Magnetic Neutron Diffraction

The inter action between the magnetic field generated by the neutron and the magnetic moment of atoms containing unpaired electrons was experimentally demonstrated for the first time about twenty years ago. The basic theory describing such an in­ teraction had already been developed and the first nuclear reactors with large available thermal neutron fluxes had recently been con­ structed. The power of the magnetic neutron interaction for in­ vestigating the structure of magnetic materials was immediately recognized and put to use where possible. Neutron diffraction, however, was practicable only in countries with nuclear reactors. The earliest neutron determinations of magnetic ordering were hence primarily carried out at Oak Ridge and Brookhaven in the US, at Chalk River in Canada and at Harwell in England. Diffraction patterns from polycrystalline ferromagnets and antiferromagnets are interpretable if produced by simple spin arrays. More complex magnetic scattering patterns could often be unravelled, in terms of a three-dimensional array of atomic moments, if the specimen studied is a single crystal. The devel­ opment of sophisticated cryogenic equipment, with independently alignable magnetic fields, opened the way to greater complexity in the magnetic structures that could be successfully determined, as did also the introduction of polarized neutron beams. By the end of the 'sixties, many countries were contributing significantly to neutron diffraction studies of a wide variety of magnetic materials.

I. Modern Views on Atomic Magnetic Ordering.- a) Magnetic Structures and Ways of Describing Them.- § 1. Types of Magnetic Structure.- § 2. Magnetic Symmetry.- § 3. Classical Problem of Finding the Spin Configurations in the Heisenberg Model.- § 4. Phenomenological Method.- b) Theory of Spin Waves.- § 5. Spin Waves in a Ferromagnetic.- § 6. Spin Waves in Complex Magnetic Structures.- § 7. Description of the State of a Ferromagnetic over a Wide Temperature Range.- § 8. Influence of Anisotropic Interactions and Other Factors.- c) Nature of Magnetic Ordering.- § 9. Direct Exchange in Ferromagnetics.- §10. Indirect Exchange through Nonmagnetic Ions.- §11. Indirect Exchange Interaction through Conduction Electrons.- §12. Problem of a Localized Magnetic Moment in a Pure Metal and in Dilute Solid Solutions.- II. Theory of the Scattering of Slow Neutrons in Magnetic Crystals.- a) General Expressions for Scattering Cross Sections.- §13. Time Formalism in Scattering Theory.- §14. Interaction of Slow Neutrons with a Magnetic.- §15. Differential Scattering Cross-Sections for Unpolarized Neutrons.- b) Elastic Scattering.- §16. Nuclear Scattering in Single Crystals and Polycrystalline Samples.- §17. Magnetic Scattering of Neutrons in Single Crystals and Polycrystalline Samples.- c) Inelastic Single-Quantum Scattering of Neutrons.- §18. Scattering of Neutrons with the Emission and Absorption of a Phonon.- §19. Scattering of Neutrons with the Emission and Absorption of a Spin Wave.- d) Critical and Paramagnetic Scattering of Neutrons.- §20. Scattering of Neutrons in a Crystal near the Néel and Curie Points.- §21. Paramagnetic Scattering of Neutrons.- e) Scattering of Polarized Neutrons.- §22. Differential Scattering Cross Section of Polarized Neutrons.- §23. Change in the Polarization of Neutrons on Scattering in a Magnetic Crystal.- f) Some Theoretical Problems.- §24. Interpretation of the Scattering of Neutrons in Metal on the Basis of the Model of Collectivized Electrons.- §25. Magnetic Form Factor of the Polarization Cloud of Conduction Electrons.- III. Method of the Neutron-Diffraction Determination of Magnetic Structures.- §26. Quantitative Description of the Magnetic Scattering of Neutrons by Crystals.- §27. Determination of Magnetic Structure.- §28. Use of Symmetry Representations in the Determination of Magnetic Structure.- §29. Use of Polarized Neutrons in the Study of Magnetic Structure.- §30. Accounting for Absorption, Extinction, and Double Bragg Reflection.- §31. Apparatus for Carrying out Neutron-Diffraction Investigations.- IV. Some Results of Neutron-Diffraction Investigations on Magnetic Structures.- §32. Rare-Earth Elements and Some of Their Compounds.- §33. Oxides of the Spinel Structural Type.- §34. Oxides of the Garnet Structural Type.- §35. Oxides of the Corundum and Ilmenite Structural Type.- §36. Oxides of the Perovskite Structural Type.- §37. Oxides of the YMnO3 Structural Type.- V. Distribution of Magnetic Moment in Crystals.- a) Distribution of Spin Density.- §38. X-Ray and Neutron Form Factors. Connection with the Distribution of Spin and Electron Density.- §39. Theory of the Magnetic Form Factors of d Metals.- §40. Distribution of Spin Density in d Metals and Their Compounds.- §41. Theory of the Form Factors of Rare-Earth Elements.- §42. Experimental Study of the Form Factors of Rare-Earth Elements.- b) Magnetic Moments of Atoms in Metals and Alloys.- §43. Determination of the Magnetic Moments of Atoms from the Diffuse Magnetic Scattering of Neutrons.- §44. Magnetic Moments of Atoms in Alloys of Transition Metals.- VI. Dynamics of the Magnetic Lattice.- §45. Geometrical Picture of Single-Magnon Scattering.- §46. Experimental Methods of Studying the Inelastic Scattering of Neutrons.- §47. Spin-Wave Spectrum of Magnetics.- §48. Magnetic Critical Scattering of Neutrons.- §49. Paramagnetic Scattering.- VII. Ferromagnetism of Crystals Containing Impurities and the Scattering of Neutrons in These.- §50. Spin Excitations of a Ferromagnetic Crystal Containing an Impurity Atom.- §51. Density of States and Characteristics of the Spin-Wave Spectrum.- §52. Generalization of the Theory of Other Cases.- §53. Spin Waves in a Ferromagnetic with a Finite Impurity Concentration.- §54. Theory of Inelastic Neutron Scattering in Ferromagnetics Containing Impurities.- §55. Experimental Study of Inelastic Scattering in Impurity Ferromagnetics.- Appendix I. Systematic Extinctions of Reflections Due to the Presence of Symmetry Elements in Collinear Magnetics.- Appendix II. Bravais Lattices of Black-and-White (Magnetic) Symmetry.- Appendix III. Index to Literature on the Magnetic Structure of Metals, Alloys, and Chemical Compounds.- Literature Cited.- General Index.- Substance Index.