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CNAA / Theses / 2007 / June /

Double exchange and orbitally-dependent magnetic interactions in transition metal clusters


Author: Andrei Palii
Degree:doctor habilitat of physics and mathematics
Speciality: 01.04.02 - Theoretical and mathematical physics
Year:2007
Institution:
Scientific council:

Status

The thesis was presented on the 29 June, 2007
Approved by NCAA on the 18 October, 2007

Abstract

Adobe PDF document – 0.60 Mb / in romanian
Adobe PDF document – 0.49 Mb / in english

Thesis

CZU 544.1+535.349

Adobe PDF document 4.52 Mb / in english
228 pages

Keywords

Exchange coupled clusters, mixed valence clusters, double exchange, mixed valence iron-sulfur clusters, mixed valence polyoxometalates, diphtalocyanine based mixed valence chains, vibronic coupling, unquenched orbital angular momentum, magnetic anisotropy, single-ion anisotropy, exchange anisotropy, single molecule magnets, magnetization reversal barrier, orbitally-dependent exchange, orbitally-dependent double exchange

Summary

The present Thesis is devoted to the study of polynuclear mixed valence systems and clusters containing paramagnetic ions with unquenched orbital angular momenta.

General microscopic approach to the problem of electronic interactions in such type systems is elaborated. The analytical expressions for the matrix elements of double exchange, two-electron transfer and exchange-transfer are obtained for mixed valence systems containing arbitrary numbers of spin-cores, localized electrons and itinerant electrons. The concept of two kinds of exchange-transfer (kinetic and potential) is introduced and different mechanisms of the exchange-transfer are analyzed. On the basis of the developed approach the magnetic properties of tetrahedral and distorted tetranuclear iron-sulfur clusters [Fe4S4]+, [Fe4S4]3+ and [Fe4S4]2+, hexanuclear octahedral clusters [Fe6(µ3-X)8(PEt3)6]+ (X=S, Se), two-electron-reduced polyoxoanion with Keggin structure and diphtalocyanine based MV chains [YPc2]•CH2Cl2 and [ScPc2]•CH2Cl2 are explained.

The generalization of the vibronic Piepho model to the case of many-electron mixed valence dimers is performed, and on this basis the localization – delocalization phenomenon in these systems are investigated as well as their “vibronic” magnetic properties. Refinement of the conventional Robin and Day classification of mixed valence compounds is proposed. The analytical expressions for the effective “vibronic” hyperfine parameters are deduced. The localization-delocalization phenomenon in mixed valence trimers and tetramers is studied as well.

The isotropic Lines model is extended to the case of heteronuclear clusters containing orbitally degenerate Co(II) ions octahedrally coordinated by the ligands. On this basis the magnetic behavior of heteronuclear iron-cobalt complex [Fe2CoO(CH3COO)6(3-Cl-Py)3] is interpreted. The Lines model is also generalized to the case of axially and rhombically distorted octahedral surroundings of ions with unquenched orbital angular momenta (anisotropic Lines model). The microscopic approach to the problem of exchange interaction between Co(II) ions in the ground Kramers doublet states is elaborated on the basis of the anisotropic Lines model. The magnetic behavior of trigonal bipyramidal cyano-bridged single molecule magnet [MnIII(CN)6]2[MnII(tmphen)2]3 is explained.

General microscopic approach to the problem of the orbitally-dependent kinetic exchange is developed. With the aid of the developed approach the magnetic behavior of [Ti2Cl9]3- cluster is explained, the main factors governing the magnetic anisotropy in Co(II)-dimers are elucidated and the conditions for the applicability of the isotropic Lines model are found. The role of the orbitally-dependent exchange in the formation of the magnetization reversal barrier in linear cyano-bridged manganese clusters (models of single molecule magnets) is revealed. An enigmatic isotropy of exchange interaction in Cs3Yb2Cl9 and Cs3Yb2Br9 crystals is explained on the basis of the microscopic theory of the orbitally-dependent kinetic exchange.

The theory of the orbitally-dependent double exchange in mixed valence dimers containing metal ions with unquenched orbital angular momenta is developed and the magnetic anisotropy of such type systems is investigated. The combined effect of anisotropic double exchange and vibronic coupling on the magnetic anisotropy of mixed valence dimers is studied in the framework of generalized Piepho model.

