Orbital magnetization in magnetic neutron scattering

Magnetic neutron scattering has been a powerful tool to reveal the microscopic magnetic structures of ordered and disordered magnetic systems. For magnetically ordered crystalline systems it has been a common practice to fit the elastic neutron cross-section to models of periodically arranged localized magnetic moments. However, it is unclear how the orbital magnetization which has an itinerant nature manifests in neutron scattering. The question is relevant to, e.g., metallic antiferromagnets and 4d/5d transition metal materials. We show that magnetic neutron scattering in general maps out the equilibrium electric current distribution inside the material but leaves the magnetization density unfixed because of a gauge freedom. We discuss the connection between the equilibrium current density and the modern theory of orbital magnetization, and provide examples on calculating the orbital contribution to elastic neutron cross-section using models and first-principles methods.