Bragg diffraction by a magnetic all-in-all-out configuration with application to a cubic cerium pyrochlore oxide

Abstract

The Bragg diffraction of neutrons and x-rays are well-suited to the task of determining the distribution of magnetization in crystals. Applications of the two techniques proceed by contrasting observed intensities with intensities calculated with a specific model, and changing the model as need be to achieve satisfactory agreement. An all-in-all-out (AIAO) magnetic configuration of magnetic dipoles on a cubic face-centred lattice with networks of corner-sharing tetrahedra is often mentioned in the context of pyrochlore oxides, for example, but the corresponding neutron and x-ray diffraction patterns appear not have been calculated. Our results for patterns of Bragg spots from an AIAO magnetic configuration defined by a magnetic space group are symmetry informed and yield exact reflection conditions. Specifically, a long-range order of magnetic dipoles is forbidden in our model. Bulk properties arise from higher-order multipoles that include quadrupoles and octupoles. Bragg spots that exclude all magnetic multipoles other than an octupole have been discovered, and they can be observed by both neutron diffraction and resonant x-ray diffraction. All magnetic multipoles allowed in diffraction by cerium ions (4f 1 ) are presented in terms of coefficients in a welldocumented and unusual magnetic ground state. Symmetry of the cerium site in the cubic structure constrains the coefficients. Our scattering amplitudes have an application in both neutron and x-ray diffraction experiments on Ce2Zr2O7, for example, and searches for the sought-after cerium octupole. Also presented for future use is a result for the total, energyintegrated magnetic neutron scattering intensity by a powder sample.