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# Estimation of J magnetic coupling

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 J

_{2}between the next nearest neighbors (d

_{Ni-Ni}= 4.17 A) by varying the U

_{eff}value. The following equation J

_{2}= (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 J

_{1}between the nearest neighbors is neglected. The theoretical results can be compared to the experimental one : J

_{2}= 19.01 meV (Hutchings M. T., Samuelsen E. J.,

*Phys. Rev. B 6*, 9,

**1972**, 3447)

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 = 2 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

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.