Electronically competing phases and their magnetic field dependence in electron-doped nonsuperconducting and superconducting ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_{4\pm \delta }$

We present comprehensive neutron scattering studies of nonsuperconducting and superconducting electron-doped ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_{4\pm \delta }$ (PLCCO). At zero field, the transition from antiferromagnetic (AF) as-grown PLCCO to superconductivity without static antiferromagnetism can be achieved by annealing the sample in pure Ar at different temperatures, which also induces an epitaxial ${(\mathrm{Pr},\mathrm{La},\mathrm{Ce})}_2{\mathrm{O}}_3$ phase as an impurity. When the superconductivity first appears in PLCCO, a quasi-two-dimensional (2D) spin-density-wave (SDW) order is also induced, and both coexist with the residual three-dimensional (3D) AF state. A magnetic field applied along the $[\overline{1},1,0]$ direction parallel to the ${\mathrm{CuO}}_2$ plane induces a “spin-flop” transition, where the noncollinear AF spin structure of PLCCO is transformed into a collinear one. The spin-flop transition is continuous in semiconducting PLCCO, but gradually becomes sharp with increasing doping and the appearance of superconductivity. A $c$-axis aligned magnetic field that suppresses the superconductivity also enhances the quasi-2D SDW order at (0.5,0.5,0) for underdoped PLCCO. However, there is no effect on the 3D AF order in either superconducting or nonsuperconducting samples. Since the same field along the $[\overline{1},1,0]$ direction in the ${\mathrm{CuO}}_2$ plane has no (or little) effect on the superconductivity, (0.5,0.5,0) and ${(\mathrm{Pr},\mathrm{La},\mathrm{Ce})}_2{\mathrm{O}}_3$ impurity positions, we conclude that the $c$-axis field-induced effect is intrinsic to PLCCO and arises from the suppression of superconductivity.

Figure 1

Comparison of the phase diagrams between hole-doped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ (LSCO) and electron-doped ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_{4\pm \delta }$ (PLCCO). (a) Properties of the PLCCO samples investigated in this work. Since the exact oxygen concentrations in our samples are unknown, the values of $4-\delta$ in the horizontal axis are obtained using Fig. 8 of Ref. 32 by assuming that PLCCO samples with the same $T_c$’s as those of ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_{4-\delta }$ have the same oxygen content. When superconductivity is first established in PLCCO, a commensurate static SDW order also appears. The open and filled circles are data from Ref. 36. (b) Phase diagram of LSCO as a function of Sr doping from neutron scattering results of Refs. 7, 8, 9. In the spin-glass (SG) phase of LSCO, two static incommensurate SDW peaks at $(0.5+\Delta H,0.5-\Delta K)$ and $(0.5-\Delta H,0.5+\Delta K)$ (see inset) are observed for $0.02⩽x⩽0.05$. When superconductivity sets in at $x⩾0.05$, two pairs of incommensurate SDW peaks appear simultaneously at ($0.5\pm \Delta H$,0.5) and (0.5,$0.5\pm \Delta K$). The data in (b) are from Refs. 7, 8, 9.

Figure 2

(a) Schematic diagram of the noncollinear spin structure of PLCCO, (b) allowed AF Bragg peaks from the spin structure of (a), (c) reciprocal space probed in the $[H,K,0]$ scattering plane where the applied field is along the $c$ axis. Solid circles are allowed AF Bragg peak positions in the $[H,K,0]$ plane. (d) Similar experiments in the $[H,H,L]$ zone where the field is along the $[\overline{1},1,0]$ direction in the ${\mathrm{CuO}}_2$ plane. Arrows indicate the scan directions in our experiments.

Figure 3

(a) Magnetic susceptibility measurements of ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_{4\pm \delta }$ single crystals under a small (5–10 G) field in the ${\mathrm{CuO}}_2$ plane. (b) Temperature dependence of weight change and its derivative of a ${\mathrm{Pr}}_{1.18}{\mathrm{La}}_{0.7}{\mathrm{Ce}}_{0.12}{\mathrm{CuO}}_{4-\delta }$ in the annealing process.

Figure 4

Temperature dependence of integrated intensities at $(0.5,0.5,L)$ for the $T_c=16\mathrm{K}$ PLCCO. The solid lines are guides to the eye. The arrows indicate $T_c$ and $T_N$, respectively.

