Theoretical investigations of magnetic properties of a system. An attempt at interpreting the magnetic susceptibility of WV2O6

Drillon, Marc; Padel, L.; Bernier, J.C.

doi:10.1016/0378-4363(80)90021-2

Cited by 2 publications

(6 citation statements)

References 14 publications

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“…This hamiltonian will be denoted as (A) in the following. Similar hamiltonians were used in most other approaches [2][3][4][5][6][7]. It was shown in [9] that the hamiltonian (A) reduces to an HDvV hamiltonian in the absence of orbital degeneracy.…”

Section: ) Caqpb Gas Abt Aqt Aps Abs Pqtmentioning

confidence: 99%

“…However, for the case of compared with those of an HDvV operator. Hamiltonian (A) has been used to describe dimers containing single ions with orbitally degenerate ground-states [2,3,7,9]. This hamiltonian has been especially applied to the ground-state of the dimer Ti2 X3-which occurs in nature as A3Ti2X 9 (A = Cs, Rb; X = CI, Br) [2,9].…”

Section: ) Caqpb Gas Abt Aqt Aps Abs Pqtmentioning

confidence: 99%

“…This justifies our approach of using the same symbol C,qpb for the exchange parameters in equations (2) and (3). For the application of hamiltonian (A), the second quantization operators are usually transformed onto spin and angular momentum space [2][3][4][5][6][7][8][9]. It is interesting to note, that the spin part is always given as the dot product of single electron spin operators and therefore resembles the HDvV operator.…”

Section: Theoretical Proceduresmentioning

confidence: 99%

“…In [1][2][3][4][5][6][7][8][9] it was shown, that the exchange hamiltonian (A) actually contains an additional term not included in equation (2) which can be condensed into the (trigonal) ligand field term. This term, which was called exchangeinduced ligand field term, contains the exchange parameters Vo 2 and V2+.…”

Section: A(~() -A(~q) Jmentioning

confidence: 99%

“…Different theoretical approaches have been discussed for the case of orbital degeneracy [2][3][4][5][6][7][8][9][10]. Most applications have been devoted to orbitally degenerate ground-states [2,3,7,9]. In [9] we have developed a general form of a hamiltonian for exchange interactions between two ions by using the second quantization formalism…”

Section: Introductionmentioning

confidence: 99%

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Exchange interaction between ions in excited orbitally degenerate states

Leuenberger

1986

Molecular Physics

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A recently developed theory for exchange interactions is applied to singly and doubly excited states of Cr2X~-. The present approach is compared with a different theoretical model, which has been widely used to discuss exchange interactions in excited states of transition metal dimers. The comparison of the two theories is elaborated in a general form and illustrated for the specific example of Cr2X9 3-. While significant differences exist between the two theories, they agree for the singly excited states of Cr2X~-. However, large differences exist for doubly excited states.

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Section: ) Caqpb Gas Abt Aqt Aps Abs Pqtmentioning

confidence: 99%

Section: ) Caqpb Gas Abt Aqt Aps Abs Pqtmentioning

confidence: 99%

Section: Theoretical Proceduresmentioning

confidence: 99%

Section: A(~() -A(~q) Jmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Exchange interaction between ions in excited orbitally degenerate states

Leuenberger

1986

Molecular Physics

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Magnetic Exchange between Orbitally Degenerate Ions: A New Development for the Effective Hamiltonian

et al. 1998

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A new approach to the problem of the kinetic exchange for orbitally degenerate ions is developed. The constituent multielectron metal ions are assumed to be octahedrally coordinated, and strong crystal field scheme is employed, making it possible to take full advantage from the symmetry properties of the fermionic operators and collective electronic states. In the framework of the microscopic approach, the highly anisotropic effective Hamiltonian of the kinetic exchange is constructed in terms of spin operators and standard orbital operators (matrices of the unit cubic irreducible tensors). As distinguished from previous considerations, the effective Hamiltonian is derived for a most general case of the multielectron transition metal ions possessing orbitally degenerate ground states and for arbitrary topology of the system. The overall symmetry of the system is introduced through the restricted set of the one-electron transfer integrals implied by the symmetry conditions. All parameters of the effective Hamiltonian are expressed in terms of the relevant transfer integrals and fundamental parameters of the two moieties, namely crystal field and Racah parameters for the metal ions in their normal, reduced, and oxidized states. The developed approach is applied to two kinds of systems: edge-shared (D 2 h ) and corner-shared (D 4 h ) bioctahedral clusters. In the particular case of d ions (2T2−T2 problem) the energy pattern in both cases consists of several multiplets splitted by the isotropic part of exchange. In both cases we have found a weak ferromagnetic splitting for several multiplets of the system. This splitting is due to the competition of ferro- and antiferromagnetic contributions arising from the high- and low-spin reduced states in line with Anderson's considerations, Goodenough−Kanamori rules, and McConnell mechanism of ferromagnetic interaction. On the contrary, these weak ferromagnetic interaction are found to coexist with strong ferro- and antiferromagnetic contributions in which only high-spin and low-spin excited states are respectively involved. In addition to these unexpected results in both topologies the ferro- and antiferromagnenic contributions vanish separately for one of the level, the last being thus paramagnetic. These results are in a strike contradiction with the generally accepted point of view on the ferromagnetic role of orbital degeneracy in the magnetic exchange. They also show that the simple qualitative models have a restricted area of applications and that the peculiarities of the exchange problem in the case of orbital degeneracy are much more complicated. The energy pattern of the exchange levels is closely related to the topology of the system and to the network of the one-electron transfer intercenter connections forming effective parameters of the kinetic exchange in the case of orbital degeneracy.

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Theoretical investigations of magnetic properties of a system. An attempt at interpreting the magnetic susceptibility of WV2O6

Cited by 2 publications

References 14 publications

Exchange interaction between ions in excited orbitally degenerate states

Exchange interaction between ions in excited orbitally degenerate states

Magnetic Exchange between Orbitally Degenerate Ions: A New Development for the Effective Hamiltonian

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