| Summary: | We address magnetic neutron scattering in the presence of local noncentrosymmetric asymmetries of the magnetization density. Such inversion-symmetry breaking, combined with the absence of time-reversal symmetry, can be described in terms of magnetoelectric multipoles which form the second term after the magnetic dipole in the multipole expansion of the magnetization density. We provide a pedagogical review of the theoretical formalism of magnetic neutron diffraction in terms of the multipole expansion of the scattering cross-section. In particular, we show how to compute the contribution of magnetoelectric multipoles to the scattering amplitude starting from ab initio calculations. We also provide general guidelines on how to experimentally detect long-range order of magnetoelectric multipoles using either unpolarized or polarized neutron scattering. We apply the formalism to CuO, and we discuss first-principles predictions and experimental spherical neutron polarimetry measurements that are consistent with the presence of magnetoelectric multipoles in CuO.
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