Competing orders in LSCO probed by heat transport

We elucidate the nature of the thermal metal-to-insulator transition in La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) [1] through measurements of the thermal conductivity $\kappa$ performed very close to the transition, down to temperatures as low as 50 mK and in magnetic fields $H$ up to 17 T. For a single crystal with x = 0.15, a monotonic increase in the residual linear term $\kappa_0$/$T$ is observed up to 17 T, as expected for a d-wave superconductor. For a crystal with x = 0.144, however, we observe an initial increase in $\kappa_0$/$T$ at low field, followed by a decrease when $H$ exceeds a critical field $H^*$. This result is consistent with recent neutron scattering measurements on a similar sample [2], which show that static spin-density-wave (SDW) order is not present in zero field, but sets in at a critical magnetic field $H^*$, and then co-exists/competes with superconductivity (SC) for $H > H^*$. Taken together, these two measurements reveal that the SC phase gives way to a phase which is both magnetic and insulating, whether by increasing magnetic field or by decreasing doping. Using low-energy quasiparticle transport, we map out the $T$ = 0 field-doping ($H-x$) phase diagram of LSCO. [1] D.G. Hawthorn et al., Phys. Rev. Lett. 90, 197004 (2003); X.F. Sun et al., Phys. Rev. Lett. 90, 117004 (2003). [2] B. Khaykovich et al., Phys. Rev. B 71, 220508(R) (2005).