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

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

Figure 1

(Color online) Magnetic susceptibility of both sample arrays used in this experiment. Onset superconducting temperatures occur at 88.8 K for samples with ${}^{18}\mathrm{O}$ and 90 K for ${}^{16}\mathrm{O}$. The curve of each mounting has been obtained by weighting the susceptibility curve of each individual single crystal by their mass. The dispersion of $T_c$ for the samples of each array is less than 0.3 K.

Figure 2

(Color online) Neutron intensity measured at $Q=(-0.5,-0.5,10.3)$ and at $T=100\mathrm{K}$ showing an oxygen phonon mode in both the ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ samples.

Figure 3

(Color online) Resonant magnetic peak intensity in both the ${}^{16}\mathrm{O}$ and ${}^{18}\mathrm{O}$ samples: (a) Raw neutron intensity at 12 and 100 K for both samples; (b) Difference of the neutron intensity 12–100 K for each sample. The total counting time reached 1.5 h per point at each temperature to reduce the error bar on the energy of the resonance to 0.12 meV. The curves are not normalized by samples mass.