Linked e-resources
Details
Table of Contents
Intro
Preface
Acknowledgements
Contents
Editor and Contributors
About the Editor
Contributors
1 Introduction to Single-Molecule Toroics
1.1 Background
1.2 The Birth of SMTs and Their Rapidly Evolving Family Tree
1.3 Classification of SMTs
1.4 The Impetus for Single-Molecule Toroic Research
1.5 Important Criteria and Techniques
1.6 Key Recent Advances and Future Challenges in SMTs
References
2 Mixed d-f Block Single-Molecule Toroics
2.1 Introduction
2.2 "Pair of MIII-bridged Dy3 Triangles" of Type [MIIIDyIII6(OH)8(o-tol)12(NO3)(MeOH)5]3MeOH
2.2.1 Synthesis, Characterization and Structure of the Parent Heptanuclear Complex MIII == CrIII, Labelled CrDy6 [17]
2.2.2 Magnetic Properties and Ferrotoroidicity [17]
2.2.3 Micro-SQUID Hysteresis Loops on Single Crystals [17]
2.2.4 EPR Spectra [17]
2.2.5 Theory
Single Ion Calculations-Blocking Barriers
Relaxation Effects [17]
2.2.6 Magnetically Coupled States in MDy6 [19]
2.2.7 Role of Coupled Toroidal States in Spin Dynamics: Direct Simulation of the Magnetic Hysteresis Experiments [17, 19]
2.2.8 Spin Dynamics of Decoupled Toroidal Moments: The Case of the Dy3 Single Triangle
2.3 Changes in MIII, LnIII and Counter-anion, NO3 vs Cl, in [MIIIDyIII6(OH)8(o-tol)12(NO3)(MeOH)5]3MeOH
2.3.1 Changing the LnIII Ion [18]
2.3.2 Changing the MIII Ion and Counter-Ion in MDy6 Species [19]
2.3.3 Toroido-Structural Correlations: Ways of Optimizing Ferrotoroidic Coupling [19]
2.3.4 Simulations of the Hysteretic Dynamics: Important Role of the M-Linker in Tuning Toroidal-Magnetic Zeeman Level Crossings [19]
2.4 Other Mixed d-block/f-block Single-Molecule Toroics with Ring Structures
2.4.1 Mn8Dy8
2.4.2 Fe8Dy8
2.4.3 Cu6Ln6
2.4.4 Fe18Dy6
2.5 Conclusions and Future Directions
References.
3 Single-Molecule Toroics: Design and Synthetic Strategies
3.1 Introduction
3.2 The Seminal Dy3 SMT: The Archetype of the Noncollinear Ising Model
3.3 New Ln3 (DyIII, TbIII, HoIII) and Dy4-SMT Systems
3.4 SMTs Based on Seminal Dy3 Triangle and Dy6 Wheel SMTs
3.5 Coupling Dy3 Triangular SMTs
3.6 Heterometallic 3d4f Metallocycle SMTs
3.7 Conclusion
References
4 Rationalization of Room-Temperature Single-Molecule Toroics via Exchange Coupling
4.1 Introduction
4.2 Survey of Typical SMTs
4.2.1 The Pioneering Dy3 SMT
4.2.2 Other Dysprosium SMTs
4.2.2.1 Trinuclear "4266308 Dy3"5267309 Triangle
4.2.2.2 Tetranuclear "4266308 Dy4"5267309 Squares
4.2.2.3 Hexanuclear "4266308 Dy6"5267309 Wheel
4.2.2.4 Tetranuclear "4266308 Dy4"5267309 Cubane
4.2.2.5 Octanuclear "4266308 Dy8"5267309 "Christmas-Star"
4.2.2.6 Coupled "4266308 Dy3"5267309 Triangle
4.2.2.7 Higher-Dimensional SMTs
4.2.3 Heterometallic 3d-4f SMTs
4.2.3.1 "4266308 Cr-Dy"5267309 Sandwich
4.2.3.2 "4266308 Mn-Dy"5267309 Wheel
4.2.3.3 "4266308 Fe-Dy"5267309 Wheel
4.2.3.4 "4266308 Fe-Dy"5267309 Sandwich
4.2.3.5 "4266308 Cu-Dy"5267309 Chain
4.2.3.6 "4266308 Cu-Dy"5267309 Wheel
4.2.3.7 "4266308 M-Dy"5267309 Sandwiches
4.3 Strategies on Pursuing Room-Temperature SMTs
4.3.1 The Exchange Coupling Approach
4.3.2 The Enhanced Toroidal Moment Approach
4.4 Conclusion and Perspective
References
5 Spin-Electric Coupling, Magnetoelectricity, and Quantum Dynamics of Toroidal Moment in Lanthanide-Based Single Molecule Toroics
