Thermal Hall conductivity of electron-doped cuprates: Electrons and phonons

It has recently become clear that phonons generate a sizable thermal Hall effect in cuprates, whether they are undoped, electron-doped or hole-doped (inside the pseudogap phase). At higher doping, where cuprates are reasonably good metals, mobile electrons also generate a thermal Hall effect, the thermal equivalent of the standard electrical Hall effect. Here we show that in the cleanest crystals of the electron-doped cuprate Nd$_{2-x}$Ce$_{x}$CuO$_{4}$, at high doping, the phonon and electron contributions to the thermal Hall conductivity $\kappa_{\rm {xy}}$ are of comparable magnitude, but of opposite sign. In samples of lower quality, phonons dominate $\kappa_{\rm {xy}}$, resulting in a negative $\kappa_{\rm {xy}}$ at all temperatures. The fact that the negative phononic $\kappa_{\rm {xy}}$ in the metallic state is similar in magnitude and temperature dependence to that found in the insulating state at lower doping rules out any mechanism based on skew scattering of phonons off charged impurities, since a local charge should be screened in the metallic regime. The phononic $\kappa_{\rm {xy}}$ is found to persist over the entire doping range where antiferromagnetic correlations are known to be significant, suggesting that such correlations may play a role in generating the phonon thermal Hall effect in electron-doped cuprates. If the same mechanism is also at play in hole-doped cuprates, the presence of a phononic $\kappa_{\rm {xy}}$ below (and only below) the critical doping $p^{\star}$ would be evidence that spin correlations are a property of the pseudogap phase.