Feedback Effect on High-Energy Magnetic Fluctuations in the Model High-Temperature Superconductor ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$ Observed by Electronic Raman Scattering

We use electronic Raman scattering to study the model single-layer cuprate superconductor ${\mathrm{HgBa}}_2{\mathrm{CuO}}_{4+\delta }$. In an overdoped sample, we observe a pronounced amplitude enhancement of a high-energy peak related to two-magnon excitations in insulating cuprates upon cooling below the critical temperature $T_c$. This effect is accompanied by the appearance of the superconducting gap and a pairing peak above the gap in the Raman spectrum, and it can be understood as a hitherto-undetected feedback effect on the high-energy magnetic fluctuations due to the Cooper pairing interaction. This implies a direct involvement of the high-energy magnetic fluctuations in the pairing mechanism. All of these effects occur already above $T_c$ in two underdoped samples, demonstrating a related feedback mechanism associated with the pseudogap.

Figure 1

(a) Raman spectra for sample UD77. (b) Differential spectra relative to 330 K.

Figure 2

Main panels: $\Delta {\chi }^{\prime \prime }$ relative to the highest temperatures. The dashed lines indicate $T_c$. Insets: $\Delta {\chi }^{\prime \prime }$ at energies indicated by the color- and symbol-coded arrows, normalized to the lowest temperature. The solid curves are guides to the eye. The dashed lines (identical in all insets) describe the high-temperature behavior of the two-magnon amplitude in OV90.

Figure 3

Differential spectra relative to 300 K near the pairing peak. Phonon peaks in UD94 and OV90 were removed prior to the subtraction. The data are offset for clarity. The dashed lines indicate the peak positions determined at 10 K.

Figure 4

(a) Solid curves represent raw data at 10 K. The cross symbols represent model calculations for $\omega$ up to $4J^{*}$. (b) $\Delta {\chi }^{\prime \prime }$ between 10 and 300 K. Phonon peaks in UD94 and OV90 are removed prior to the subtraction. The inset shows an enlarged view of the two-magnon peak. (c) Characteristic energies in Hg1201 (see text). The dome-shaped curve represents $4.28k_B{T}_c$. (d) Values of $J^{*}={\omega }_{2\mathrm{mag}}^{\mathrm{peak}}/3$ [except for the cross symbols, which are from the calculations in (a)] and (e) ${\omega }_{\mathrm{pair}}$, in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (upward triangles), ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6+\delta }$ (rightward triangles), ${\mathrm{Bi}}_{2.1}{\mathrm{Sr}}_{1.9}{\mathrm{Ca}}_{1-x}{\mathrm{Y}}_x{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$ (leftward triangles) [24], and Hg1201 (filled symbols, this work). The dashed line in (e) summarizes the ${\omega }_{\mathrm{pair}}$ for Hg1201 reported in Ref. 22.