  Topologically ordered states of matter are generically characterized by
excitations with quantum number fractionalization. A prime example is the spin
liquid realized in Kitaev's honeycomb-lattice compass model where spin-flip
excitations fractionalize into Majorana fermions and Ising gauge fluxes. While
numerous compounds have been proposed to be proximate to such a spin-liquid
phase, clear-cut evidence for fractionalized excitations is lacking. Here we
employ microwave absorption measurements to study the low-energy excitations in
$\alpha$-RuCl$_3$ over a wide range of frequencies, magnetic fields, and
temperatures, covering in particular the vicinity of the field-driven quantum
phase transition where long-range magnetic order disappears. In addition to
conventional gapped magnon modes we find a highly unusual broad continuum
characteristic of fractionalization which -- most remarkably -- extends to
energies below the lowest sharp mode and to temperatures significantly higher
than the ordering temperature, and develops a gap of a nontrivial origin in
strong magnetic fields. Our results unravel the signatures of fractionalized
excitations in $\alpha$-RuCl$_3$ and pave the way to a more complete
understanding of the Kitaev spin liquid and its instabilities.
