Inelastic Neutron Scattering Investigation of Quantum Order-by-disorder in Bi₂CuO₄

Order by disorder (ObD), where ground state is selected from a continuous manifold of classically degenerate states by either thermal or quantum fluctuation has been intensively studied theoretically. However, experimental realizations of ObD in real materials are still very rare. In this talk, we present strong evidence from neutron scattering for quantum ObD in tetragonal cuprate Bi₂CuO₄. With high resolution inelastic neutron scattering, we observed a gapless and a gapped magnon mode due to in-plane and out-of-plane spin fluctuation. By studying field dependence of the in-plane mode and magnetic Bragg peak, we directly observed a spin-flop transition at ∼0.4T and demonstrated the existence of a small magnetic anisotropy within the ab plane. Since any in-plane anisotropy is prohibited by symmetry in Bi₂CuO₄ on a classical level, we attribute its existence to quantum ObD. We investigated quantum ObD in Bi₂CuO₄ theoretically by spin-wave analysis. By taking into account quantum zero-point fluctuation of the spin wave modes in Bi₂CuO₄, we found a small in-plane anisotropy favouring an ordered moment 45 degrees from the crystallographic a and b directions. Our model quantitatively explained the size of critical field for spin-flop transition in our data.