5.1 Introduction
5.1.1 The Concepts of Molecular Spintronics
5.1.2 Single Molecule Magnets
5.1.3 Single Molecule Toroics
5.2 The Toroidal Moment
5.2.1 Toroidal Moment in Electrodynamics
5.2.2 Toroidal Moment in Condensed Matter Physics.
5.2.3 Toroidal Moment and Magnetoelectric Effect
5.3 Spin-Electric Coupling and Magnetoelectricity in Rare-Earth SMTs
5.3.1 The Model Hamiltonian
5.3.2 The Spin-Electric Interactions in SMTs
5.3.3 The Magnetoelectric Effect
5.3.3.1 The Case of Small Fields
5.3.3.2 The Case of Large Fields
5.3.3.3 The Case of Intermediary Fields
5.3.3.4 Non-equilibrium MEE and Rabi Oscillations
5.4 The Dynamics of Toroidal Moment in SMTs
5.4.1 Macroscopic Quantum Tunneling of the Toroidal Moment: The Quasi-Classical Approach
5.4.2 Toroidal Qubit
5.4.2.1 Scalability
5.4.2.2 Initialization
5.4.2.3 Coherence
5.4.2.4 Logical Gates
5.4.2.5 Reading Out
5.4.3 The Dynamics of Toroidal Qubit
5.4.4 The Quantum Coherent Effects
5.5 Conclusion
References
6 Quantum Toroidicity in Single-Molecule Toroics: A Unifying Model Based on Heisenberg Spin Rings
6.1 Introduction
6.2 Toroidal Moments in Quantum Rings with Strong On-Site Magnetic Anisotropy
6.2.1 Theoretical Treatment of Non-collinear Quantum Spin Rings
6.2.1.1 The Model Hamiltonian
6.2.1.2 The Semi-classical Non-collinear Ising Picture: Emergence of SMTs
6.2.1.3 Quantum Fluctuations: Quantum Tunnelling of the Toroidal Moment
6.2.2 The Molecular Triangle
6.2.3 Hunting Quantum Toroidal Moments in Even-membered Rings
6.3 Emergence of Molecular Toroidal Moments in the Weak Spin-Orbit Coupling Limit
6.3.1 Spin Frustrated Triangles
6.3.2 Generalisation to Larger Rings
6.3.3 Magnetic Dipole-Dipole Coupling
6.3.4 Toroidal Moments in Heterometallic Rings
6.4 Conclusions
References
Index.
Preface
Acknowledgements
Contents
Editor and Contributors
About the Editor
Contributors
1 Introduction to Single-Molecule Toroics
1.1 Background
1.2 The Birth of SMTs and Their Rapidly Evolving Family Tree
1.3 Classification of SMTs
1.4 The Impetus for Single-Molecule Toroic Research
1.5 Important Criteria and Techniques
1.6 Key Recent Advances and Future Challenges in SMTs
References
2 Mixed d-f Block Single-Molecule Toroics
2.1 Introduction
2.2 "Pair of MIII-bridged Dy3 Triangles" of Type [MIIIDyIII6(OH)8(o-tol)12(NO3)(MeOH)5]3MeOH
2.2.1 Synthesis, Characterization and Structure of the Parent Heptanuclear Complex MIII == CrIII, Labelled CrDy6 [17]
2.2.2 Magnetic Properties and Ferrotoroidicity [17]
2.2.3 Micro-SQUID Hysteresis Loops on Single Crystals [17]
2.2.4 EPR Spectra [17]
2.2.5 Theory
Single Ion Calculations-Blocking Barriers
Relaxation Effects [17]
2.2.6 Magnetically Coupled States in MDy6 [19]
2.2.7 Role of Coupled Toroidal States in Spin Dynamics: Direct Simulation of the Magnetic Hysteresis Experiments [17, 19]
2.2.8 Spin Dynamics of Decoupled Toroidal Moments: The Case of the Dy3 Single Triangle
2.3 Changes in MIII, LnIII and Counter-anion, NO3 vs Cl, in [MIIIDyIII6(OH)8(o-tol)12(NO3)(MeOH)5]3MeOH
2.3.1 Changing the LnIII Ion [18]
2.3.2 Changing the MIII Ion and Counter-Ion in MDy6 Species [19]
2.3.3 Toroido-Structural Correlations: Ways of Optimizing Ferrotoroidic Coupling [19]
2.3.4 Simulations of the Hysteretic Dynamics: Important Role of the M-Linker in Tuning Toroidal-Magnetic Zeeman Level Crossings [19]
2.4 Other Mixed d-block/f-block Single-Molecule Toroics with Ring Structures
2.4.1 Mn8Dy8
2.4.2 Fe8Dy8
2.4.3 Cu6Ln6
2.4.4 Fe18Dy6
2.5 Conclusions and Future Directions
References.
