Estimation of J magnetic coupling: Difference between revisions

Latest revision as of 08:48, 11 April 2023

Description: Estimation of the J magnetic exchange coupling using the GGA+U method.

Switching off the symmetry (ISYM = 0) is often necessary to generate different magnetic configurations.

Exercise : Study the change of the 180° superexchange coupling J₂ between the next nearest neighbors (d_Ni-Ni = 4.17 A) by varying the U_eff value. The following equation J₂ = (E_FM - E_AFM) / 12 expresses the super exchange Ni-O-Ni coupling as a function of the energy difference of the ferromagnetic (FM) and antiferromagnetic (AFM) configurations. In this case, the superexchange coupling J₁ between the nearest neighbors is neglected. The theoretical results can be compared to the experimental one : J₂ = 19.01 meV (Hutchings M. T., Samuelsen E. J., Phys. Rev. B 6, 9, 1972, 3447)

INCAR

NiO GGA+U AFM
  SYSTEM    = "NiO"
    
Electronic minimization
  ENCUT     = 450
  EDIFF     = 1E-4
  LORBIT    = 11
  LREAL     = .False.
  ISTART    = 0
  ISYM      = 0
  NELMIN    = 6
    
DOS
  ISMEAR    = -5
    
Magnetism
  ISPIN     = 2
  MAGMOM    = 2.0 -2.0 2*0  # AFM conf.
  # MAGMOM    = 2*2.0 2*0  # FM conf.

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

KPOINTS

k-points
 0
gamma
 4  4  4 
 0  0  0

POSCAR

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

Necessarely, the J magnetic coupling decreases with the increasing of the U_eff value. To assess the obtained value, similar calculations could be done using a hybrid functional.

Download

nio_Jcoupl.tgz

@@ Line 1: / Line 1: @@
-Description: Estimation of the J magnetic coupling using the GGA+U method (Dudarev's approach).
+Description: Estimation of the J magnetic exchange coupling using the GGA+U method.
-Using the relation J = (EFM - EAFM) / 4, antiferromagnetic (AFM) and ferromagnetic (FM) configurations have to be studied
+Switching off the symmetry ([[ISYM|ISYM]] = 0) is often necessary to generate different magnetic configurations.
-----
-*INCAR
-<pre>
-NiO GGA+U AFM
-  SYSTEM    = "NiO"
-Electronic minimization
+''<u>Exercise :</u>'' Study the change of the 180° superexchange coupling J<sub>2</sub> between the next nearest neighbors (d<sub>Ni-Ni</sub> = 4.17 A) by varying the U<sub>eff</sub> value. The following equation J<sub>2</sub> = (E<sub>FM</sub> - E<sub>AFM</sub>) / 12 expresses the super exchange Ni-O-Ni coupling as a function of the energy difference of the ferromagnetic (FM) and antiferromagnetic (AFM) configurations. In this case, the superexchange coupling J<sub>1</sub> between the nearest neighbors is neglected. The theoretical results can be compared to the experimental one : J<sub>2</sub> = 19.01 meV (Hutchings M. T., Samuelsen E. J., ''Phys. Rev. B 6'', 9, '''1972''', 3447)
-  ENCUT     = 300
-  EDIFF     = 1E-4
-  LORBIT    = 11
-  LREAL     = .False.
-  ISTART    = 0
-  ISYM      = -1
-  NELMIN    = 6
-DOS
+----
-  ISMEAR    = -5
+*{{TAG|INCAR}}
-Magnetism
+ NiO GGA+U AFM
-  ISPIN     = 2
+   {{TAGBL|SYSTEM}}    = "NiO"
-  MAGMOM    = 2.0 -2.0 2*0  # AFM conf.
-  #MAGMOM    = 2*2.0 2*0  # FM conf.
+ Electronic minimization
+   {{TAGBL|ENCUT}}     = 450
+   {{TAGBL|EDIFF}}     = 1E-4
+   {{TAGBL|LORBIT}}    = 11
+   {{TAGBL|LREAL}}     = .False.
+   {{TAGBL|ISTART}}    = 0
+   {{TAGBL|ISYM}}      = 0
+   {{TAGBL|NELMIN}}    = 6
+ DOS
+   {{TAGBL|ISMEAR}}    = -5
+ Magnetism
+   {{TAGBL|ISPIN}}     = 2
+   {{TAGBL|MAGMOM}}    = 2.0 -2.0 2*0  # AFM conf.
+   # {{TAGBL|MAGMOM}}    = 2*2.0 2*0  # FM conf.
-Mixer
+ Mixer
-  AMIX      = 0.2
+   {{TAGBL|AMIX}}      = 0.2
-  BMIX      = 0.00001
+   {{TAGBL|BMIX}}      = 0.00001
-  AMIX_MAG  = 0.8
+   {{TAGBL|AMIX_MAG}}  = 0.8
-  BMIX_MAG  = 0.00001
+   {{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
-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
+*{{TAG|KPOINTS}}
 <pre>
 k-points
@@ Line 51: / Line 54: @@
 </pre>
-*POSCAR
+*{{TAG|POSCAR}}
 <pre>
 NiO
@@ Line 67: / Line 70: @@
 ----
+Necessarely, the J magnetic coupling decreases with the increasing of the U<sub>eff</sub> value. To assess the obtained value, similar calculations could be done using a [[NiO HSE06|hybrid functional]].
-Necessarely, the J magnetic coupling decreases with the increasing of the Ueff value. To assess the obtain value, similar calculations could be done using a [[NiO HSE06|hybrid functional]].
 == Download ==
-[http://www.vasp.at/vasp-workshop/examples/4_3_NiO_LSDA+U.tgz 4_3_NiO_LSDA+U.tgz]
+[[Media:nio_Jcoupl.tgz| nio_Jcoupl.tgz]]
 ----
-[[VASP_example_calculations|To the list of examples]] or to the [[The_VASP_Manual|main page]]
 [[Category:Examples]]