The Inelastic Scattering of Neutrons by Magnetic Spin Waves

The inelastic scattering of neutrons by ferromagnetic and antiferromagnetic crystals is considered on spin-wave theory, using the formalism of Holstein & Primakoff. The influence of dipole-dipole interaction and of an applied magnetic field is examined in detail for ferromagnetic crystals. Scattered intensity distributions and total cross-sections are derived in terms of the angular setting of the crystal; they are valid at temperatures low compared with the relevant critical temperatures. The spin-wave interaction leads to magnetic diffuse reflexion of neutrons from the crystal planes, closely analogous to the phonon diffuse reflexion of neutrons and X-rays. These reflexions become intense near the positions for magnetic Bragg scattering; with antiferromagnetic crystals there is an additional set of feeble diffuse reflexions near the directions of nuclear Bragg scattering. The spin-wave diffuse reflexions are always superposed on phonon reflexions. However, in antiferromagnetics the nuclear and magnetic parts of phonon scattering are separated, so that the principal spin-wave reflexions fall on the magnetic part only. Anisotropy forces affect the intensity only for settings very near the Bragg angle. The phenomenon is capable of giving very direct information on the low-lying energy states of magnetic crystals. Cross-sections, however, are of the order of millibams and detailed consideration is given to the problem of their experimental isolation.