Persistence of High-Frequency Spin Fluctuations in Overdoped Superconducting ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ ($x=0.22$)

We report a detailed inelastic neutron scattering study of the collective magnetic excitations of overdoped superconducting ${\mathrm{La}}_{1.78}{\mathrm{Sr}}_{0.22}{\mathrm{CuO}}_4$ for the energy range 0–160 meV. Our measurements show that overdoping suppresses the strong response present for optimally doped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$ which is peaked near 50 meV. The remaining response is peaked at incommensurate wave vectors for all energies investigated. We observe a strong high-frequency magnetic response for $E\gtrsim 80\mathrm{meV}$ suggesting that significant antiferromagnetic exchange couplings persist well into the overdoped part of the cuprate phase diagram.

Figure 1

(a) The doping dependence of $T_c$ in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$. Open circles [15], closed circles: $\mathrm{LSCO}(x=0.16)$ [8], and $\mathrm{LSCO}(x=0.22)$ (this work). (b) Magnetization of $\mathrm{LSCO}(x=0.22)$ used in this work ($H=10\mathrm{Oe}\parallel c$, field cooled).

Figure 2

(a)–(f) Constant-$E$ slices of ${\chi }^{\prime \prime }(\mathbf{q},\omega )$ for ${\mathrm{La}}_{1.78}{\mathrm{Sr}}_{0.22}{\mathrm{CuO}}_4$ at $T=6\mathrm{K}$. Data are cut off due to finite detector coverage. (g)–(l) Fits of model [Eq. (2)] convolved with instrument resolution. (a) and (b) show the low-$E$ four-peak structure which is suppressed in (c) and (d). (e) and (f) show the reemergence of a ringlike response at high energy. (a)–(d) have the same intensity ranges, (e) and (f) are $\times 10$ and $\times 16.5$, respectively. $E_i$’s for (a)–(f) were 40, 40, 90, 120, 160, 240 meV.

Figure 3

(a)–(f) Constant-$E$ cuts through the raw data [see trajectory in Fig. 2g]. A background proportional to $|\mathbf{Q}{|}^2$ has been subtracted. The energies are the same as the slices in Fig. 2. Solid lines are fits of Eq. (2) convolved with the instrument resolution. Background points (▵) for (e), (f) measured along ($h$, 0.05). Scattering near $h=0.2$ in (c) is due to phonons.

Figure 4

(a)–(c) $E$ dependence of $\delta$, $\kappa$, and ${\chi }^{\prime \prime }(\omega )$ in $\mathrm{LSCO}(x=0.22)$. $\delta$, $\kappa$ define the dispersion, and ${\chi }^{\prime \prime }(\omega )$ the strength of the spin excitations. The inset shows how the response at 7 meV weakens on warming. Dashed line in (c) is ${\chi }^{\prime \prime }(\omega )$ in $\mathrm{LSCO}(x=0.16)$ for comparison [8]. Lines are guides to the eye. (d) $E$ dependence of out-of-plane wave vector, $l$, at ($1/2$, $1/2$) for each $E_i$. Symbols indicate $E_i$: 30 (▴), 40 (▾), 55 (◆), 90 (▸), 120 (◂), 160 (■), 240 meV (●).