Plaquette instability competing with bicollinear ground state in detwinned FeTe

We use inelastic neutron scattering to show that long-range spin waves arising from the static bicollinear antiferromagnetic (AF) order in FeTe, which have twofold rotational symmetry in a fully detwinned crystal, rapidly dissolve above E≈26meV into ridges of scattering with fourfold rotational symmetry and a nearly isotropic magnetic fluctuation spectrum. With increasing temperature above TN≈68K, the twofold spin waves change into broad regions of scattering with fourfold symmetry. Since the scattering patterns from plaquette magnetic order generated within a bilinear biquadratic Hamiltonian have fourfold rotational symmetry consistent with the high-energy, spin-isotropic spin waves of FeTe, we conclude that the bicollinear AF state in FeTe is quasidegenerate with plaquette magnetic order, providing evidence of the strongly frustrated nature of the local moments in the iron chalcogenide family of iron-based superconductors.