Extended scattering continua characteristic of spin fractionalization in the two-dimensional frustrated quantum magnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ observed by neutron scattering

The magnetic excitations of the quasi-2D spin-1/2 frustrated Heisenberg antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ are explored throughout the 2D Brillouin zone using high-resolution time-of-flight inelastic neutron scattering. Measurements are made both in the magnetically ordered phase, stabilized at low temperatures by the weak interlayer couplings, as well as in the spin liquid phase above the ordering temperature $T_N,$ when the 2D magnetic layers are decoupled. In the spin liquid phase the dynamical correlations are dominated by highly dispersive excitation continua, a characteristic signature of fractionalization of $S=1\mathrm{}$ spin waves into pairs of deconfined $S=1/2\mathrm{}$ spinons and the hallmark of a resonating-valence-bond (RVB) state. The boundaries of the excitation continua have strong 2D-modulated incommensurate dispersion relations. Upon cooling below $T_N$ magnetic order in an incommensurate spiral forms due to the 2D frustrated couplings. In this phase sharp magnons carrying a small part of the total scattering weight are observed at low energies, but the dominant continuum scattering which occurs at medium to high energies is essentially unchanged compared to the spin liquid phase. 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 parametrized two-spinon cross section. Those results suggest a crossover in the nature of the excitations from $S=1\mathrm{}$ spin waves at low energies to deconfined $S=1/2\mathrm{}$ spinons at medium to high energies, which could be understood if ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$ was in the close proximity of transition between a fractional RVB spin liquid and a magnetically ordered state. A large renormalization factor of the excitation energies $[R=1.63\mathrm{}(5\left)\mathrm{}\right],$ indicating strong quantum fluctuations in the ground state, is obtained using the exchange couplings determined from saturation-field measurements. We provide an independent consistency check of this quantum renormalization factor using measurements of the second moment of the paramagnetic scattering.