As a simple cubic system with only one f electron per cerium ion, CeB6 is of model character to investigate the interplay of orbital phenomena with magnetism. It is also a textbook example of a compound that exhibits magnetically hidden order -- a low-temperature magnetic phase with ordered quadrupolar moments. It is difficult to identify the symmetry of such hidden-order states in common x-ray or neutron scattering experiments, as there is no signal in zero field, however alternative techniques like neutron diffraction in external field, resonant x-ray scattering, or ultrasonic investigations can be applied. Another possible method for characterizing hidden order is to look at the magnetic excitation spectrum, which carries the imprint of the multipolar interactions and the hidden order parameter in its dispersion relations. Using a specific candidate model, the dispersion is calculated and then compared to that measured with inelastic neutron scattering. Until recently, only a limited amount of data which show the presence of dispersing excitations measured along a few high-symmetry directions in an applied magnetic field were available. Early attempts to compare such calculations with experiments showed that only strongest modes at high-symmetry points could be identified. The present review of the most recent neutron-scattering results is intended to satisfy the need of more accurate inelastic neutron-scattering experiments as a function of field and temperature, giving us the opportunity to identify existing excitation branches in CeB6 and conclusively compare them with the theoretically predicted multipolar excitations.
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