Determining the Magnetic Anisotropy: Difference between revisions

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Description: Magnetocrystalline Anisotropy Energy
Description: Magnetocrystalline Anisotropy Energy determined non-self-consistently


The Magnetocrystalline Anisotropy Energy is determined by rotating all spins according to different directions. First of all, an accurate ([[PREC|PREC]] = Accurate, [[LREAL|LREAL]] = .False.) collinear calculation (using the vasp-std script) in the ground state has to be done because of the very low changes in measured energies (sometimes, it could be about the micro-eV). Next, the Spin-Orbit Coupling ([[LSORBIT|LSORBIT]] = .True. ; using the vasp-ncl script) is took into account non-self-consistently ([[ICHARG|ICHARG]] = 11) for several spin orientations. The number of bands has to be twice compared to a collinear run).
The Magnetocrystalline Anisotropy Energy is determined by rotating all spins according to different directions. First of all, an accurate ([[PREC|PREC]] = Accurate, [[LREAL|LREAL]] = .False.) collinear calculation (using the <tt>vasp_std</tt> version) in the ground state has to be done. Next, the spin-orbit coupling ([[LSORBIT|LSORBIT]] = .True. using the <tt>vasp_ncl</tt> version) is taken into account non-self-consistently ([[ICHARG|ICHARG]] = 11) for several spin orientations. In most cases, the changes in energies are very low (sometimes around micro-eV). The number of bands for the has to be doubled compared to the collinear run.


To modify the orientation of the spins in the crystal, we consider the second approach describes [[SAXIS|here]]. For the [[MAGMOM|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 [uvw] is defined by the [[SAXIS|SAXIS]]-tag in the Cartesian frame. The Magnetocrystalline Anisotropy Energy is calculated by orientating the spins in different directions and the following equation : E<sub>MAE</sub> = E<sub>[uvw]</sub> - E<sub>min</sub>, with E<sub>min</sub> the energy of the most stable spin orientation.
To modify the orientation of the spins in the crystal, we consider the second approach described [[SAXIS|here]]. For the [[MAGMOM|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 <math>(u,v,w)</math> is defined by the [[SAXIS|SAXIS]]-tag in the Cartesian frame. The Magnetocrystalline Anisotropy Energy is calculated by orientating the spins in different directions and the following equation


::<math>E_{\text{MAE}} = E_{(u,v,w)} - E_0</math>


with <math>E_0</math> the energy of the most stable spin orientation.
More details are available in the [[SAXIS|SAXIS]] and [[LSORBIT|LSORBIT]] pages.
More details are available in the [[SAXIS|SAXIS]] and [[LSORBIT|LSORBIT]] pages.


''<u>Exercise :</u>'' Determine the Magnetocrystalline Anisotropy Energy of NiO in a non self-consistent approach by orientating the spins along the following path : (2,2,2) --> (2,2,1) --> (2,2,0) --> ... --> (2,2,-6). Compare to the [[Including_the_Spin_Orbit_Coupling|self-consistent approach]].
''<u>Exercise :</u>'' Determine the Magnetocrystalline Anisotropy Energy of NiO in a non self-consistent approach by orientating the spins along the following path : (2,2,2) --> (2,2,1) --> (2,2,0) --> ... --> (2,2,-6). Compare to the [[Including_the_Spin-Orbit_Coupling|self-consistent approach]].


----
----
*INCAR
*{{TAG|INCAR}}
<pre>
NiO MAE
  SYSTEM    = "NiO"


Electronic minimization
NiO MAE
  PREC = Accurate
  {{TAGBL|SYSTEM}}    = "NiO"
  ENCUT        = 450
   
  EDIFF        = 1E-7
Electronic minimization
  LORBIT        = 11
  {{TAGBL|PREC}} = Accurate
  LREAL        = .False.
  {{TAGBL|ENCUT}}         = 450
  ISYM          = -1
  {{TAGBL|EDIFF}}         = 1E-7
  NELMIN        = 6
  {{TAGBL|LORBIT}}       = 11
  #  ICHARG = 11
  {{TAGBL|LREAL}}         = .False.
  #  LCHARG = .FALSE.
  {{TAGBL|ISYM}}         = -1
  #  LWAVE = .FALSE.
  {{TAGBL|NELMIN}}       = 6
  #  NBANDS = 52
  {{TAGBL|ICHARG}} = 11
  #  GGA_COMPAT = .FALSE.
  {{TAGBL|LCHARG}} = .FALSE.
  {{TAGBL|LWAVE}} = .FALSE.
  {{TAGBL|NBANDS}} = 52
  {{TAGBL|GGA_COMPAT}} = .FALSE.
   
