Magnetic excitations and amplitude fluctuations in insulating cuprates

We present results from light scattering experiments on three insulating antiferromagnetic cuprates, ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.05}$, ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{YCu}}_2{\mathrm{O}}_{8+\delta }$, and ${\mathrm{La}}_2{\mathrm{CuO}}_4$ as a function of polarization and excitation energy using samples of the latest generation. From the raw data we derive symmetry-resolved spectra. The spectral shape in $B_{1g}$ symmetry is found to be nearly universal and independent of excitation energy. The spectra agree quantitatively with predictions by field theory [Eur. Phys. J. B 88, 237 (2015)] facilitating the precise extraction of the Heisenberg coupling $J$. In addition, the asymmetric lineshape on the high-energy side is found to be related to amplitude fluctuations of the magnetization. In ${\mathrm{La}}_2{\mathrm{CuO}}_4$ alone, minor contributions from resonance effects may be identified. The spectra in the other symmetries are not universal. The variations may be traced back to weak resonance effects and extrinsic contributions. For all three compounds we find support for the existence of chiral excitations appearing as a continuum in $A_{2g}$ symmetry having an onset slightly below $3J$. In ${\mathrm{La}}_2{\mathrm{CuO}}_4$ an additional isolated excitation appears on top of the $A_{2g}$ continuum.

Figure 1

Symmetry-resolved Raman response $R{\chi }_{\mu }^{″}(\mathrm{\Omega },T)$ of ${\mathrm{CuO}}_2$ compounds as indicated. The spectra are the result of linear combinations of in total six spectra as described in Appendix pp2.

Figure 2

Raman response $R{\chi }^{″}(\mathrm{\Omega },T)$ in $x^{\prime }{y}^{\prime }$ polarization ($B_{1g}+A_{2g}$ symmetry) as a function of excitation energy for Y123, Bi2212:Y, and La214. (a)–(c) Raw data. (d)–(f) Spectra are multiplied by factors as indicated so as to match the peak intensities.

Figure 3

$B_{1g}$ spectra of ${\mathrm{YBa}}_2{\mathrm{Cu}}_3{\mathrm{O}}_{6.05}$ (black), ${\mathrm{La}}_2{\mathrm{CuO}}_4$ (green), and ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{YCu}}_2{\mathrm{O}}_{8+\delta }$ (red). The spectra are reproduced from Fig. 1 with the intensities scaled as indicated. The energy axis is given in units of the exchange coupling $J$. The normalized position of the peak maxima matches the theoretically predicted energy of $2.84J$ [32].

Figure 4

Influence of the surface treatment in La214. There is a small intensity difference between the polished and the cleaved surface of the $B_{1g}$ spectra. All structures appear at the same position for both surfaces. The increase towards high energies for the cleaved sample has its origin in edge effects due to the small area available.

Figure 5

Raman spectra of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ at the six main polarization configurations (raw data after division by the Bose factor). (a) All spectra comprise two symmetries. (b) Each sum of two spectra with the same incident and orthogonal outgoing polarizations contains all four (in-plane) symmetries. Thus, the spectra shown should be equal. The discrepancies above 5000 ${\mathrm{cm}}^{-1}$ indicate extrinsic problems.

Figure 6

Symmetry-resolved Raman spectra of ${\mathrm{La}}_2{\mathrm{CuO}}_4$ at 100 K and excitation energies as indicated. (b), (c) The highest intensity of the $A_{2g}$ and $B_{1g}$ spectra is observed for $\hslash {\omega }_I=2.5$ eV (496 nm). (a), (d) In $A_{1g}$ and $B_{2g}$ symmetry the overall intensity increases monotonically towards low excitations energies, and the shape changes qualitatively. (b) The onset of the $A_{2g}$ intensity at 3000 ${\mathrm{cm}}^{-1}$ (dashed vertical line) is independent of the excitation. The peak energy varies slightly for reasons we do not know.

Figure 7

$A_{2g}+B_{1g}$ ($x^{\prime }{y}^{\prime }$) spectra at 100 K for various excitation lines as indicated. (a) Raw data (including the calibration and Bose correction). The phonons below 1500 ${\mathrm{cm}}^{-1}$ resonate strongly toward the lower excitation energies. The two-magnon peak intensity is maximal for $\hslash {\omega }_I=2.5$ eV (496 nm). The secondary maximum close to 4600 ${\mathrm{cm}}^{-1}$ becomes monotonically weaker between 2.71 and 2.41 eV and is out of the range of the spectrometer for $\hslash {\omega }_I=2.16$ eV (575 nm). (b) Normalized spectra. Close to the two-magnon excitation the shape is nearly universal in the range of photon energies studied here.