Relation between cuprate superconductivity and magnetism: A Raman study of ${\left(\mathrm{CaLa}\right)}_1{\left(\mathrm{BaLa}\right)}_2{\mathrm{Cu}}_3{\mathrm{O}}_y$

We present an investigation of charge-compensated antiferromagnetic $\left({\mathrm{Ca}}_x{\mathrm{La}}_{1-x}\right){(\mathrm{Ba}}_{1.75-x}{\mathrm{La}}_{0.25+x}{)\mathrm{Cu}}_3{\mathrm{O}}_y$ single crystals using Raman scattering as well as muon spin rotation. In this system the parameter $x$ controls the Cu-O-Cu superexchange interaction via bond distances and buckling angles. The oxygen content $y$ controls the charge doping. In the absence of doping the two-magnon peak position is directly proportional to the superexchange strength $J$. We find that both $x$ and $y$ affect the peak position considerably. The Néel temperature determined from muon spin rotation on the same samples independently confirms the strong dependence of the magnetic interaction on $x$ and $y$. We find a considerable increase in the maximum superconducting transition temperature $T_c^{\max }$ with $J$. This is strong evidence of the importance of orbital overlap to superconductivity in this family of cuprates.

Figure 1

(a) Phase diagram of CLBLCO for the four families $x=0.1$, 0.2, 0.3, and 0.4. $T_N,T_g$ (open symbols) and $T_c$ are plotted as a function of oxygen composition $y$. The long arrows point to the $y$ values where $T_N$ starts to drop, which defines $y_N$. The samples $\alpha =(0.1,6.4),\beta =(0.4,6.4),\gamma =(0.1,6.75),\delta =(0.4,6.73)$, and $\varepsilon =(0.2,6.64)$ are marked by their $(x,y)$ values. (b) $J$ and the critical temperatures normalized by $T_c^{\max }$ as a function of doping variation $\Delta n_{p\sigma }$. $\alpha$–$\varepsilon$ indicate the positions of the five samples in the phase diagram.

Figure 2

The two-magnon mode for samples $\alpha$–$\delta$, measured at $T=20$ K.

Figure 3

(a) Temperature dependence of the two-magnon mode in $\left(x^{\prime }{y}^{\prime }\right)$ polarization for the $x=0.1$ sample. (b) Polarization dependence of the two-magnon mode measured at $T=300$ K.

Figure 4

(a) Comparison of the $B_{1g}$ phonon mode of samples $\alpha$ and $\beta$. The atomic displacement pattern for this phonon mode is indicated in the inset; the red and blue spheres correspond to oxygen and copper, respectively. (b) Full width at half maximum (FWHM) of the $B_{1g}$ phonon mode at $300 \mathrm{cm}{}^{-1}$ for both $x=0.1$ and $0.4$ families as a function of oxygen composition $y$. The $x=0.2$ sample is indicated as well. The lines are guides to the eyes.

Figure 5

(a) Magnetization as function of temperature for optimally doped samples of $x=0.1$ and $x=0.4$. (b) Néel temperature determined for samples $\alpha ,\beta$, and $\gamma$ as indicated in the phase diagram using $\mu \mathrm{SR}$.

Figure 6

(a) Doping dependence of the two-magnon mode energy $E_{\max }$ for the families $x=0.1$ (black) and $x=0.4$ (red). Samples $\alpha$–$\delta$, as well as sample $\varepsilon$ from the $x=0.2$ family, are indicated. The green arrow denotes the crossing regime. (b) $E_{\max }$ measured for the $\Delta n_{p\sigma }\simeq 0$ samples $\gamma ,\varepsilon$, and $\beta$ as a function of $T_c^{\max }$ obtained from the phase diagram in Fig. 1 for the optimally doped samples of the $x=0.1,x=0.2$, and $x=0.4$ families. The solid line is a linear fit through the data points; the dashed line denotes a proportionality behavior between $T_c^{\max }$ and $J$.