Electronic interaction in trimeric mixed valence clusters

Abstract

The theory of double exchange is generalized to mixed valence (MV) trinuclear clusters. The results obtained by quantum-theoretical calculations of exchange and resonance splittings are compared to the results of the model theory which takes account of Heisenberg and double exchange. The comparison demonstrates unambiguously the coincidence of transfer parameters and the model double exchange parameters. The double exchange parameters of trinuclear MV clusters depend on total and intermediate spins as well as individual ion spin. The common effect of electron (or hole) migration and interion exchange interaction on the magnetic properties of ae'-d"-d" + 1 (n = 0, 1, 2, 3, 4, 5) and am-ae'-d H-1 (n = 1, 2, 3, 4) MV trimers is considered. Heisenberg and double exchange form exchange-resonance multiplets which are characterized by irreducible representations F of Dab symmetry group of MV clusters. Double exchange splits Heisenberg multiplets but does not mix the states of different S. Level correlation diagrams for MV trimer clusters are plotted. The level trends and magnetic behaviour of MV trimers differ significantly from the classical Anderson-Hasegawa model obtained for dimeric MV clusters. In MV dimers strong double exchange (]p] >> I J[) leads to ferromagnetic ground state (Sss ---Sn~ ) irrespective of the signs for p and J. In MV trimers several types of magnetic behaviour are possible depending on the signs and values for J and p parameters. In antiferromagnetic clusters (J < 0) with the migrating electron (p < 0) or hole (p > 0) strong double exchange reduces antiferromagnetic Heisenberg-type ordering and leads to ferromagnetic spins alignment (S~=S .... when [pl>>lJ[). In antiferromagnetic trimers, a~-ff'-d ~+1 (p > 0) and dm-a~-a ~-t ~ < 0), the level with Sgs = Smin i$ the ground state irrespective of the value of p/J. In ferromagnetic exchange clusters (J > 0) with the migrating hole strong double exchange disorders the ferromagnetic spin ordering of the MV system.

The Mechanism of the Magnetodielectric Response in a Molecule‐Based Trinuclear Iron Cluster Material

“…100 K), a double exchange (p = À1816.39 AE 0.43 cm À1 ) interaction slightly reduced isotropic Heisenberg-type exchange interaction (À81.48 AE 0.02 cm À1 ) because of the electronic delocalization effect. [21] The energy level plot ( Figures S12-S13) indicated that the delocalized state 1 has the same antiferromagnetic ground state (S T = 2) as its localized state, compatible with previous conclusions. [22] The energy level gap between ground state (S T = 2) and the first excited state S T = 1) is 37.12 cm À1 at zero field.…”

“…Thus, the double exchange interaction cannot completely suppress antiferromagnetic Heisenberg-type ordering, and 1 still exhibits spin-frustration. [21] To investigate the effect of the electron-hopping property on magnetoelectric property of the trinuclear iron, constraint density function theory (CDFT) calculations with and without applied electric field were performed using CP2K program. [23] For charge-frustration, two different states, including (Fe1 III , Fe2 III , Fe3 II ) and (Fe1 II , Fe2 III , Fe3 III ), were involved.…”

Magnetic Field Effects in Charge-Ordered Mixed-Valence Trimeric Clusters

“…Electron transfer theory has been further developed in Refs. [6][7][8][9][10][11][12][13]. A detailed discussion of the state of the double exchange theory can be found in a number of monographs and ample overviews [14][15][16][17][18][19].…”

MVPACK: A package to calculate energy levels and magnetic properties of high nuclearity mixed valence clusters

“…One can see that these clusters are quite different from the MV dimmers in which the double exchange always stabilizes the ferromagnetic ground state. 4 On the other hand these systems are similar to triangular MV trimmers, [27][28][29] tetrahedral MV tetramers, [30][31][32] and hexanuclear octahedral d 2 25d 1 clusters 33 exhibiting transfer frustration that seems to be a common feature of all MV clusters with symmetric triangular faces (for a more detailed discussion see ref.…”