Electronic inhomogeneity and competing phases in electron-doped superconducting ${\mathrm{Pr}}_{0.88}\mathrm{La}{\mathrm{Ce}}_{0.12}\mathrm{Cu}{\mathrm{O}}_{4-\delta }$

We use neutron scattering to demonstrate that electron-doped superconducting ${\mathrm{Pr}}_{0.88}\mathrm{La}{\mathrm{Ce}}_{0.12}\mathrm{Cu}{\mathrm{O}}_{4-\delta }$ in the underdoped regime is electronically phase separated in the ground state, showing the coexistence of a superconducting phase with a three-dimensional antiferromagnetically ordered phase and a quasi-two-dimensional spin-density wave modulation. The Néel temperature of both antiferromagnetic phases decreases linearly with increasing superconducting transition temperature $\left(T_c\right)$ and vanishes when optimal superconductivity is achieved. These results indicate that the electron-doped copper oxides are close to a quantum critical point, where the delicate energetic balance between different competing states leads to microscopic heterogeneity.

Figure 1

Spin structure models, magnetic susceptibilities, and summary of results in the neutron experiments. For magnetic susceptibility, we used a $7\text{−}\mathrm{T}$ SQUID magnetometer. Our neutron-scattering experiments were performed on HB-1, HB-1A, and HB-3 triple-axis spectrometers at the High-Flux Isotope Reactor (HFIR), Oak Ridge National Laboratory. Typical collimations were, proceeding from the reactor to the detector, ${48}^{\prime }\text{−}{40}^{\prime }\text{−}{40}^{\prime }\text{−}{120}^{\prime }$ (full width at half maximum), and the final neutron energy was fixed at $E_f=14.78\mathrm{meV}$ with $\sim 1\mathrm{meV}$ energy resolution. The monochromator, analyzer; and filters were all pyrolytic graphite. (a) The noncollinear type-I/III spin structure of the 3D AF order in PLCCO (Refs. 23, 24). (b) Expected Bragg peaks from the AF structure of (a). (c) $T$ dependence of the magnetic susceptibility for the four crystals investigated. The $T_c=24$- and $21\text{−}\mathrm{K}$ samples were obtained by annealing as-grown single crystals in pure Ar at 970 and $940°\mathrm{C}$ for $24\mathrm{h}$, respectively. To obtain the $T_c=16\text{−}\mathrm{K}$ crystal, the as-grown sample was annealed in pure Ar at $915°\mathrm{C}$ for $1\text{week}$. (d) Simplified model for AF order in the $\mathrm{Cu}{\mathrm{O}}_2$ plane, but weakly correlated along the $c$ axis. For clarity we plot the moment direction along the $c$ axis, whereas the actual spin direction is in the $a\text{−}b$ plane. (e) Expected scattering in reciprocal space from (d). (f) The relationship between $T_c$ and $T_N$ for samples investigated.

Figure 2

Wave-vector scans in the $[H,K,0]$ zone around (0.5,0.5,0) and (0.5,1.5,0) at different temperatures for the four PLCCO samples. The in-plane and out-of-plane (vertical) resolutions of the spectrometers at (0.5,0.5,0) are $\sim 0.025$ and $\sim 0.1–0.2{\mathrm{\AA }}^{-1}$, respectively. (a-d) Scans along the $[H,H,0]$ direction around (0.5,0.5,0) at different temperatures. (e-h) Similar scans around (0.5,1.5,0). Solid lines are Gaussian fits to the peaks on sloping backgrounds. The peaks are resolution limited and give a minimum coherence length of $\sim 200\mathrm{\AA }$.

Figure 3

(a,b) Wave-vector scans through (0.5,0.5,1) and (0.5,0.5,3) for $T_c=24\mathrm{K}$ PLCCO at $4.2\mathrm{K}$. $T$ dependence of the scattering at (0.5,0.5,0) and (0.5,1.5,0) in the $[H,K,0]$ zone for (c,d) $T_c=21\mathrm{K}$, (e,f) $T_c=16\mathrm{K}$, and (g) NSC PLCCO samples used to extract their $T_N$’s. The solid lines in (d,f) and (g) are power-law fits describing the contribution of Cu spins (Ref. 23). The ordered Cu moments $\left(M_{cu}\right)$ in (d,f) are estimated by normalizing the magnetic intensity to the weak (1,1,0) nuclear Bragg peaks without considering absorption or extinction effects. At $97\mathrm{K}$, $M_{cu}=0.12{\mu }_B$ in (g). No measurable Pr moment was induced in (d,f) while an induced Pr moment is clearly evident below $95\mathrm{K}$ in (g) (see Ref. 24).

Figure 4

Measurements in the $[H,H,L]$ zone on the $T_c=16\text{−}\mathrm{K}$ crystal. Scans along the $L$ direction around (a) (0.5,0.5,0) and (b) (0.5,0.5,1) at different temperatures. The magnetic peak in (b) is resolution limited and gives a $c$ axis $\left({\xi }_c\right)$ AF coherence length of $790\mathrm{\AA }$. (c) Scans along the $[0.5,0.5,L]$ direction at $6\mathrm{K}$ (closed circles) and $60\mathrm{K}$ (open circles). The peaks at $L\sim 0.2$, 0.8 are nonmagnetic. The magenta areas in (c) and (d) mark the $L$ region probed in the two-axis integration mode. (d) The experimental geometry in the two-axis mode in the $[H,H,L]$ zone (Ref. 26). (e) scans along the $[H,H]$ direction around (0.5,0.5) with a range of $L$ at different temperatures.