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

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. 0535titl......Page 1 0535pref......Page 5 0535toc......Page 8 0535lisc......Page 10 1 Overview......Page 12 2 Kinked Partial Waves......Page 25 2.2 Screened MTOs......Page 28 2.3 Hard-Sphere Interpretation and Redefinitions......Page 32 2.4 Re-screening the Green Matrix......Page 39 2.5 Green Functions, Matrix E ements, and Charge Density......Page 40 3 Polynomial M O Approximations......Page 43 3.1 Energy-Independent NMTOs......Page 44 3.2 Variationa NMTO Method......Page 53 4 Energy-Dependent Linear Transformations......Page 70 5 Hamiltonian Energy Matrices and Orthonormal Sets......Page 73 6 Connecting Back to the ASA Formalism......Page 79 9 Appendix: Classical Polynomial Approximations......Page 84 References......Page 91 1 Introduction......Page 94 2 Energy Functional......Page 96 3 Construction of the Charge Density......Page 105 4 Shape Function Technique......Page 108 5 Discussion......Page 112 6 Conclusions......Page 116 8 Appendix A......Page 117 9 Appendix B......Page 118 10 Appendix C......Page 120 References......Page 121 1 Introduction......Page 124 2.1 The Central Role of the Interstitial Potential Integrals......Page 126 2.2 Smooth Hankel Functions......Page 128 2.3 Augmentation......Page 134 2.4 Representation of the Density and Potential......Page 140 3.1 Dependence on l- and k-Cutoffs......Page 146 3.2 Dependence on MT and Smoothing Radii......Page 148 3.3 Dependence of the Total Energy on Basis......Page 149 3.4 Comparison with Other Density-Functional Calculations......Page 152 References......Page 156 1 Introduction......Page 158 2.1 Interstitial......Page 160 2.2 Muffin Tins......Page 161 3.1 Muffin-Tin Matrix Elements......Page 164 3.2 Interstitial Matrix Elements......Page 165 4 Charge Density......Page 168 6.1 Coulomb Potentia......Page 169 7.1 Symmetry......Page 171 7.2 Force Calculations......Page 172 8 Conclusion......Page 176 References......Page 177 1 Introduction......Page 178 2 Density Functional Theory......Page 179 3 Quasiparticle Theory and Local-Density Approximation Link......Page 181 4 The Full-Potential LMTO Basis Set......Page 182 5.1 Dynamical Dielectric Function......Page 184 5.2 Momentum Matrix Elements......Page 185 5.3 Velocity Operator and Sum Rules......Page 188 6.1 Optical Properties......Page 189 6.2 Magnetic Circular Magnetic Dichroism......Page 191 7 Conclusion......Page 195 References......Page 196 1 Introduction......Page 201 2 Formalism......Page 205 3 Applications......Page 221 4 Summary......Page 248 References......Page 249 1 Introduction......Page 257 2 Introductory Remarks on Electronic Structure Theory......Page 259 3.1 The Hohenberg Kohn Theorem......Page 260 3.2 The Kohn-Sham Approach......Page 262 4 Solving the Kokn–Sham Equations: Bulk......Page 266 4.1 Different Type of k-Space Integration......Page 268 4.2 The FP-LMTO Method......Page 269 4.3 Defining the LMTO Basis Functions......Page 270 4.4 The Muffin-Tin Matrix Element......Page 271 4.5 The Interstitial Matrix Element......Page 272 5.2 Shape Anisotropy......Page 273 5.3 Orbital Moment and Orbital Polarization......Page 274 6.1 Fe, Co and Ni......Page 278 6.2 Effects of Straining the Crystal Structure......Page 282 6.3 The Correlation between MAE and Orbital Moment......Page 285 7.1 FeX and MnX Compound (X=Ni, Pd or Pt)......Page 286 8.1 Spin and Orbital Moments of Selected Surfaces and Interfaces......Page 288 9 Magneto–Striction......Page 291 10 Summary......Page 292 References......Page 293 1 Introduction......Page 296 2 The SIC Formalism......Page 299 3 The Unified Hamiltonian Approach......Page 305 4 The Steepest Descent Approach......Page 309 5 The Relativistic Extension......Page 311 6.1 NiO......Page 313 6.2 Cerium......Page 316 6.3 Cerium Monopnictides......Page 319 7 Conclusions......Page 320 References......Page 321 1 Introduction......Page 323 2 Formalism......Page 325 3 Numerical Results and Discussion......Page 338 4 Conclusions......Page 346 5 Vertex Cancellation Theorem......Page 347 6 The Interface –Interface Part of the Grandcanonical Potential......Page 350 7 Useful Mathematical Tools......Page 351 8 Inversion of Block-Tridiagonal Matrices......Page 353 References......Page 354 1 Introduction......Page 357 2 Green Functions in the Atomic Sphere Approximation......Page 359 3 The Coherent Potential Approximation......Page 362 3.1 Site-Diagonal Quantities......Page 366 3.2 Site Non-Diagonal Quantities......Page 368 3.3 Transformati n Properties of the LMTO-CPA......Page 371 3.4 Solution of the CPA Selfconsistency......Page 372 4 Surfaces and Interfaces......Page 374 5 Charge Selfconsistency for Random Alloys......Page 377 6 Extensions and Applications of the LMTO-CPA......Page 382 References......Page 383 1 Introduction......Page 387 2 Locally Self-Consistent Green ’s Function Method......Page 390 3Taking Advantages of Tight-Binding LMTO Representation......Page 398 4 Summary......Page 403 References......Page 404 1 Introduction......Page 407 2 The General Approach......Page 409 3 Frontal Methods......Page 412 4 Multifrontal Methods......Page 414 5 A Comparison of Codes......Page 415 6 Computing the Inverse of a Sparse Matrix......Page 417 7 Eigenvalue Problems......Page 418 9 Availability of Software......Page 419 References......Page 420 1 Introduction......Page 422 2 TB-LMTO Approach and Real-Space Recursion Formalism......Page 423 2.1 Magnetocrystalline Anisotropy......Page 425 2.2 Exchange coupling constants......Page 427 3.1 Atomic Structure......Page 428 3.2 Magnetic Structure......Page 430 References......Page 437 1 Introduction......Page 440 2.1 The Recursion Technique......Page 441 2.2 Tight Binding Hamiltonian......Page 444 2.3 Clusters for the Recursion Method......Page 446 3 Periodic Versus Real Space Cells for Studying Bulk Magnetic Wall in Cr......Page 450 4.1 Continuous Fraction Expansion and Non-Collinear Magnetism......Page 452 4.2 Angular Dependence of the Interlayer Magnetic Couplings in Fe/Cr Multilayers......Page 456 4.3 Step Induced Non-Coll near Magnetism......Page 460 References......Page 463 This book displays the latest developments in the determinatioin of the electronic structure of solids and the physical properties which can be described from the electronic structure. Special emphasis is placed on the Linear Muffin Tin Orbital method for ground state and excited state calculation. The state-of-the-art of the formalisms is presented, from the venerable Atomic Sphere Approximation to the Full Potential schemes. The efficiency of this method is shown in various situations: magnetic properties, interlayer exchange coupling, metallic alloys, d- and f-electron systems. The latter part of the book is devoted to large-scale real-space calculations, including an introduction to sparse direct methods. With the aim of maximizing tutorial value, experts in each domain present over ten years of work, which has been published only in specialised papers before and now becomes available for researchers as well as students and teachers in solid state physics or materials science.