Magnetic-Field-Induced Spin Excitations and Renormalized Spin Gap of the Underdoped ${\mathrm{La}}_{1.895}{\mathrm{Sr}}_{0.105}{\mathrm{CuO}}_4$ Superconductor

High-resolution neutron inelastic scattering experiments in applied magnetic fields have been performed on ${\mathrm{La}}_{1.895}{\mathrm{Sr}}_{0.105}{\mathrm{CuO}}_4$ (LSCO). In zero field, the temperature dependence of the low-energy peak intensity at the incommensurate momentum transfer ${\mathbf{Q}}_{\mathrm{IC}}=(0.5,0.5\pm \delta ,0),(0.5\pm \delta ,0.5,0)$ exhibits an anomaly at the superconducting $T_c$ which broadens and shifts to lower temperature upon the application of a magnetic field along the $c$ axis. A field-induced enhancement of the spectral weight is observed, but only at finite energy transfers and in an intermediate temperature range. These observations establish the opening of a strongly downward renormalized spin gap in the underdoped regime of LSCO. This behavior contrasts with the observed doping dependence of most electronic energy features.

Figure 1

(a) Phase diagram of underdoped LSCO ($x=0.105$) as a function of a magnetic field $H$ and temperature $T$ [20]. ● are the measured values for the melting line of the vortex lattice [20]. The straight line is the position of $T_c$ as a function of $H$. The dashed arrows indicate the $T$ and $H$ scans that are described in this Letter. (b) Two $T$ scans at ${\mathbf{Q}}_{\mathrm{IC}}$ and $\hslash \omega =1\mathrm{meV}$ transfer. ▵ (■) denote the measured intensity at $H=10\mathrm{T}$ ($H=0\mathrm{T}$); solid lines are guides to the eye.

Figure 2

Magnetic field dependence of the response at ${\mathbf{Q}}_{\mathrm{IC}}$ for LSCO ($x=0.105$). (a) Elastic response with $T=2\mathrm{K}$. The solid line is a theoretical prediction [15]. (b) Inelastic response with $T=22.3\mathrm{K}$; solid lines are guides to the eye.

Figure 3

Energy and $\mathbf{Q}$ dependence of magnetic scattering from LSCO ($x=0.105$). Energy scans are taken at ${\mathbf{Q}}_{\mathrm{IC}}$: (a) comparison of the response in the SC phase with that of the normal state in zero field. (c) Effect of a 10 T field at $T=22.3\mathrm{K}$. $Q$ scans through ${\mathbf{Q}}_{\mathrm{IC}}$: (b) comparison of the response in the SC phase with that of the normal state using $\hslash \omega =0.5\mathrm{meV}$. (d) The effect of a 10 T field at 22.3 K, $\hslash \omega =0.3\mathrm{meV}$, $E_f=3.5\mathrm{meV}$. In this configuration the resolution (HWHM) was 0.03 meV. The data have been background subtracted and lines are guide to the eye.

Figure 4

(a) Normalized ${\Delta }_{\mathrm{SG}}$ vs normalized $T_c$ for LSCO (open symbols) and YBCO (● [10] and ■ [11] ). ○ are taken from previously published data, $x=0.14$, $x=0.16$, and $x=0.17$ while □ are from this work ($x=0.105$) and Ref. 23 ($x=0.14$). (b) Intensity at ${\mathbf{Q}}_{\mathrm{IC}}$, at the energy transfer $\hslash \omega =0.5{\Delta }_0$, and at $H=0\mathrm{T}$ vs $T$ calculated within a phenomenological Fermi-liquid (PFL) approach. The solid (dashed) line uses the inverse lifetime $\Gamma =0.2{\Delta }_0$ ($\Gamma =0.8{\Delta }_0$).