Coherent modulation of the $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$ atomic structure by displacive stimulated ionic Raman scattering

We discuss the mechanism of coherent phonon generation by stimulated ionic Raman scattering, a process different from conventional excitation with near visible optical pulses. Ionic Raman scattering is driven by anharmonic coupling between a directly excited infrared-active phonon mode and other Raman modes. We experimentally study the response of $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$ to the resonant excitation of apical oxygen motions at 20 THz by midinfrared pulses, which has been shown in the past to enhance the interlayer superconducting coupling. We find coherent oscillations of four totally symmetric $\left({\mathrm{A}}_{\mathrm{g}}\right)$ Raman modes and make a critical assessment of the role of these oscillatory motions in the enhancement of superconductivity.

Figure 1

(a) Response of the infrared-active normal coordinate $Q_{IR}$ (light red) to resonant excitation by a 140 fs midinfrared pulse (red). (b) Within cubic coupling, a directional force proportional to $Q_{IR}^2$ (light blue) is exerted on the coupled mode $Q_R$, which displaces the atoms as long as the infrared mode oscillates coherently and drives coherent oscillations for modes $Q_R$ with a period long compared to the rise time of this force. (c) $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$ is a layered superconductor in which $\mathrm{Cu}{\mathrm{O}}_2$ planes, shown in blue, form bilayers separated by an insulating yttrium layer. Holes are doped in these planes by changing the oxygen content of Cu-O chains, which are alternatingly filled and empty in the ortho-II ordered structure of $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$ for $x=0.5$ or $0.55$. The resonantly excited $B_{1u}$ mode consists of movements of the apical oxygen atoms between these bilayers at chain sites with an oxygen vacancy.

Figure 2

(a) Time-resolved reflectivity changes at 800 nm following resonant excitation of the $B_{1u}$ infrared mode in $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.55}$. Changes for probe polarizations out of plane and in plane are shown in blue and red, respectively. The inset shows the oscillatory signal at 10 K sample temperature, obtained by subtracting a fit to the data (thin black line). (b) The Fourier transformations of these oscillations, showing spectral weight at four frequencies coinciding with $A_g$ phonon modes. (c) Same as panel (b) for $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.5}$. (d) Zoom into the individual oscillatory components in $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6.55}$ (10 K, in plane), extracted from fitting the oscillations shown in panel (a). The phase of the oscillatory components at time zero is cosinelike.

Figure 3

(a) Four lowest frequency $A_g$ modes of the ortho-II ordered $\mathrm{YB}{\mathrm{a}}_2\mathrm{C}{\mathrm{u}}_3{\mathrm{O}}_{6+x}$ structure [9]. (b) Calculated ratio between oscillation and displacement amplitude of the five lowest frequency $A_g$ phonon modes after excitation of the $B_{1u}$ infrared mode with 140 fs midinfrared pulses.

Figure 4

(a) The combined atomic motions of the $A_g$ modes primarily involve $c$-axis movement of the planar Cu atoms. To describe the structural dynamics, we define $d_1$ and $d_2$ as the distances between Cu atoms (large blue spheres) of neighboring $\mathrm{Cu}{\mathrm{O}}_2$ planes at vacant and filled chain sites, respectively. (b) Changes in these distances due to excitation of the $A_g$ phonon modes. We estimate oscillation amplitudes of 0.9 and 0.5 pm in $d_1$ and $d_2$, with a relaxation time of 3 ps. (c) The full dynamics including the displacive response involve an increase in both $d_1$ and $d_2$ accompanied by oscillations.