  Conventionally ordered magnets possess bosonic elementary excitations, called
magnons. By contrast, no magnetic insulators in more than one dimension are
known whose excitations are not bosons but fermions. Theoretically, some
quantum spin liquids (QSLs) -- new topological phases which can occur when
quantum fluctuations preclude an ordered state -- are known to exhibit Majorana
fermions as quasiparticles arising from fractionalization of spins. Alas,
despite much searching, their experimental observation remains elusive. Here,
we show that fermionic excitations are remarkably directly evident in
experimental Raman scattering data across a broad energy and temperature range
in the two-dimensional material $\alpha$-RuCl$_3$. This shows the importance of
magnetic materials as hosts of Majorana fermions. In turn, this first
systematic evaluation of the dynamics of a QSL at finite temperature emphasizes
the role of excited states for detecting such exotic properties associated with
otherwise hard-to-identify topological QSLs.
