  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 (4f1) are presented in terms of coefficients in a well-documented
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, energy-integrated magnetic neutron
scattering intensity by a powder sample.
