8 - Coherent, Inelastic, Magnetic Neutron Scatter, Spin Waves, and Magnons

Abstract

In this chapter, the topics of coherent, inelastic scatter of neutrons in magnetic materials, electron spin waves, and magnons in magnetic materials are covered. Specific topics covered include electron spin and magnetic dipole moment, electron spin precession in an applied magnetic field, and the Heisenberg model of unpaired electron spin in magnetic materials. We also examine spin waves, the dispersion relation, and magnons in ferromagnetic and antiferromagnetic materials. The exchange and anisotropy energy and domain formation in magnetic materials and the Hamiltonian eigenequation for 1-D ferromagnetic spin lattice is then discussed, followed by spin and spin deviation operators, creation and annihilation operators, Holstein–Primakoff transformations, and the linear approximation of Heisenberg Hamiltonian. Also derived is the coherent, inelastic partial differential cross section for one-magnon absorption or emission for neutron scatter in a ferromagnetic crystal. Finally, the spontaneous magnetization in a ferromagnetic cubic crystal as a function of temperature T T in the low-temperature limit is derived.