Polarization-dependent infrared reflectivity study of ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ under pressure: Charge dynamics, charge distribution, and anisotropy

We present a polarization-dependent infrared reflectivity study of the spin-ladder compound ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ under pressure. The optical response is strongly anisotropic, with the highest reflectivity along the ladders/chains $\left(\mathbf{E}\parallel c\right)$ revealing a metallic character. For the polarization direction perpendicular to the ladder plane, an insulating behavior is observed. With increasing pressure the optical conductivity for $\mathbf{E}\parallel c$ shows a strong increase, which is most pronounced below $2000{\mathrm{cm}}^{-1}$. According to the spectral weight analysis of the $\mathbf{E}\parallel c$ optical conductivity the hole concentration in the ladders increases with increasing pressure and tends to saturate at high pressure. At $\sim 7.5$ GPa the number of holes per Cu atom in the ladders has increased by $\Delta \delta =0.09(\pm 0.01)$, and the Cu valence in the ladders has reached the value $+2.33$. The optical data suggest that ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ remains electronically highly anisotropic up to high pressure, also at low temperatures.

Figure 1

(a)–(c) Reflectivity spectra $R_{s\text{−}d}$ of ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ for the polarization E of the radiation along the three crystal axes at room temperature. (d)–(f) Real part of the optical conductivity ${\sigma }_1$ obtained from the Drude-Lorentz fitting of the reflectivity spectra.

Figure 2

Real part of the optical conductivity ${\sigma }_1$ for $\mathbf{E}\parallel c$ at the lowest applied pressure at room temperature and the various contributions (Drude term, MIR band, and phonon modes) as obtained from the Drude-Lorentz fits.

Figure 3

MIR band as a function of pressure at room temperature, as obtained from the Drude-Lorentz fits of the reflectivity spectra. Inset: position of the MIR band as a function of pressure.

Figure 4

Frequencies of the phonon modes as a function of pressure at room temperature, as obtained from the Drude-Lorentz fits of the reflectivity spectra, for (a) $\mathbf{E}\parallel a$ and (b) $\mathbf{E}\parallel b$.

Figure 5

Reflectivity spectra of ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ for (a) $\mathbf{E}\parallel c$ and (b) $\mathbf{E}\parallel a$ up to 15 GPa at room temperature.

Figure 6

Estimated unit cell volume of ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ as a function of pressure at room temperature.

Figure 7

(a) Effective charge concentration $N_{\mathrm{eff}}$ per Cu atom obtained according to Eq. (2). (b) Cu valence in the ladders as a function of pressure. At high pressure the increase of holes in the ladders saturates. Inset: relative increase of the number of holes per Cu atoms in the ladders.

Figure 8

Room-temperature reflectivity of ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ at 1000 ${\mathrm{cm}}^{-1}$ for $\mathbf{E}\parallel c,\mathbf{E}\parallel a$, and $\mathbf{E}\parallel b$ as a function of pressure.

Figure 9

Reflectivity spectra $R_{s\text{−}d}$ of ${\mathrm{Sr}}_{2.5}{\mathrm{Ca}}_{11.5}{\mathrm{Cu}}_{24}{\mathrm{O}}_{41}$ at 10 K for the lowest $(\sim 1$ GPa) and highest $(\sim 4$ GPa) pressure for the two polarization directions $\mathbf{E}\parallel c$ and $\mathbf{E}\parallel a$ within the ladder/chain plane.