Intermediate Field Spin(on) Dynamics in $\alpha$-RuCl$_3$

We present comprehensive inelastic neutron spectroscopic maps of the magnetic field-induced disordered phase of the Kitaev quantum spin liquid candidate material $\alpha$-RuCl$_3$. For fields along both in-plane high-symmetry directions we observe that the spin excitation spectrum at and above a magnetic field of 8~T is gapped. Excitation modes then sharpen for increasing field but are consistently broader than experimental resolution even at 13.5~T. The out-of-plane dispersion diminishes in the 7-10~T regime, signifying enhanced two-dimensional behavior as the in-plane liquid correlations are established. In this regime, excitations are very broad and largely flat for all accessible energy-momenta, which is kinematically at odds with a magnon-decay picture. By contrast, a continuum of fractionalized excitations naturally yields a broad continuum response, which crucially may be accompanied by sharper modes of bound states of fractionalized excitations. Their damping by the continuum accounts for the observed spectral broadening and field dependence. Our results provide strong evidence for the existence of fractionalized excitations in $\alpha$-RuCl$_3$ in a magnetic field.