  In contrast to magnetic order formed by electrons' dipolar moments, ordering
phenomena associated with higher-order multipoles (quadrupoles, octupoles,
etc.) are more difficult to characterize because of the limited choice of
experimental probes that can distinguish different multipolar moments. The
heavy-fermion compound CeB6 and its La-diluted alloys are among the
best-studied realizations of the long-range-ordered multipolar phases, often
referred to as "hidden order". Previously the hidden order in phase II was
identified as primary antiferroquadrupolar (AFQ) and field-induced octupolar
(AFO) order. Here we present a combined experimental and theoretical
investigation of collective excitations in the phase II of CeB6. Inelastic
neutron scattering (INS) in fields up to 16.5 T reveals a new high-energy mode
above 14 T in addition to the low-energy magnetic excitations. The experimental
dependence of their energy on the magnitude and angle of the applied magnetic
field is compared to the results of a multipolar interaction model. The
magnetic excitation spectrum in rotating field is calculated within a localized
approach using the pseudo-spin presentation for the Gamma8 states. We show that
the rotating-field technique at fixed momentum can complement conventional INS
measurements of the dispersion at constant field and holds great promise for
identifying the symmetry of multipolar order parameters and the details of
inter-multipolar interactions that stabilize hidden-order phases.
