Highly Anisotropic Anomaly in the Dispersion of the Copper-Oxygen Bond-Bending Phonon in Superconducting ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$ from Inelastic Neutron Scattering

Motivated by predictions of a substantial contribution of the “buckling” vibration of the ${\mathrm{CuO}}_2$ layers to $d$-wave superconductivity in the cuprates, we have performed an inelastic neutron scattering study of this phonon in an array of untwinned crystals of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_7$. The data reveal a pronounced softening of the phonon at the in-plane wave vector $\mathbf{q}=(0,0.3)$ upon cooling below $\sim 105\mathrm{K}$, but no corresponding anomaly at $\mathbf{q}=(0.3,0)$. Based on the observed in-plane anisotropy, we argue that the electron-phonon interaction responsible for this anomaly supports an electronic instability associated with a uniaxial charge-density modulation and does not mediate $d$-wave superconductivity.

Figure 1

(a)–(e) Constant-$\mathbf{Q}$ scans at $\mathbf{Q}=(0,0.3,10)$. The profile at energy 40–42 meV arises from the bucking mode. Panel (a) shows raw data. A sloping background (dotted line) was subtracted in the other profiles for clarity. The black and green lines are results of fits to a phenomenological expression comprising two Voigt functions and to a full resolution calculation, respectively, as described in the text. (f) Temperature dependence of the line shape parameterized by the intensity of the two peaks in the phenomenological expression.

Figure 2

Constant-$\mathbf{Q}$ scans of the buckling mode at $\mathbf{Q}=(0.3,0,10)$ and $(0,0.3,10)$. A sloping background [Fig. 1a] was subtracted.

Figure 3

Dispersion of the buckling mode along the $a$ and $b$ axes. The black line is the dispersion used for the resolution calculation. A projection of the four-dimensional resolution ellipsoid is shown for comparison. The data point at $\mathbf{q}=(0,0.3)$ is the result of the resolution convolution described in the text; the remaining points were determined by fits to standard Voigt functions. The inset shows the eigenvector of the buckling mode at $\mathbf{q}=(0,0.3)$. The elongations of the apical oxygen atoms and of the in-plane oxygen atoms along $b$ were enlarged by a factor of 4 for clarity.