Figure 5

$\mathbf{Q}$ scans in the $[H,K,0]$ zone at low and high temperatures for different PLCCO samples. (a)–(d) Scans along the $[H,H,0]$ direction around (0.5,0.5,0) for $T_c=24\mathrm{K}$, 21 K, 16 K, and NSC PLCCO. (e)–(h) Similar scans along the $[H,3H,0]$ direction around (0.5,1.5,0). This figure is reproduced from Fig. 2 of Ref. 36.

Figure 6

(a) $[H,H,0]$ scans around (0.5,0.5,0) at 5.6 K and 56 K for the optimally doped $T_c=24\mathrm{K}$ PLCCO. The observed peak at (0.5,0.5,0) has nonmagnetic origin. (b) The temperature dependence of the integrated intensities at (0.5,1.5,0) for the $T_c=24\mathrm{K}$ PLCCO. There is no evidence for static SDW and∕or AF orders in the optimally doped PLCCO. (c) and (d) Two-axis mode scans along the $[H,H,0]$ direction around $(0.5,0.5,L)(0.4<L<0.6)$ at different temperatures for underdoped SC $T_c=21$ K and 16 K PLCCO, respectively. Magnetic scattering clearly decreases with increasing temperature for both compounds.

Figure 7

Magnetic structures of ${\mathrm{Cu}}^{2+}$ ions in PLCCO. (a) Noncollinear structure at zero field. (b) Collinear structure transformed by a magnetic field applied along the $[\overline{1},1,0]$ direction.

Figure 8

Magnetic field dependence of the scattering around $(0.5,0.5,L)$ at 5 K, a temperature well below the perspective $T_N$’s for various SC and NSC PLCCO samples. (a)–(c) $L$ scans around (0.5,0.5,1), (d)–(f) $L$ scans around (0.5,0.5,2) for $T_c=21\mathrm{K}$, 16 K and NSC PLCCO samples. The $T_c=21\mathrm{K}$ sample shows an abrupt spin-flop transition and the $T_c=16\mathrm{K}$ and the NSC samples display a more gradual spin-flop transition. The solid lines are Gaussian fits to the data.

Figure 9

Integrated intensities of $(0.5,0.5,L)$ as a function of a magnetic field for (a) $T_c=21\mathrm{K}$, (b) $T_c=16\mathrm{K}$, (c) NSC samples at 5 K. The inset in (b) shows that the sample with higher Néel temperature requires a higher critical field to induce the spin-flop transition.

Figure 10

The temperature dependence of the integrated magnetic Bragg intensities for $(0.5,0.5,L)$ with $L=2$,4,6 at 1.5 T and 6 T for the $T_c=16$ K PLCCO. The spin-flop transition should have occurred above 1.5 T [see Fig. 9b]. The negligible changes of the integrated intensities indicate that an in-plane magnetic field of 6 T does not affect the Cu and Pr moment. It only transforms the magnetic structure from a noncollinear to a collinear one (Fig. 7).

Figure 11

The comparison of the influence of an in-plane field on the magnetic Bragg peaks of PLCCO and NCCO. (a) and (b) Low-temperature $L$ scans across the magnetic peaks at (0.5,0.5,2) and (0.5,0.5,4) in NCCO (from Ref. 40). (c) and (d) Similar $L$ scans across (0.5,0.5,2) and (0.5,0.5,4) in PLCCO. The intensity differences between NCCO and PLCCO is due the induced moment on ${\mathrm{Nd}}^{3+}$ in NCCO. (e) Integrated intensity of (0.5,0.5,2) as a function of a field. Right after spin-flop transition, the integrated intensity shows no field dependence up to 14 T. This confirms that Pr moment is not induced by a field up to 14 T.

Figure 12

(a) and (b) Magnetic field dependent scattering around $(0.5,-0.5,0)$ and $(0.5,-1.5,0)$ of NSC PLCCO in the $[H,K,0]$ scattering plane. Radial scans across (a) $(0.5,-0.5,0)$ and (b) $(0.5,-1.5,0)$ at 5 K with zero and 6 T fields, respectively. The magnetic field is applied along the $c$ axis. While the scattering at $(0.5,-1.5,0)$ is mostly magnetic from the noncollinear AF order [Fig. 2a], the peak at $(0.5,-0.5,0)$ does not arise from ${(\mathrm{Pr},\mathrm{La},\mathrm{Ce})}_2{\mathrm{O}}_3$ but is diffusive structural scattering of PLCCO similar to those seen in the SC ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_4$ (Ref. 41). This conclusion is confirmed by (c) $[0.5,0.5,L]$ and (d) $[H,H,2.2]$ scans across the impurity positions of NSC PLCCO in the $[H,H,L]$ scattering plane.

