How to calculate the magnetic moment from magnetic structure observed by neutron diffraction
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Neutron diffraction is a powerful tool for studying magnetic materials. Neutrons have a magnetic moment, and are scattered by the magnetic moments of atoms in a sample. The cross section for magnetic scattering is sensitive to the relative orientation of the neutron magnetic moment, the atomic magnetic moment, and the scattering vector. This allows magnetic structures to be determined from the intensities of magnetic diffraction peaks, in much the same way that crystal structures are determined from the intensities of nuclear diffraction peaks (Rodriguez-Carvajal 1993). Small-angle neutron scattering and polarized-neutron reflectometry can yield magnetic information over a range length scales, and can be applied to the study of magnetic nanoparticles, spin glasses, and magnetic multilayers (Arai et al. 1985a,b; Arai and Ishikawa 1985; Mangin et al. 1993; Ott et al. 2004). Inelastic magnetic scattering can be used to probe a range of magnetic excitations, providing quantitative information about the magnetic exchange forces between neighboring spins (Brockhouse 1957; Alperin et al. 1967; Samuelsen 1969; Samuelsen and Shirane 1970; Hansen et al. 1997, 2000; Lefmann et al. 1999, 2001; Klausen et al. 2003, 2004). The earliest neutron diffraction study of a magnetic material was performed by Shull and Smart (1949), who provided the first experimental proof of the existence of antiferromagnetic ordering in MnO. Since then, neutron diffraction has been used to study magnetic structures of increasing complexity, from simple commensurate structures with collinear spins to complex incommensurate structures with non-collinear spins. This review is aimed at researchers requiring an introduction to the use of neutron diffraction to determine the magnetic structure of a material. The essential equations required to interpret neutron scattering from magnetic materials will be presented, along with practical information on how to …