  The layered honeycomb iridate $\alpha$-Li$_2$IrO$_3$ displays an
incommensurate magnetic structure with counterrotating moments on
nearest-neighbor sites, proposed to be stabilized by strongly-frustrated
anisotropic Kitaev interactions between spin-orbit entangled Ir$^{4+}$ magnetic
moments. Here we report powder inelastic neutron scattering measurements that
observe sharply dispersive low-energy magnetic excitations centered at the
magnetic ordering wavevector, attributed to Goldstone excitations of the
incommensurate order, as well as an additional intense mode above a gap
$\Delta\simeq2.3$ meV. Zero-field muon-spin relaxation measurements show clear
oscillations in the muon polarization below the N\'{e}el temperature $T_{\rm
N}\simeq15$ K with a time-dependent profile consistent with bulk incommensurate
long-range magnetism. Pulsed field magnetization measurements observe that only
about half the saturation magnetization value is reached at the maximum field
of 64 T. A clear anomaly near 25 T indicates a transition to a phase with
reduced susceptibility. The transition field has a Zeeman energy comparable to
the zero-field gapped mode, suggesting gap suppression as a possible mechanism
for the field-induced transition.
