Superconductivity and Field-Induced Magnetism in ${\mathrm{P}\mathrm{r}}_{2-x}{\mathrm{C}\mathrm{e}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_4$ Single Crystals

We report muon-spin rotation and relaxation ($\mu \mathrm{S}\mathrm{R}$) measurements on single crystals of the electron-doped high-$T_c$ superconductor ${\mathrm{P}\mathrm{r}}_{2-x}{\mathrm{C}\mathrm{e}}_x{\mathrm{C}\mathrm{u}\mathrm{O}}_4$. In a zero external magnetic field, superconductivity is found to coexist with dilute Cu spins that are static on the $\mu \mathrm{S}\mathrm{R}$ time scale. In an applied field, we observe a ${\mu }^{+}$-Knight shift that is primarily due to the magnetic moment induced on the Pr ions. Below the superconducting transition temperature $T_c$, an additional source of local magnetic field appears throughout the volume of the sample. This finding is shown to be consistent with field-induced antiferromagnetic ordering of the Cu spins. Measurements of the temperature dependence of the in-plane magnetic penetration depth ${\lambda }_{ab}$ in the vortex state are also presented.

Figure 1

Time evolution of the asymmetry [i.e., $A(t)=AP(t)$, where $A$ is the signal amplitude] in zero external field at $T=80$, 40, and 2.3 K. The initial muon-spin polarization was parallel to the ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ layers. Inset: Temperature dependence of the resistivity (solid diamonds), and the bulk susceptibility at $H=1\mathrm{O}\mathrm{e}$ under FC and ZFC conditions.

Figure 2

FFTs of the muon-spin precession signal in PCCO taken under FC conditions. The dashed vertical line indicates the external field $H=90\mathrm{O}\mathrm{e}$. Inset: Asymmetry spectra taken at $T=2.3\mathrm{K}$ under both FC and ZFC conditions.

Figure 3

$K_{\mu }^{\perp }$ vs ${\chi }^{\perp }$ at $H=3\mathrm{k}\mathrm{O}\mathrm{e}$. The solid line is a fit to Eq. (2). Left inset: Temperature dependence of the bulk susceptibility at $H=10\mathrm{k}\mathrm{O}\mathrm{e}$ applied parallel (${\chi }^{\parallel }$) and perpendicular (${\chi }^{\perp }$) to the ${\mathrm{C}\mathrm{u}\mathrm{O}}_2$ layers. Right inset: Magnetic field dependence of $B_0-{\mu }_{0}H$ at $T=5\mathrm{K}$ and 25 K. Each data point at $T=5\mathrm{K}$ represents a single FC measurement.

Figure 4

$B_0^{\mathrm{S}}(T)-B_0^{\mathrm{N}}$ vs $B_0^{\mathrm{N}}$ at $T=5\mathrm{K}$ (solids circles) and 10 K (open circles). The solid curves are described in the text. Inset: Temperature dependence of $B_0$ and ${\chi }^{\perp }$ taken under FC conditions.

Figure 5

${\lambda }_{ab}^{-2}$ vs $T$ in PCCO at $H=90\mathrm{O}\mathrm{e}$. The solid curve is a fit described in the text.