  A significant number of Kondo-lattice ferromagnets order perpendicular to the
easy magnetization axis dictated by the crystalline electric field. The nature
of this phenomenon has attracted considerable attention, but remains poorly
understood. In the present paper we use inelastic neutron scattering supported
by magnetization and specific heat measurements to study the spin dynamics in
the hard-axis ferromagnet CeAgSb2. In the zero field state we observed two
sharp magnon modes, which are associated with Ce ordering and extended up to
$\approx 3 meV with a considerable spin gap of 0.6 meV. Application of a
magnetic field perpendicular to the moment direction reduces the spectral
intensity and suppresses the gap and significantly enhances the low-temperature
specific heat at a critical field of Bc ~ 2.8 T via a mean-field-like
transition. Above the transition, in the field polarized state, the gap
eventually reopens due to the Zeeman effect. We modeled the observed dispersion
using linear spin-wave theory (LSWT) taking into account the ground state Gamma
6 doublet and exchange anisotropy. Our model correctly captures the essential
features of the spin dynamics including magnetic dispersion, distribution of
the spectral intensity as well as the field-induced behavior, although several
minor features remain obscure. The observed spectra do not show significant
broadening due to the finite lifetime of the quasiparticles. Along with a
moderate electronic specific heat coefficient gamma = 46 mJ/mol K2 this
indicates that the Kondo coupling is relatively weak and the Ce moments are
well localized. Altogether, our results provide profound insight into the spin
dynamics of the hard-axis ferromagnet CeAgSb2 and can be used as solid ground
for studying magnetic interactions in isostructural compounds including
CeAuSb2, which exhibits nematicity and unusual mesoscale magnetic textures.
