View source for Estimation of J magnetic coupling

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

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


''<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)

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*{{TAG|INCAR}}

 NiO GGA+U AFM
   {{TAGBL|SYSTEM}}    = "NiO"
     
 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
   {{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 


*{{TAG|KPOINTS}}
<pre>
k-points
 0
gamma
 4  4  4 
 0  0  0
</pre>

*{{TAG|POSCAR}}
<pre>
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
</pre>

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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]].

== Download ==
[[Media:nio_Jcoupl.tgz| nio_Jcoupl.tgz]]
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[[Category:Examples]]