Magnetic coupling constants

To compare measured magnetic coupling constants with values obtained from theoretical calculations, the signs of the magnetic parameters should be known. In the following, different approaches for the determination of absolute and relative signs of the principal values of hf and quadrupole tensors will be discussed. 

The values of the electron relaxation rates of the coupled metal ion strongly depend both on the relative electron relaxation rates of the isolated ions and on the value of the magnetic coupling constant J. When the absolute value of J (expressed as J /K) is smaller than both electronic relaxation rates, no effect on the electronic relaxation of the pair is expected. When J /H > (electron relaxation rate of the first ion) but smaller than T[ 2) (electron relaxation rate of the second ion), from first order perturbation... 

Figure 5.7. Correlation of the scalar coupling constants JLL., LL = HH, HD, HT of transition metal dihydride-dihydrogen complexes with d. Solid line Eq. (5.6). Upper dotted line first term of Eq. (5.6). Lower dotted line second term of Eq. (5.6). For complexes with dHH > 2.0 A, negative signs for the scalar magnetic coupling constants were assumed. Reprinted with permission from Grundemann et at.53 Copyright 1999 American Chemical Society.

Whenever HF and standard (LDA/GGA) DFT functionals yield systematically errors with opposite sign with respect to experiment, the formulation of hybrid functionals improves the accuracy of the calculations. This is the case for band gaps, phonon spectra, magnetic coupling constants, and all properties that depend on the extent of electronic localisation at either perfect or defective lattice sites. This feature is particularly important at lattice defects that break the translational symmetry of the crystal in this case, non orbital-dependent DFT functionals appear unable to localise the defect states, even in simple matrices as MgO. 

Magnetic coupling constants determined by EPR and ENDOR techniques permit a direct comparison with experimental data. Table 28 shows that, in the particular case of the Li defect, the agreement is reasonable for the UHF result, where the hole is localized at Oi. Eor the other Hamiltonians, the disagreement increases in parallel with the delocalization of the hole. 

The sum of the three contributions is close to the magnetic coupling constant that is obtained in a standard calculation when the Kohn-Sham orbitals are optimized without imposing any restriction on the variational process. 

A set of equations relating the energy differences for the FM, AAF, GAF and CAF configurations with the magnetic coupling constants sought for was used ... 

Table 9.23. The energy (in meV per unit cell) of the different magnetic phases for orthorhombic LaMnOa for the experimental structure [641]. The energy of the FM configuration is taken as zero energy. Magnetic moments on the Mn atom in /rg, magnetic coupling constants Jab and Jc in meV. Experimental data /u =3.87 for AAF [632], Jc=-1.2, Jat= 1.6 [640]...

Table 9.24. Energy difference (eV) between the AF and the FM states of ScMnOs, estimated magnetic coupling constant (meV), Mulliken charges q (a.u.), magnetic moment of Mn ions /jIb) obtained with three different Hamiltonians [653]...

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