Neutron-Spin Resonance in the Optimally Electron-Doped Superconductor ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_{4-\delta }$

We use inelastic neutron scattering to probe magnetic excitations of an optimally electron-doped superconductor ${\mathrm{Nd}}_{1.85}{\mathrm{Ce}}_{0.15}{\mathrm{CuO}}_{4-\delta }$ above and below its superconducting transition temperature $T_c=25\mathrm{K}$. In addition to gradually opening a spin pseudogap at the antiferromagnetic ordering wave vector $\mathbf{Q}=(1/2,1/2,0)$, the effect of superconductivity is to form a resonance centered also at $\mathbf{Q}=(1/2,1/2,0)$ but at energies above the spin pseudogap. The intensity of the resonance develops like a superconducting order parameter, similar to those for hole-doped superconductors and electron-doped ${\mathrm{Pr}}_{0.88}{\mathrm{LaCe}}_{0.12}{\mathrm{CuO}}_4$. The resonance is therefore a general phenomenon of cuprate superconductors, and must be fundamental to the mechanism of high-$T_c$ superconductivity.

Figure 1

(a) Schematic diagrams of real and reciprocal space of the ${\mathrm{CuO}}_2$ with the transverse and longitudinal scans marked as a and b, respectively. Magnetic susceptibility measurements of $T_c$. (b) Summary of the resonance energy as a function of $T_c$ for various hole- and electron-doped superconductors from 16 with NCCO (this work) and LSCO [13] added. (c) Energy scans at $\mathbf{Q}=(-0.5,1.5,0)$ at 2 and 30 K. The three CEF levels are marked by arrows [20].

Figure 2

Transverse and radial scans through $\mathbf{Q}=(-0.5,0.5,0)$ for  (a),(b) $\hslash \omega =2.5\mathrm{meV}$ and (c),(d) 8 meV at various temperatures. Radial scans in (b),(d) are instrumental resolution limited (horizontal bars) that gives a minimum dynamic spin correlation length $\xi \approx 46\AA$ at 2.5 meV. Transverse scans around $\mathbf{Q}=(-0.5,0.5,0)$ with linear background subtracted for (e) $\hslash \omega =2.5\mathrm{meV}$, (f) 8 meV, and (g) 10 meV at temperature above and below $T_c$. (h) The transverse scan around $\mathbf{Q}=(-0.5,1.5,0)$ at $\hslash \omega =36\mathrm{meV}$ has negligible temperature dependence across $T_c$.

Figure 3

(a) The temperature dependence of the scattering at the peak [$\mathbf{Q}=(-0.5,0.5,0)$] and background [$\mathbf{Q}=(-0.34,0.66,0)$] positions below and above $T_c$. Note the intensity is plotted in log scale to display the large intensity difference between the ${\mathrm{Nd}}^{3+}$ CEF level at $\hslash \omega =12\mathrm{meV}$ and ${\mathrm{Cu}}^{2+}$ spin fluctuations centered at $\mathbf{Q}=(-0.5,0.5,0)$ for energies between 2 and 10 meV. (b) Background subtracted magnetic scattering at $\mathbf{Q}=(-0.5,0.5,0)$ below and above $T_c$. The data are cross-checked by constant-energy scans in Fig. 2. (c) The temperature difference plot showing the resonance at $E_r=9.5\pm 2\mathrm{meV}$. The large error is due to the uncertainty in obtaining ${\mathrm{Cu}}^{2+}$ magnetic signal above 10 meV.

Figure 4

Temperature dependence of the scattering at $\hslash \omega =2.5$ and 8 meV. (a) The raw data at the signal [$\mathbf{Q}=(-0.5,0.5,0)$] and background [$\mathbf{Q}=(-0.6,0.4,0)$] positions. (b) The background subtracted magnetic scattering at $\hslash \omega =2.5\mathrm{meV}$ shows no anomaly across $T_c$ but drops dramatically below 9 K. The data from the fitted $\mathbf{Q}$ scans are shown as circles. (c) Temperature dependent data for $\hslash \omega =8\mathrm{meV}$ with background at $\mathbf{Q}=(-0.4,0.6,0)$, a resonance coupled to $T_c$ like an order parameter is clearly seen in the background subtracted data in (d). The estimated temperature dependence of the ${\mathrm{Nd}}^{3+}$ CEF level at 8 meV (from 12 to 20 meV) is shown as solid line in (c) [20].