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We use inelastic neutron scattering to show that long-range spin wavesarising from the static bicollinear antiferromagnetic (AF) order in FeTe, whichhave twofold rotational symmetry in a fully detwinned crystal, rapidly dissolveabove $E\approx 26$ meV into ridges of scattering with fourfold rotationalsymmetry and a nearly isotropic magnetic fluctuation spectrum. With increasingtemperature above $T_N\approx 68$ K, the twofold spin waves change into broadregions of scattering with fourfold symmetry. Since the scattering patternsfrom plaquette magnetic order generated within a bilinear biquadraticHamiltonian have fourfold rotational symmetry consistent with the high-energy,spin-isotropic spin waves of FeTe, we conclude that the bicollinear AF state inFeTe is quasidegenerate with plaquette magnetic order, providing evidence forthe strongly frustrated nature of the local moments in iron chalcogenide familyof iron-based superconductors.

Plaquette instability competing with bicollinear ground state in detwinned FeTe