Theory of neutron scattering by electrons in magnetic materials

TL;DR

This paper reviews the theory of neutron scattering in magnetic materials, emphasizing the role of electronic multipoles beyond the traditional dipole approximation to reveal electronic complexity.

Contribution

It introduces a comprehensive framework incorporating magnetic multipoles, including anapoles, to enhance understanding of electronic degrees of freedom in neutron scattering.

Findings

Dipole approximation has been standard in neutron scattering analysis.

Magnetic multipoles provide additional insights into electronic structure.

Anapoles serve as signatures of electronic complexity in materials.

Abstract

A theory of neutron scattering by magnetic materials is reviewed with emphasis on the use of electronic multipoles that have universal appeal, because they are amenable to calculation and appear in theories of many other experimental techniques. The conventional theory of magnetic neutron scattering, which dates back to Schwinger (1937) and Trammell (1953), yields an approximation for the scattering amplitude in terms of magnetic dipoles formed with the spin (S) and orbital angular momentum (L) of valence electrons. The so-called dipole-approximation has been widely adopted by researchers during the past few decades that has seen neutron scattering develop to its present status as the method of choice for investigations of magnetic structure and excitations. Looking beyond the dipole-approximation, however, reveals a wealth of additional information about electronic degrees of freedom conveniently encapsulated in magnetic multipoles. In this language, the dipole-approximation retains electronic axial dipoles, S and L. At the same level of approximation are polar dipoles - called anapoles or toroidal dipoles - allowed in the absence of a centre of inversion symmetry. Anapoles are examples of magneto-electric multipoles, time-odd and parity-odd irreducible tensors, that have come to the fore as signatures of electronic complexity in materials.