Absence of an isotope effect in the magnetic resonance in high-$T_c$ superconductors

Abstract

An inelastic neutron scattering experiment has been performed in the high-temperature superconductor $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.89}$ to search for an oxygen-isotope shift of the well-known magnetic resonance mode at 41 meV. Contrary to a recent prediction (I. Eremin, {\it et al.}, Phys. Rev. B {\bf 69}, 094517 (2004)), a negligible shift (at best $\le$ +0.2 meV) of the resonance energy is observed upon oxygen isotope substitution (${}^{16}$O${\to }^{18}$O). This suggests a negligible spin-phonon interaction in the high-$T_c$ cuprates at optimal doping.

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