Summary


PART 1. Electronic and vibronic interactions in mixed-valence clusters
  • 1.1. Basic concepts of the theory of the double exchange
  • 1.1.1. Mechanisms of the indirect electron transfer
  • 1.1.2. Classical spin model of the double exchange
  • 1.1.3. Quantum mechanical description of the double exchange
  • 1.1.4. Combined effect of double exchange and exchange interactions
  • 1.2. General approach to the problem of electronic interactions in polynuclear mixed valence systems
  • 1.2.1. Difficulties of the convential computational approach 25
  • 1.2.2. Solution of the problem of double exchange in the case of less than half-filled d-shells
  • 1.2.2.1. Model of mixed valence system
  • 1.2.2.2. Localized states of mixed valence system
  • 1.2.2.3. Full Hamiltonian of mixed valence system
  • 1.2.2.4. Double exchange Hamiltonian
  • 1.2.2.5. Matrix elements of double exchange in the representation
  • 1.2.2.6. Matrix elements of double exchange in the representation
  • 1.2.3. Double exchange in the case of more than half-filled d-shells
  • 1.2.4. Two-electron transfer
  • 1.2.5. Exchange interaction
  • 1.2.6. Exchange transfer in high-nuclearity mixed-valence systems
  • 1.2.6.1. Kinetic and potential exchange transfer: general remarks
  • 1.2.6.2. Matrix elements of the kinetic exchange-transfer
  • 1.2.6.3. Matrix elements of the potential exchange-transfer
  • 1.2.7. Concluding remarks
  • 1.3. Electronic states of polynuclear mixed valence clusters and mixed valence chains: application of the general approach
  • 1.3.1. Double exchange in iron-sulfur proteins [Fe4S4]+ , [Fe4S4]3+and [Fe4S4]2+.Effects of structural distortions
  • 1.3.1.1. Problem definition
  • 1.3.1.2. Double exchange and distortions in 3d 6 –d 5 cluster
  • 1.3.1.3. Double exchange and distortions in 3d 5 –d 6 cluster
  • 1.3.1.4. Combined effect of double exchange and Heisenberg exchange
  • 1.3.1.5. Double exchange in 2d 6 –2d 5 cluster
  • 1.3.1.6. Concluding remarks
  • 1.3.2. Double exchange in mixed-valence hexanuclear octahedral clusters
  • [Fe6(μ3-X)8(Pet3)6]+(X=S, Se)
  • 1.3.2.1. Problem definition
  • 1.3.2.2. The model
  • 1.3.2.3. Sample calculations
  • 1.3.2.4. Magnetic properties of [Fe6X8(PEt3)6]+
  • 1.3.3. Delocalization of the electronic pair in heteropoly complex with Keggin structure
  • 1.3.3.1. Problem definition
  • 1.3.3.2. The model
  • 1.3.3.3. The splitting of the ground manifold by one- and two-electron transfer processes and conditions for the existence of the diamagnetic ground state
  • 1.3.4. Electron delocalization in mixed valence chains
  • 1.4. Vibronic interactions in mixed valence clusters
  • 1.4.1. Vibronic coupling with single-ion vibrations and multicenter vibrations
  • 1.4.1.1. Piepho, Krausz and Schatz model and Robin and Day classification
  • of mixed valence compounds
  • 1.4.1.2. Effect of multicenter vibrations
  • 1.4.2. Piepho model for many-electron mixed valence dimers
  • 1.4.2.1. Localization vs.delocalization
  • 1.4.2.2. Refinement of Robin and Day classification
  • 1.4.2.3. Magnetic properties of many-electron mixed-valence dimers
  • 1.4.2.4. Parameters of the hyperfine interaction
  • 1.4.3. Vibronic interactions in mixed valence trimers
  • 1.4.3.1. Hamiltonian in the adiabatic approximation
  • 1.4.3.2. Piepho, Krausz and Schatz model: (A1+E) e –problem
  • 1.4.3.3. The limit of strong interaction with multicenter vibrations: (A1+E) (a1+e) –problem
  • 1.4.4. Vibronic interactions in mixed valence tetramers
  • 1.4.4.1. Hamiltonian in the adiabatic approximation 108
  • 1.4.4.2. Piepho, Krausz and Schatz model: (A1+T2) t2 –problem
  • 1.4.4.3. The limit of strong interaction with multicenter vibrations: (A1+T2) (a1+e+ t2 )–problem.
  • 1.4.5. Concluding remarks