3 Single-Molecule Toroics: Design and Synthetic Strategies
3.1 Introduction
3.2 The Seminal Dy3 SMT: The Archetype of the Noncollinear Ising Model
3.3 New Ln3 (DyIII, TbIII, HoIII) and Dy4-SMT Systems
3.4 SMTs Based on Seminal Dy3 Triangle and Dy6 Wheel SMTs
3.5 Coupling Dy3 Triangular SMTs
3.6 Heterometallic 3d4f Metallocycle SMTs
3.7 Conclusion
References
4 Rationalization of Room-Temperature Single-Molecule Toroics via Exchange Coupling
4.1 Introduction
4.2 Survey of Typical SMTs
4.2.1 The Pioneering Dy3 SMT
4.2.2 Other Dysprosium SMTs
4.2.2.1 Trinuclear "4266308 Dy3"5267309 Triangle
4.2.2.2 Tetranuclear "4266308 Dy4"5267309 Squares
4.2.2.3 Hexanuclear "4266308 Dy6"5267309 Wheel
4.2.2.4 Tetranuclear "4266308 Dy4"5267309 Cubane
4.2.2.5 Octanuclear "4266308 Dy8"5267309 "Christmas-Star"
4.2.2.6 Coupled "4266308 Dy3"5267309 Triangle
4.2.2.7 Higher-Dimensional SMTs
4.2.3 Heterometallic 3d-4f SMTs
4.2.3.1 "4266308 Cr-Dy"5267309 Sandwich
4.2.3.2 "4266308 Mn-Dy"5267309 Wheel
4.2.3.3 "4266308 Fe-Dy"5267309 Wheel
4.2.3.4 "4266308 Fe-Dy"5267309 Sandwich
4.2.3.5 "4266308 Cu-Dy"5267309 Chain
4.2.3.6 "4266308 Cu-Dy"5267309 Wheel
4.2.3.7 "4266308 M-Dy"5267309 Sandwiches
4.3 Strategies on Pursuing Room-Temperature SMTs
4.3.1 The Exchange Coupling Approach
4.3.2 The Enhanced Toroidal Moment Approach
4.4 Conclusion and Perspective
References
5 Spin-Electric Coupling, Magnetoelectricity, and Quantum Dynamics of Toroidal Moment in Lanthanide-Based Single Molecule Toroics
5.1 Introduction
5.1.1 The Concepts of Molecular Spintronics
5.1.2 Single Molecule Magnets
5.1.3 Single Molecule Toroics
5.2 The Toroidal Moment
5.2.1 Toroidal Moment in Electrodynamics
5.2.2 Toroidal Moment in Condensed Matter Physics.
5.2.3 Toroidal Moment and Magnetoelectric Effect
5.3 Spin-Electric Coupling and Magnetoelectricity in Rare-Earth SMTs
5.3.1 The Model Hamiltonian
5.3.2 The Spin-Electric Interactions in SMTs
5.3.3 The Magnetoelectric Effect
5.3.3.1 The Case of Small Fields
5.3.3.2 The Case of Large Fields
5.3.3.3 The Case of Intermediary Fields
5.3.3.4 Non-equilibrium MEE and Rabi Oscillations
5.4 The Dynamics of Toroidal Moment in SMTs
5.4.1 Macroscopic Quantum Tunneling of the Toroidal Moment: The Quasi-Classical Approach
5.4.2 Toroidal Qubit
5.4.2.1 Scalability
5.4.2.2 Initialization
5.4.2.3 Coherence
5.4.2.4 Logical Gates
5.4.2.5 Reading Out
5.4.3 The Dynamics of Toroidal Qubit
5.4.4 The Quantum Coherent Effects
5.5 Conclusion
References
6 Quantum Toroidicity in Single-Molecule Toroics: A Unifying Model Based on Heisenberg Spin Rings
6.1 Introduction
6.2 Toroidal Moments in Quantum Rings with Strong On-Site Magnetic Anisotropy
6.2.1 Theoretical Treatment of Non-collinear Quantum Spin Rings
6.2.1.1 The Model Hamiltonian
6.2.1.2 The Semi-classical Non-collinear Ising Picture: Emergence of SMTs
6.2.1.3 Quantum Fluctuations: Quantum Tunnelling of the Toroidal Moment
6.2.2 The Molecular Triangle
6.2.3 Hunting Quantum Toroidal Moments in Even-membered Rings
6.3 Emergence of Molecular Toroidal Moments in the Weak Spin-Orbit Coupling Limit
6.3.1 Spin Frustrated Triangles
6.3.2 Generalisation to Larger Rings
6.3.3 Magnetic Dipole-Dipole Coupling
6.3.4 Toroidal Moments in Heterometallic Rings
6.4 Conclusions
References
Index.