Non-linear magnons and exchange Hamiltonians of delafossite proximate quantum spin liquids

Quantum spin liquids (QSL) are theoretical states of matter with long-range entanglement and exotic quasiparticles. However, they generally elude quantitative theory, rendering their underlying phases mysterious and hampering efforts to identify experimental QSL states. Here we study triangular lattice resonating valence bond QSL candidate materials KYbSe$_2$ and NaYbSe$_2$ in their 1/3 plateau phase, where quantitative theory is tractable. We measure the magnon modes within this phase using inelastic neutron scattering and fit them using nonlinear spin wave theory. We also fit the KYbSe$_2$ heat capacity using high temperature series expansion. Both KYbSe$_2$ fits yield the same magnetic Hamiltonian to within uncertainty, confirming previous estimates and showing the Heisenberg $J_2/J_1$ to be an accurate model for these materials. Most importantly, the comparison KYbSe$_2$ and NaYbSe$_2$ shows that smaller $A$-site Na$^+$ ion has a larger $J_2/J_1$ ratio, enabling the periodic table to tune materials towards a QSL in a controlled way.