAR file cannot be reread properly if the number of k-points changes. Hence, restart the calculation without symmetry from a converged charge density by setting ICHARG=1! Also, consider the setting of LMAXMIX.

We recommend setting GGA_COMPAT = False for noncollinear calculations since this improves the numerical precision of GGA calculations.

Please check the sections on LNONCOLLINEAR, SAXIS, LMAXMIX, and GGA_COMPAT.

Related tags and articles

LNONCOLLINEAR, MAGMOM, SAXIS, LORBMOM, LORBIT, LMAXMIX, GGA_COMPAT

Examples that use this tag

References