Magnon-spinon dichotomy in the Kitaev hyperhoneycomb β-Li2IrO3

The family of edge-sharing tricoordinated iridates and ruthenates has emerged in recent years as a major platform for Kitaev spin-liquid physics, where spins fractionalize into emergent magnetic fluxes and Majorana fermions with Dirac-like dispersions. While such exotic states are usually preempted by long-range magnetic order at low temperatures, signatures of Majorana fermions with long coherent times have been predicted to manifest at intermediate and higher energy scales, similar to the observation of spinons in quasi-one-dimensional spin chains. Here we present a resonant inelastic X-ray scattering study of the magnetic excitations of the hyperhoneycomb iridate β-Li2IrO3 under a magnetic field with a record-high-resolution spectrometer. At low temperatures, dispersing spin waves can be resolved around the predicted intertwined incommensurate spiral and field-induced zigzag orders, whose excitation energy reaches a maximum of 16 meV. A 2 T magnetic field softens the dispersion around Q=0. The behavior of the spin waves under magnetic field is consistent with our semiclassical calculations for the ground state and the dynamical spin structure factor, which further predicts that the ensued intertwined uniform states remain robust up to very high fields (100 T). Most saliently, the low-energy magnonlike mode is superimposed by a broad continuum of excitations, centered around 35 meV and extending up to 100 meV. This high-energy continuum survives up to at least 300 K-well above the ordering temperature of 38 K- A nd gives evidence for pairs of long-lived Majorana fermions of the proximate Kitaev spin liquid.