Figure 13

Magnetic field effect on the impurity peak position (0,0,2.2) at low temperatures. (a)–(c) Scans along the $[H,H,2.2]$ direction for the $T_c=24\mathrm{K}$, 21 K, and 16 K PLCCO, respectively. The magnetic fields are applied along the $[\overline{1},1,0]$ direction, similar to previous work on SC NCCO (Refs. 41, 43).

Figure 14

(a) $[H,H,4.4]$ scan through (0,0,4.4) position for impurity peak ${(0,0,4)}_c$ at low and high temperatures. The temperature independent scattering indicates that the impurity peak has no magnetic component. (b) Radial $[H,0,0]$ scan across (0.5,0,0) of the impurity peak ${(1,1,0)}_c$ at zero and 14.5 T $c$-axis-aligned fields (Ref. 45). It shows no field-induced effect, indicating that the impurity phase cannot be polarized by a 14.5 T field.

Figure 15

The effect of a $c$-axis-aligned magnetic field on various SC PLCCO samples at low temperatures. The data below 7 T were taken at HB-1A of HFIR while higher field data were collected on E4 of HMI. The $[H,H,0]$ scans around (0.5,0.5,0) for (a) $T_c=24\mathrm{K}$, (b),(c) 21 K, and (d) 16 K PLCCO samples at specified temperatures. (e)–(h) $[H,3H,0]$ scans around (0.5,1.5,0) in the same experimental setup as in (a)–(d).

Figure 16

The field dependence of the scattering across (0.5,0.5,0) and (0.5,1.5,0) at temperatures above $T_c$ and below $T_N$. (a) and (b) for the $T_c=21\mathrm{K}$ sample. (c) and (d) for the $T_c=16\mathrm{K}$ sample. No field-induced effects are observed.

Figure 17

Temperature dependence of the scattering at the (0.5,0.5,0) and (0.5,1.5,0) positions for (a) and (b) $T_c=21\mathrm{K}$ and (c) and (d) $T_c=16\mathrm{K}$ samples at zero and finite $c$-axis-aligned magnetic fields. Clear low-temperature field-induced effects are seen at (0.5,0.5,0) but not at (0.5,1.5,0) for both the $T_c=21\mathrm{K}$ and 16 K PLCCO samples.

Figure 18

(a) Integrated intensity of (0.5,0.5,0) as a function of increasing field. Open circles are data from ORNL at 5 K and filled circles are HMI data at 2 K. (b) Integrated intensity of (0.5,1.5,0) is independent of applied field up to 14.5 T.

Figure 19

The influence of an in-plane magnetic field on the SDW order in the $T_c=21\mathrm{K}$ SC PLCCO. (a) $[H,H,0]$ scan around (0.5,0.5,0) for zero and 6 T at 5 K. (b) $[0.5,0.5,L]$ scan around (0.5,0.5,0). A 6 T in-plane magnetic field has no observable effect on the SDW order at 5 K. The $c$-axis coherence length of (0.5,0.5,0) is about 200 Å.

Figure 20

Anisotropic field-induced effect on the SDW order of the $T_c=21\mathrm{K}$ PLCCO by a $c$-axis-aligned magnetic field and an $ab$-plane magnetic field. (a) $[H,H,0]$ scan across (0.5,0.5,0) with zero and 14.5 T field at 2 K in the $[H,K,0]$ zone. (b) $[H,H,0]$ scan across (0.5,0.5,0) with a $\mathbf{B}\Vert ab$-plane magnetic field at zero and 14 T. (c) $[0.5,0.5,L]$ scan across (0.5,0.5,0) with zero and 14 T at 5 K.

Figure 21

Possible ${\mathrm{Cu}}^{2+}$ magnetic structures responsible for the SDW order. (a) and (b) Collinear spin model I, domains I and II. (c) and (d) Collinear spin model II, domains I and II. In collinear spin structures, the moments are in the $ab$ plane. The closed and open circles represent the $z=0$ and $z=c∕2{\mathrm{CuO}}_2$ planes, respectively. The ${\mathrm{Pr}}^{3+}$ spins are not shown, since the induced moment of ${\mathrm{Pr}}^{3+}$ is negligible in the SC PLCCO samples. Here we assumed weak (2 or 3 lattices) spin correlations along the $c$ axis. Experimentally, we probably cannot distinguish such scattering from that of random 2D sheets in the 3D AF matrix.