Direct Measurement of the Spin Hamiltonian and Observation of Condensation of Magnons in the 2D Frustrated Quantum MagnetCs2CuCl4

We propose a method for measuring spin Hamiltonians and apply it to the spin- $1/2$ Heisenberg antiferromagnet ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$, which shows a 2D fractionalized resonating valence bond state at low fields. By applying strong fields we fully align the spin moment of ${\mathrm{Cs}}_2{\mathrm{CuCl}}_4$, transforming it into an effective ferromagnet. In this phase the excitations are conventional magnons and their dispersion relation measured using neutron scattering give the exchange couplings directly, which are found to form an anisotropic triangular lattice with small Dzyaloshinskii-Moriya terms. Using the field to control the excitations we observe Bose condensation of magnons into an ordered ground state.