PART 2. Exchange and double exchange in metal clusters with unquenched orbital angular momenta
  • 2.1. Single-ion and exchange anisotropies in systems containing metal ions with unquenched orbital angular momenta
  • 2.2. Orbital magnetic contributions in the isotropic exchange model
  • 2.2.1. Lines approach to the problem of the magnetic exchange in Co(II) clusters
  • 2.2.2. Magnetic behavior of a triangular bridged heterometallic Fe2(III)Co(II) complex: evidence of strong orbital contributions
  • 2.2.2.1. The model
  • 2.2.2.2. Application of the irreducible tensor operators
  • 2.2.2.3. Magnetic behavior of Fe2(III)Co(II) cluster
  • 2.2.3. Microscopic pseudo-spin-1/2 Hamiltonian approach for exchange coupled Co(II) pairs
  • 2.2.3.1. Problem definition
  • 2.2.3.2. Second order pseudo-spin-1/2 Hamiltonian. Discussion of the magnetic anisotropy
  • 2.2.4. First order orbital magnetism and magnetic bistability of the Mn(III)2Mn(II)3 cluster
  • 2.2.4.1. The model of the Mn5-cyanide cluster
  • 2.2.4.2. Magnetic behavior of the Mn5-cyanide cluster and conditions for the existence of the barrier for the reversal of magnetization
  • 2.3. Orbitally dependent exchange and magnetic anisotropy
  • 2.3.1. Exchange Hamiltonian: general formalism
  • 2.3.1.1. Derivation of the exchange Hamiltonian
  • 2.3.1.2. Parameters of the exchange Hamiltonian
  • 2.3.1.3. Comparison with other approaches
  • 2.3.1.4. The Hamiltonian of resonance interaction
  • 2.3.2. Application of the irreducible tensor operator techniques
  • 2.3.2.1. Exchange Hamiltonian for a corner-shared bioctahedral cluster of D4h symmetry
  • 2.3.2.2. Exchange Hamiltonian in terms of spherical irreducible tensor operators
  • 2.3.2.3. Single-ion interactions in terms of spherical irreducible tensor operators
  • 2.3.2.4. Total effective Hamiltonian: matrix representation
  • 2.3.2.5. Extension of the method to the higher-nuclearity systems
  • 2.3.2.6. Magnetic anisotropy of the corner-shared bioctahedral cluster
  • 2.3.3. Orbitally dependent exchange in [Ti2Cl9]3-
  • 2.3.3.1. Exchange Hamiltonian of the face-shared bioctahedral cluster
  • 2.3.3.2. Total effective Hamiltonian of the face-shared bioctahedral cluster in terms of spherical irreducible tensor operators
  • 2.3.3.3. Energy level diagram for exchange splittings
  • 2.3.3.4. Magnetic behavior of [Ti2Cl9]3-
  • 2.3.3.5. Discussion of the existing models
  • 2.3.4. Orbitally-dependent exchange between Co(II) ions
  • 2.3.4.1. Exchange Hamiltonian for a corner-shared bioctahedral Co(II) cluster
  • of D4h symmetry
  • 2.3.4.2. Pseudo-spin-1/2 Hamiltonian and discussion of the exchange anisotropy
  • 2.3.5. Orbitally-dependent superexchange in cyano-bridged Mn(III)-Mn(II) dimer and linear cyano-bridged Mn(II)-Mn(III)-Mn(II) trimer
  • 2.3.5.1. Problem definition
  • 2.3.5.2. Exchange Hamiltonian
  • 2.3.5.3. Energy pattern formed by the orbitally-dependent exchange
  • 2.3.5.4. Combined effect of the orbitally-dependent exchange and spin-orbit coupling
  • 2.3.5.5. Combined effect of single-ion anisotropy and exchange anisotropy
  • 2.3.5.6. The reversal magnetization barrier for the linear Mn(II)-NC-Mn(III)-CN- Mn(II) trimer
  • 2.3.6. Exchange interaction in Cs3Yb2Cl9 and Cs3Yb2Br9: a special case of isotropy184
  • 2.4. Anisotropic double exchange in systems containing transition metal ions with unquenched orbital angular momenta
  • 2.4.1. Orbitally dependent double exchange in mixed-valence dimers: general formalism
  • 2.4.1.1. Orbitally dependent double exchange Hamiltonian
  • 2.4.1.2. Matrix representation of the double exchange Hamiltonian
  • 2.4.2. Orbitally dependent double exchange in the edge-shared (D2h) and corner-shared (D4h) bioctahedral mixed-valence pairs
  • 2.4.3. Orbitally-dependent double exchange in the face-shared bioctahedral dimer of D3h symmetry
  • 2.4.4. Combined effect of the orbitally-dependent double exchange and vibronic coupling
  • Conclusions