Magnetic-Field-Induced Soft-Mode Quantum Phase Transition in the High-Temperature Superconductor ${\mathrm{La}}_{1.855}{\mathrm{Sr}}_{0.145}{\mathrm{CuO}}_4$: An Inelastic Neutron-Scattering Study

Inelastic neutron-scattering experiments on the high-temperature superconductor ${\mathrm{La}}_{1.855}{\mathrm{Sr}}_{0.145}{\mathrm{CuO}}_4$ reveal a magnetic excitation gap $\Delta$ that decreases continuously upon application of a magnetic field perpendicular to the ${\mathrm{CuO}}_2$ planes. The gap vanishes at the critical field required to induce long-range incommensurate antiferromagnetic order, providing compelling evidence for a field-induced soft-mode driven quantum phase transition.

Figure 1

(a)–(e) Elastic and inelastic $\mathbf{Q}$ scans through ${\mathbf{Q}}_{\mathrm{IC}}=(1/2\pm \delta ,1/2,0),(1/2,1/2\pm \delta ,0)$ as indicated in the inset of (b) [23]. We use $\mathbf{Q}={\mathbf{Q}}_{\mathrm{IC}}+{\mathbf{Q}}_{\mathrm{scan}}$. (a) Elastic $\mathbf{Q}$ scans at external magnetic fields 0 and 13 T. (b)–(d) Magnetic field dependence of $\mathbf{Q}$ scans recorded at fixed energy transfers $\hslash \omega =0.5$, 1, and 2 meV, respectively. (e) Energy dependence of $\mathbf{Q}$ scans obtained with $H=2.5\mathrm{T}$. For clarity, the scans in (a)–(e) have been offset vertically with respect to each other. The dashed lines are guides to the eye, and the solid lines are Gaussian fits with a linear background. At 13 T, we find elastic and inelastic correlation lengths $\xi (0\mathrm{meV})\sim 150\AA$ and $\xi (2\mathrm{meV})\sim 48\AA$ obtained from the half width at half maximum $1/\kappa$ of the fitted peak.

Figure 2

Inelastic neutron-scattering response at ${\mathbf{Q}}_{\mathrm{IC}}$ as a function of energy transfer $\hslash \omega$ for $H=0\mathrm{T}$ (blue line), $H=2.5\mathrm{T}$ (black line), and $H=7\mathrm{T}$ (red line). The square points are deduced from Gaussian fits to $\mathbf{Q}$ scans as shown in Fig. 1, while circular points are from three-point (background-${\mathbf{Q}}_{\mathrm{IC}}$-background) scans. All lines are guides to the eye.

Figure 3

(a),(b) Magnetic field dependence of the inelastic neutron response at ${\mathbf{Q}}_{\mathrm{IC}}$ with $\hslash \omega =2$ and 1 meV, respectively. (c) Elastic neutron response at ${\mathbf{Q}}_{\mathrm{IC}}$ as a function magnetic field. In (a)–(c) the square points are deduced from Gaussian fits to $\mathbf{Q}$ scans as shown in Fig. 1, while circular points are from three-point (background-${\mathbf{Q}}_{\mathrm{IC}}$-background) scans. All lines are guides to the eye. (d) Field dependence of the excitation gap $\Delta$.