Inelastic Light Scattering Measurements of a Pressure-Induced Quantum Liquid in ${\mathbf{K}\mathbf{C}\mathbf{u}\mathbf{F}}_3$

Pressure-dependent, low-temperature inelastic light (Raman) scattering measurements of ${\mathrm{KCuF}}_3$ show that applied pressure above $P^{*}\sim 7\mathrm{kbar}$ suppresses a previously observed structural phase transition temperature to zero temperature in ${\mathrm{KCuF}}_3$, resulting in the development of a fluctuational (quasielastic) response near $T\sim 0\mathrm{K}$. This pressure-induced fluctuational response—which we associate with slow fluctuations of the ${\mathrm{CuF}}_6$ octahedral orientation—is temperature independent and exhibits a characteristic fluctuation rate that is much larger than the temperature, consistent with quantum fluctuations of the ${\mathrm{CuF}}_6$ octahedra. A model of pseudospin-phonon coupling provides a qualitative description of both the temperature- and pressure-dependent evolution of the Raman spectra of ${\mathrm{KCuF}}_3$.

Figure 1

(a) Temperature dependence of the $B_{1g}$-symmetry phonon mode in ${\mathrm{KCuF}}_3$. All spectra have the same $y$-axis scale and have been offset in the $y$-axis direction for clarity. Inset shows $B_{1g}$ phonon normal mode vibration of $F^{-}$ ions (blue arrows), and dashed red arrow depicts octahedral orientation (pseudospin). (b) Summary of the temperature dependence of the peak energy (circles) and linewidth (squares) of the $B_{1g}$ phonon mode. The inset shows the calculated temperature dependence of the normalized peak frequencies, $\omega /{\omega }_0$, using Eq. (1) for the case $\gamma =10{\omega }_0$, from Ref. 17. (c) Temperature dependence of the $E_g$-symmetry phonon mode in ${\mathrm{KCuF}}_3$. All spectra have the same $y$-axis scale and have been offset in the $y$-axis direction for clarity. (d) Summary of the temperature dependence of the peak energy of the $E_g$ phonon mode, showing a splitting of the mode at the tetragonal-to-orthorhombic structural transition at $T=50\mathrm{K}$.

Figure 2

(a) Pressure dependence of Raman spectra of ${\mathrm{KCuF}}_3$ at $T=3\mathrm{K}$. The arrow indicates a frequency corresponding to $40k_{B}T$. All spectra have the same $y$-axis scale and have been offset in the $y$-axis direction for clarity. Dashed lines indicate the common baseline for all the spectra. The inset illustrates the pressure dependence of the $E_g$ phonon mode at $T=3\mathrm{K}$. (b) Pressure dependence of the integrated quasielastic scattering response intensity, $I(P)$, at $T=3\mathrm{K}$ for three different samples of ${\mathrm{KCuF}}_3$. The inset shows the pressure dependence of the peak energies of the $E_g$ phonon mode at 3 K for four different samples, showing evidence for an orthorhombic-to-tetragonal transition near $P^{*}=7\mathrm{kbar}$. (c) Calculated normalized phonon frequency $\omega /{\omega }_0$ (black circles) and quasielastic scattering response integrated intensity (blue squares) as a function of ${\omega }_0/\gamma$, using Eq. (1) from Ref. 17. (d) Temperature dependence of quasielastic scattering response of ${\mathrm{KCuF}}_3$ at $P=42.3\mathrm{kbar}$. All spectra have the same $y$-axis scale and all spectra have been shifted by the same amount in the -$y$ direction to emphasize the quasielastic contribution to the spectra. The low energy ($55{\mathrm{cm}}^{-1}$) cutoff in (a) and (d) reflects the low energy limit of the spectral window defined by our spectrometer.

Figure 3

$PT$ phase diagram for the ${\mathrm{CuF}}_6$ octahedral fluctuations in ${\mathrm{KCuF}}_3$. Horizontal axes represent the temperature and pressure. The contour plot on the horizontal plane represents the measured fluctuational response integrated intensity, with $\mathrm{\text{dark green}}=2000$ counts and $\mathrm{\text{white}}=0$ counts, based on temperature sweeps at the following pressures: $P=0$, 5, 13, 18.7, 27, 35, 42 kbar. The vertical axis shows the mode frequency, with both the $\sim 79{\mathrm{cm}}^{-1}$ $B_{1g}$ and $\sim 261{\mathrm{cm}}^{-1}$ $E_g$ phonon frequencies shown as functions of temperature (filled red and green circles, respectively) and pressure (open red and green circles, respectively). Filled squares illustrate the characteristic energy $\gamma$ of the fluctuational response. Diagrams on top depict (left) thermally activated hopping between ${\mathrm{CuF}}_6$ configurations in the fast-fluctuating regime of ${\mathrm{KCuF}}_3$ and (right) the quantum tunneling between ${\mathrm{CuF}}_6$ configurations in the pressure-tuned slow-fluctuating regime.