  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.