DOS
  {{TAGBL|ISMEAR}}    = -5
   
Magnetism
  {{TAGBL|ISPIN}}    = 2
  {{TAGBL|MAGMOM}} = 2.0 -2.0 2*0.0
  # {{TAGBL|MAGMOM}}    = 0 0 2 0 0 -2 6*0 # Including Spin-orbit
  # {{TAGBL|LSORBIT}}      = .True.
  # {{TAGBL|SAXIS}} = 1 0 0 # Quantization axis used to rotate all spins in a direction defined in the (O,x,y,z) Cartesian frame
   
Orbital mom.
  {{TAGBL|LORBMOM}} = T
   
Mixer
  {{TAGBL|AMIX}}      = 0.2
  {{TAGBL|BMIX}}      = 0.00001
  {{TAGBL|AMIX_MAG}}  = 0.8
  {{TAGBL|BMIX_MAG}}  = 0.00001
   
GGA+U
  {{TAGBL|LDAU}}      = .TRUE.
  {{TAGBL|LDAUTYPE}}  = 2
  {{TAGBL|LDAUL}}    = 2 -1
  {{TAGBL|LDAUU}}    = 5.00 0.00
  {{TAGBL|LDAUJ}}    = 0.00 0.00
  {{TAGBL|LDAUPRINT}} = 1
  {{TAGBL|LMAXMIX}}  = 4


DOS
*{{TAG|KPOINTS}}
  ISMEAR    = -5
 
Magnetism
  ISPIN    = 2
  MAGMOM = 2.0 -2.0 2*0.0
  # MAGMOM    = 0 0 2 0 0 -2 6*0 # Including Spin-orbit
  # LSORBIT      = .True.
  # SAXIS = 1 0 0 # Quantization axis used to rotate all spins in a direction defined in the (O,x,y,z) Cartesian frame
 
Orbital mom.
  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
</pre>
 
*KPOINTS
<pre>
<pre>
k-points
k-points
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</pre>
</pre>


*POSCAR
*{{TAG|POSCAR}}
<pre>
<pre>
NiO
NiO
Line 82: Line 83:
  1.5 1.5 1.5
  1.5 1.5 1.5
</pre>
</pre>
----


== Download ==
== Download ==
[http://www.vasp.at/vasp-workshop/examples/4_3_NiO_LSDA+U.tgz 4_3_NiO_LSDA+U.tgz]
[[Media:nio_noSOC.tgz| nio_noSOC.tgz]]
 
----
----
[[VASP_example_calculations|To the list of examples]] or to the [[The_VASP_Manual|main page]]


[[Category:Examples]]
[[Category:Examples]]

Latest revision as of 08:48, 11 April 2023

Description: Magnetocrystalline Anisotropy Energy determined non-self-consistently

The Magnetocrystalline Anisotropy Energy is determined by rotating all spins according to different directions. First of all, an accurate (PREC = Accurate, LREAL = .False.) collinear calculation (using the vasp_std version) in the ground state has to be done. Next, the spin-orbit coupling (LSORBIT = .True. using the vasp_ncl version) is taken into account non-self-consistently (ICHARG = 11) for several spin orientations. In most cases, the changes in energies are very low (sometimes around micro-eV). The number of bands for the has to be doubled compared to the collinear run.

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 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

with the energy of the most stable spin orientation. More details are available in the SAXIS and LSORBIT pages.

Exercise : Determine the Magnetocrystalline Anisotropy Energy of NiO in a non self-consistent approach by orientating the spins along the following path : (2,2,2) --> (2,2,1) --> (2,2,0) --> ... --> (2,2,-6). Compare to the self-consistent approach.


NiO MAE
  SYSTEM    = "NiO"
    
Electronic minimization
  PREC = Accurate
  ENCUT         = 450
  EDIFF         = 1E-7
  LORBIT        = 11
  LREAL         = .False.
  ISYM          = -1
  NELMIN        = 6
  #  ICHARG = 11
  #  LCHARG = .FALSE.
  #  LWAVE = .FALSE.
  #  NBANDS = 52
  #  GGA_COMPAT = .FALSE.
    
DOS
  ISMEAR    = -5
    
Magnetism
  ISPIN     = 2
  MAGMOM = 2.0 -2.0 2*0.0
  # MAGMOM    = 0 0 2 0 0 -2 6*0 # Including Spin-orbit
  # LSORBIT       = .True.
  # SAXIS = 1 0 0 # Quantization axis used to rotate all spins in a direction defined in the (O,x,y,z) Cartesian frame
    
Orbital mom.
  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 = 1
  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

Download

nio_noSOC.tgz