No abstract

Sample characterizationIn this section we show resistivity data measured on the samples we studied. The sample growth technique is described in the Methods section of the main text. Fig. S1 shows the resistivity curves for different dopant concentrations. Note that the rough La concentrations reported in the graph are determined by energy dispersive x--ray spectroscopy (EDX), and this method averages over variations of the doping concentration. We estimate these variations to occur on a length--scale of hundreds of micrometers, and the magnitude to be of the order of a few percentage points. These variations in doping concentrations have to be considered when interpreting resistivity ( Figure S1) and magnetization data of the iridate samples. SUPPLEMENTARY INFORMATION Set--up effect in topographs

The collective magnetic excitations in the spin-orbit Mott insulator (Sr 1−x La x ) 2 IrO 4 (x = 0, 0.01, 0.04, 0.1) were investigated by means of resonant inelastic x-ray scattering. We report significant magnon energy gaps at both the crystallographic and antiferromagnetic zone centers at all doping levels, along with a remarkably pronounced momentum-dependent lifetime broadening. The spin-wave gap is accounted for by a significant anisotropy in the interactions between J eff = 1/2 isospins, thus marking the departure of Sr 2 IrO 4 from the essentially isotropic Heisenberg model appropriate for the superconducting cuprates.

We study the structural evolution of Sr 3 Ir 2 O 7 as a function of pressure using x-ray diffraction. At a pressure of 54 GPa at room temperature, we observe a first-order structural phase transition, associated with a change from tetragonal to monoclinic symmetry and accompanied by a 4% volume collapse. Rietveld refinement of the high-pressure phase reveals a novel modification of the Ruddlesden-Popper structure, which adopts an altered stacking sequence of the perovskite bilayers. As the positions of the oxygen atoms could not be reliably refined from the data, we use density functional theory (local-density approximation+U +spin orbit) to optimize the crystal structure and to elucidate the electronic and magnetic properties of Sr 3 Ir 2 O 7 at high pressure. In the low-pressure tetragonal phase, we find that the in-plane rotation of the IrO 6 octahedra increases with pressure. The calculations further indicate that a bandwidth-driven insulator-metal transition occurs at ∼20 GPa, along with a quenching of the magnetic moment. In the high-pressure monoclinic phase, structural optimization resulted in complex tilting and rotation of the oxygen octahedra and strongly overlapping t 2g and e g bands. The t 2g bandwidth renders both the spin-orbit coupling and electronic correlations ineffectual in opening an electronic gap, resulting in a robust metallic state for the high-pressure phase of Sr 3 Ir 2 O 7 .

The magnetic critical scattering in Sr 2 IrO 4 has been characterized using x-ray resonant magnetic scattering (XRMS) both below and above the three-dimensional antiferromagnetic ordering temperature T N . The order parameter critical exponent below T N is found to be β = 0.195(4), in the range of the two-dimensional (2D) XY h 4 universality class. Over an extended temperature range above T N , the amplitude and correlation length of the intrinsic critical fluctuations are well described by the 2D Heisenberg model with XY anisotropy. This contrasts with an earlier study of the critical scattering over a more limited range of temperature, which found agreement with the theory of the isotropic 2D Heisenberg quantum antiferromagnet, developed to describe the critical fluctuations of the conventional Mott insulator La 2 CuO 4 and related systems. Our study therefore establishes the importance of XY anisotropy in the low-energy effective Hamiltonian of Sr 2 IrO 4 , the prototypical spin-orbit Mott insulator. The Ruddlesden-Popper series Sr n+1 Ir n O 3n+1 of perovskite iridates has emerged as a fruitful arena in which to explore the effects of electron correlations in the strong spin-orbit coupling limit. The first two members of this series, single-layer Sr 2 IrO 4 (n = 1) and bilayer Sr 3 Ir 2 O 7 (n = 2), are believed to exemplify a new class of spin-orbit Mott insulators. Of central importance to our understanding of these materials is the emergence of a j eff = 1/2 ground state by the combined action of a strong cubic crystal field and spin-orbit interactions on the 5d 5 electrons of the Ir 4+ ions [1]. The weakened electron correlations typical of the 5d elements then split the j eff = 1/2 band, opening a gap, leading to a Mott-like state.Sr 2 IrO 4 in particular has attracted considerable attention because of its striking similarities to La 2 CuO 4 in terms of both its structural and magnetic properties. The magnetic structures and excitations of Sr 2 IrO 4 have been investigated in a number of x-ray resonant magnetic scattering (XRMS) studies [1][2][3][4][5][6][7] which have allowed an effective low-energy Hamiltonian to be proposed and refined. Sr 2 IrO 4 forms an antiferromagnetic structure below T N ∼ 225 K in which the moments are confined to the a − b planes and canted to follow rigidly the correlated rotation of the oxygen octahedra of the I 4 1 /acd crystal structure [8]. A resonant inelastic x-ray scattering (RIXS) experiment [2] has revealed a dispersion relation somewhat reminiscent of that displayed by La 2 CuO 4 , albeit with a lower-energy scale and much stronger further neighbor couplings, which can be derived from a smaller ratio of on-site repulsion over hopping amplitude [9]. This result * j.vale@ucl.ac.uk suggests that the low-energy isospin dynamics of the j eff = 1/2 states in Sr 2 IrO 4 may, to leading order, be mapped onto an effective isotropic two-dimensional Heisenberg Hamiltonian, in agreement with predictions by Jackeli and Khaliullin [10].Critical scattering studies provide informa...