Link between magnetism and resistivity upturn in cuprates: a thermal conductivity study of La${}_{2-x}$Sr${}_x$CuO${}_4$

A key unexplained feature of cuprate superconductors is the upturn in their normal state electrical resistivity $\rho (T)$ seen at low temperature inside the pseudogap phase. We examined this issue via measurements of the thermal conductivity $\kappa (T)$ down to 50 mK and in fields up to 17 T on the cuprate La${}_{2-x}$Sr${}_x$CuO${}_4$ at dopings $p=0.13$, 0.136, 0.143 and 0.18. At $p$ = 0.136, 0.143, and 0.18, we observe an initial increase of the electronic thermal conductivity ${\kappa }_0\mathrm{/}T$ as a function of field, as expected in a $d$-wave superconductor. For $p$ = 0.136 and 0.143, further increasing the field then leads to a decrease of ${\kappa }_0\mathrm{/}T$, which correlates with the onset of spin density-wave order as observed in neutron scattering experiments on the same samples. This decrease of ${\kappa }_0\mathrm{/}T$ with field is imposed by the Wiedemann-Franz law and the high value of the resistivity in the high-field normal state of these samples. Our study therefore provides a direct link between magnetism and the resistivity upturn in the pseudogap phase of cuprates. We discuss this scenario in the broader context of other cuprates.