Neutron Diffraction of Magnetic Materials

Abstract

Detennination of the magnetic structure of magnetic materials is a fundamental problem that can be solved by magnetic neutron diffraction techniques. By magnetic structures we refer to the mutual alignment of the magnetic moments of the atoms in a crystal and their overall alignment relative to the crystallographic axes. Some indirect, tentative data on the magnetic structure of magnetic materials can be obtained from research on their magnetic, mechanical, thermal, and other properties. But only neutron diffraction is a unique direct method of detennining the magnetic structure of a crystal. The magnetic structure of more than one thousand crystals with magnetic order has been studied during 30 years of neutron diffraction research made on reactors in a large number of laboratories in the world. The results of this research work are extensively described in the handbook Magnetic Structures Determined by Neutron Diffraction [176]; in the present book, we will often refer to this handbook. The first extensive theoretical generalization of the principles of magnetic neutron diffraction and the results of research on magnetic structures appeared in the book by Yu. A. Izyumov and R.P. Ozerov Magnetic Neutron Diffraction [24, 134]. 1 Theory of Symrnetry of Magnetically Ordered Crystals -- 1. Space Groups of Crystals -- 2. Irreducible Representations of Space Groups -- 3. Shubnikov Groups of Crystals with Magnetic Order -- 4. Representations of Shubnikov Groups -- 5. Classification Methods of Magnetic Structures -- 6. Insufficiency of the Description of the Symmetry of Magnetic Bodies with the Aid of Shubnikov Groups -- 7. Colored Magnetic Symmetry -- 2 Symmetry Analysis of Magnetic Structures on the Basis of the Theory of Representations -- 8. Reducible Representations of aSpace Group on the Basis of Localized Atomic Functions -- 9. The Basis Functions of the Irreducible Representations of the Space Groups -- 10. The Concept of Phase Transitions in the Description of Magnetic Structures -- 11. Construction of Magnetic Structures from the Basis Functions -- 12. Symmetry Analysis of the Exchange Hamiltonian -- 3 Examples of the Symmetry Analysis of Magnetic Structures -- 13. The Magnetic Structures of the Orthoferrites -- 14. Magnetic Structures in Crystals with the Group D3d6 -- 15. Long-Period Magnetic Structures in Hexagonal Rare-Earth Metals -- 16. The Possible Magnetic Structures of Spinels -- 4 Theoretical Principles of the Neutron Diffraction of Magnetic Structures -- 17. The Scattering of Neutrons by a Crystal with Magnetic Order -- 18. The Possible Types of Magnetic Lattices -- 19. Detennination of the Transition Channel or of the Star of the Wave Vector from a System of Magnetic Reflections -- 20. Detenninations of a Magnetic Structure-The Second Stage of Neutron-Diffraction Work -- 21. The Features of Scattering at Modulated Structure -- 22. The Scattering of Polarized Neutrons at Magnetic Structures -- 23. Domain Structures in Neutron Diffraction Studies of Magnetic Materials -- 24. The Magnetic Scattering of Neutrons in Crystals with Distorted Structures -- 5 Intensity of Magnetic Reflections -- 25. The Atomic Form Factor of Magnetic Scattering -- 26. Methods of Separating the Magnetic Component in Neutron Scattering -- 27. Factors Influencing Intensity -- 6 Examples of Neutron-Diffraction Research on Magnetic Structures -- 28. Types of Magnetic Order in a Face-Centered Cubic Lattice -- 29. Garnets with Magnetic Ions in an Octahedral Sublattice -- 30. Garnets with Magnetic Ions in the Tetrahedral Sublattice -- 31. Garnets with Magnetic Ions in a Dodecahedral Sublattice -- 32. Garnets with Magnetic Ions in Several Sublattices -- Conclusion -- References.