Sample Characteristics

Figure 3.1 shows the crystal structures of the electron-doped cuprate Pr$_{2-x}$Ce$_x$CuO$_4$ and the hole-doped cuprate La$_{2-x}$Sr$_x$CuO$_4$. The hole-doped compound has a $T$-phase structure where the copper atom is octahedrally coordinated with six oxygen atoms. On the other hand, Pr$_{2-x}$Ce$_x$CuO$_4$ has a $T'$-phase where there are no interstitial oxygen atoms.

Fig. 3.1: Crystal structure of La$_{2-x}$Sr$_x$CuO$_4$ and Pr$_{2-x}$Ce$_x$CuO$_4$.

The results reported in this thesis are mainly from measurements on one of the single crystals, having a thickness of $0.07$ mm, an $\hat{a}$-$\hat{b}$ plane surface area of $\sim 6.5$ mm$^2$ and a mass of $3.74$ mg. It is the smallest single crystal measured by $\mu$SR using surface muons. Figure 3.2 shows the results of resistivity and bulk magnetic susceptibility measurements performed on this crystal. The resistivity measurements performed in zero external magnetic field, indicate that $T_c \approx 25 \pm 1$ K. This suggests that the crystal is near optimally doped with $x \approx 0.15$. However, the bulk magnetic susceptibility, measured using a Superconducting Quantum Interference Device (SQUID), reaches a constant value only below $\sim 16$ K. Given that resistivity measurements are sensitive to the ``path of least resistance'', the magnetic susceptibility is a better indication of the average value of $T_c$ in the bulk of the sample.

Fig. 3.2: Bulk magnetic susceptibility measurements taken under field-cooled (FC) and zero-field cooled (ZFC) conditions with $H$ = $1$ Oe and resistivity measurements (solid triangles) in zero external magnetic field. The applied field is directed along the crystallographic $\hat{c}$-axis.

Fig. 3.3: Schematic of the experimental setup. All the components are contained within a $^4$He gas-flow cryostat.