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Spin-orbit entangled pseudospins hold promise for a wide array of exotic magnetism ranging from a Heisenberg antiferromagnet to a Kitaev spin liquid depending on the lattice and bonding geometry, but many of the host materials suffer from lattice distortions and deviate from idealized models in part due to inherent strong pseudospin-lattice coupling. Here, we report on the synthesis of a magnetic superlattice comprising the single ($n$=1) and the double ($n$=2) layer members of the Ruddlesden-Popper series iridates Sr$_{n+1}$Ir$_{n}$O$_{3n+1}$ alternating along the $c$-axis, and provide a comprehensive study of its lattice and magnetic structures using scanning transmission electron microscopy, resonant elastic and inelastic x-ray scattering, third harmonic generation measurements and Raman spectroscopy. The superlattice is free of the structural distortions reported for the parent phases and has a higher point group symmetry, while preserving the magnetic orders and pseudospin dynamics inherited from the parent phases, featuring two magnetic transitions with two symmetry-distinct orders. We infer weaker pseudospin-lattice coupling from the analysis of Raman spectra and attribute it to frustrated magnetic-elastic couplings. Thus, the superlattice expresses a near ideal network of effective spin-one-half moments on a square lattice.

In the context of correlated insulators, where electron-electron interactions (U) drive the localization of charge carriers, the metal-insulator transition (MIT) is described as either bandwidth (BC) or filling (FC) controlled. Motivated by the challenge of the insulating phase in Sr$_2$IrO$_4$, a new class of correlated insulators has been proposed, in which spin-orbit coupling (SOC) is believed to renormalize the bandwidth of the half-filled $j_{\mathrm{eff}} = 1/2$ doublet, allowing a modest U to induce a charge-localized phase. Although this framework has been tacitly assumed, a thorough characterization of the ground state has been elusive. Furthermore, direct evidence for the role of SOC in stabilizing the insulating state has not been established, since previous attempts at revealing the role of SOC have been hindered by concurrently occurring changes to the filling. We overcome this challenge by employing multiple substituents that introduce well defined changes to the signatures of SOC and carrier concentration in the electronic structure, as well as a new methodology that allows us to monitor SOC directly. Specifically, we study Sr$_2$Ir$_{1-x}$T$_x$O$_4$ (T = Ru, Rh) by angle-resolved photoemission spectroscopy (ARPES), combined with ab-initio and supercell tight-binding calculations. This allows us to distinguish relativistic and filling effects, thereby establishing conclusively the central role of SOC in stabilizing the insulating state of Sr$_2$IrO$_4$. Most importantly, we estimate the critical value for spin-orbit coupling in this system to be $\lambda_c = 0.42 \pm 0.01$ eV, and provide the first demonstration of a spin-orbit-controlled MIT.

Over the last few years, Sr$_2$IrO$_4$, a single-layer member of the Ruddlesden-Popper series iridates, has received much attention as a close analog of cuprate high-temperature superconductors. Although there is not yet firm evidence for superconductivity, a remarkable range of cuprate phenomenology has been reproduced in electron- and hole-doped iridates including pseudogaps, Fermi arcs, and $d$-wave gaps. Further, a number of symmetry breaking orders reminiscent of those decorating the cuprate phase diagram have been reported using various experimental probes. We discuss how the electronic structures of Sr$_2$IrO$_4$ through strong spin-orbit coupling leads to the low-energy physics that had long been unique to cuprates, what the similarities and differences between cuprates and iridates are, and how these advance the field of high-temperature superconductivity by isolating essential ingredients of superconductivity from a rich array of phenomena that surround it. Finally, we comment on the prospect of finding a new high-temperature superconductor based on the iridate series., Comment: Annu. Rev. Condens. Matter Phys. (in press)