Switching the d-wave gap in layered perovskite iridates via spin reorientation

We demonstrate switching of the $d$-wave charge gap in electron-doped Sr$_{\mathrm{3}}$Ir$_{\mathrm{2}}$O$_{\mathrm{7}}$ through changing the spin easy axis. The pristine, undoped Sr$_{\mathrm{3}}$Ir$_{\mathrm{2}}$O$_{\mathrm{7\thinspace }}$has $c$-axis collinear antiferromagnetic structure with strong Ising anisotripy, which gaps out magnons with an unprecedentedly large energy scale of 90 meV. However, a metastable phase with \textit{ab} easy-plane anisotropy is found in some surfaces of Sr$_{\mathrm{3}}$Ir$_{\mathrm{2}}$O$_{\mathrm{7}}$, for which low-energy magnons are expected. Doping electrons to the latter leads to opening of a $d$-wave charge gap below \textasciitilde 30 K, which is not found in the former. Our results indicate the magnetic origin of the $d$-wave gap in electron-doped layered perovskite iridates, and suggest a mechanism to control the charge gap via the spin degrees of freedom.