Electronic Structure and Physical Properties of Solids: The Uses of the LMTO Method

✍ Scribed by Hugues Dreysse (editor)

• Publisher: Springer
• Year: 2000
• Tongue: English
• Leaves: 453
• Edition: 2000
• Category: Library

✦ Synopsis

A very comprehensive book, enabling the reader to understand the basic formalisms used in electronic structure determination and particularly the "Muffin Tin Orbitals" methods. The latest developments are presented, providing a very detailed description of the "Full Potential" schemes. This book will provide a real state of the art, since almost all of the contributions on formalism have not been, and will not be, published elsewhere. This book will become a standard reference volume. Moreover, applications in very active fields of today's research on magnetism are presented. A wide spectrum of such questions is covered by this book. For instance, the paper on interlayer exchange coupling should become a "classic", since there has been fantastic experimental activity for 10 years and this can be considered to be the "final" theoretical answer to this question. This work has never been presented in such a complete form.

✦ Table of Contents

Chapter 1
1 Overview
2 Kinked Partial Waves
2.2 Screened MTOs
2.3 Hard-Sphere Interpretation and Redefinitions
2.4 Re-screening the Green Matrix
2.5 Green Functions, Matrix E ements, and Charge Density
3 Polynomial M O Approximations
3.1 Energy-Independent NMTOs
3.2 Variationa NMTO Method
4 Energy-Dependent Linear Transformations
5 Hamiltonian Energy Matrices and Orthonormal Sets
6 Connecting Back to the ASA Formalism
7 Outlook
8 Acknowledgments
9 Appendix: Classical Polynomial Approximations
References
Chapter 2
1 Introduction
2 Energy Functional
3 Construction of the Charge Density
4 Shape Function Technique
5 Discussion
6 Conclusions
7 Acknowledgements
8 Appendix A
9 Appendix B
10 Appendix C
References
Chapter 3
1 Introduction
2 Description of the Method
2.1 The Central Role of the Interstitial Potential Integrals
2.2 Smooth Hankel Functions
2.3 Augmentation
2.4 Representation of the Density and Potential
3 Tests of the Method
3.1 Dependence on l- and k-Cutoffs
3.2 Dependence on MT and Smoothing Radii
3.3 Dependence of the Total Energy on Basis
3.4 Comparison with Other Density-Functional Calculations
4 Summary
References
Chapter 4
1 Introduction
2 Basis Set
2.1 Interstitial
2.2 Muffin Tins
3 Matrix Elements
3.1 Muffin-Tin Matrix Elements
3.2 Interstitial Matrix Elements
4 Charge Density
5 Core States
6 Potential
6.1 Coulomb Potentia
6.2 Density Gradients
7 All-Electron Force Calculations
7.1 Symmetry
7.2 Force Calculations
8 Conclusion
9 Acknowledgments
References
Chapter 5
1 Introduction
2 Density Functional Theory
3 Quasiparticle Theory and Local-Density Approximation Link
4 The Full-Potential LMTO Basis Set
5 Dielectric function
5.1 Dynamical Dielectric Function
5.2 Momentum Matrix Elements
5.3 Velocity Operator and Sum Rules
6 Applications
6.1 Optical Properties
6.2 Magnetic Circular Magnetic Dichroism
7 Conclusion
References
Chapter 6
1 Introduction
2 Formalism
3 Applications
4 Summary
Acknowledgements
References
Chapter 7
1 Introduction
2 Introductory Remarks on Electronic Structure Theory
3 Density Functional Theory
3.1 The Hohenberg Kohn Theorem
3.2 The Kohn-Sham Approach
4 Solving the Kokn–Sham Equations: Bulk
4.1 Different Type of k-Space Integration
4.2 The FP-LMTO Method
4.3 Defining the LMTO Basis Functions
4.4 The Muffin-Tin Matrix Element
4.5 The Interstitial Matrix Element
5 Magneto–Crystalline Anisotropy of Selected Materials
5.1 General Remarks
5.2 Shape Anisotropy
5.3 Orbital Moment and Orbital Polarization
6 MAE of 3d Elements
6.1 Fe, Co and Ni
6.2 Effects of Straining the Crystal Structure
6.3 The Correlation between MAE and Orbital Moment
7 Selected Compounds
7.1 FeX and MnX Compound (X=Ni, Pd or Pt)
8 Surface and Interface Magnetism
8.1 Spin and Orbital Moments of Selected Surfaces and Interfaces
9 Magneto–Striction
10 Summary
Acknowledgment
References
Chapter 8
1 Introduction
2 The SIC Formalism
3 The Unified Hamiltonian Approach
4 The Steepest Descent Approach
5 The Relativistic Extension
6 Applications
6.1 NiO
6.2 Cerium
6.3 Cerium Monopnictides
7 Conclusions
References
Chapter 9
1 Introduction
2 Formalism
3 Numerical Results and Discussion
4 Conclusions
5 Vertex Cancellation Theorem
6 The Interface –Interface Part of the Grandcanonical Potential
7 Useful Mathematical Tools
8 Inversion of Block-Tridiagonal Matrices
References
Chapter 10
1 Introduction
2 Green Functions in the Atomic Sphere Approximation
3 The Coherent Potential Approximation
3.1 Site-Diagonal Quantities
3.2 Site Non-Diagonal Quantities
3.3 Transformati n Properties of the LMTO-CPA
3.4 Solution of the CPA Selfconsistency
4 Surfaces and Interfaces
5 Charge Selfconsistency for Random Alloys
6 Extensions and Applications of the LMTO-CPA
References
Chapter 11
1 Introduction
2 Locally Self-Consistent Green ’s Function Method
3Taking Advantages of Tight-Binding LMTO Representation
4 Summary
Acknowledgement
References
Chapter 12
1 Introduction
2 The General Approach
3 Frontal Methods
4 Multifrontal Methods
5 A Comparison of Codes
6 Computing the Inverse of a Sparse Matrix
7 Eigenvalue Problems
8 Brief Summary
9 Availability of Software
Acknowledgements
References
Chapter 13
1 Introduction
2 TB-LMTO Approach and Real-Space Recursion Formalism
2.1 Magnetocrystalline Anisotropy
2.2 Exchange coupling constants
3 Ni/Cu(001) Films
3.1 Atomic Structure
3.2 Magnetic Structure
4 Conclusions
Acknowledgments
References
Chapter 14
1 Introduction
2 Tight Binding Parameterisation and Recursion Technique
2.1 The Recursion Technique
2.2 Tight Binding Hamiltonian
2.3 Clusters for the Recursion Method
3 Periodic Versus Real Space Cells for Studying Bulk Magnetic Wall in Cr
4 Non-Collinear Magnetism
4.1 Continuous Fraction Expansion and Non-Collinear Magnetism
4.2 Angular Dependence of the Interlayer Magnetic Couplings in Fe/Cr Multilayers
4.3 Step Induced Non-Coll near Magnetism
5 Summary
References