  The magnetic excitations of the quasi-2D spin-1/2 Heisenberg antiferromagnet
on an anisotropic triangular lattice Cs2CuCl4 are explored throughout the 2D
Brillouin zone using inelastic neutron scattering. In the spin liquid phase
above the transition to magnetic order extended excitation continua are
observed, characteristic of fractionalization of S=1 spin waves into pairs of
deconfined S=1/2 spinons and the hallmark of a resonating-valence-bond (RVB)
state. The weak inter-layer couplings stabilize incommensurate spiral order at
low temperatures and in this phase sharp magnons carrying a small part of the
total scattering weight are observed at low energies below the continuum lower
boundary. Linear spin-wave theory including one- and two-magnon processes can
describe the sharp magnon excitation, but not the dominant continuum
scattering, which instead is well described by a parameterized two-spinon
cross-section. Those results suggest a cross-over in the nature of excitations
from S=1 spin waves at low energies to S=1/2 spinons at medium to high
energies, which could be understood if Cs2CuCl4 was in the close proximity of a
transition between a fractional spin liquid and a magnetically-ordered phase.
