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Spin nematic (SN) is a magnetic analog of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid. Particularly intriguing is a valence-bond SN, in which spins are quantum entangled to form a multi-polar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here, we establish a SN phase in the square-lattice iridate Sr$_2$IrO$_4$, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet (AF) in the strong spin-orbit coupling limit. Upon cooling, the transition into the SN phase at T$_C$ $\approx$ 263 K is marked by a divergence in the static spin quadrupole susceptibility extracted from our Raman spectra, and concomitant emergence of a collective mode associated with the spontaneous breaking of rotational symmetries. The quadrupolar order persists in the antiferromagnetic (AF) phase below T$_N$ $\approx$ 230 K, and becomes directly observable through its interference with the AF order in resonant x-ray diffraction, which allows us to uniquely determine its spatial structure. Further, we find using resonant inelastic x-ray scattering a complete breakdown of coherent magnon excitations at short-wavelength scales, suggesting a resonating-valence-bond-like quantum entanglement in the AF state. Taken together, our results reveal a quantum order underlying the N\'eel AF that is widely believed to be intimately connected to the mechanism of high temperature superconductivity (HTSC)., Comment: Published in https://www.nature.com/articles/s41586-023-06829-4

Quantum materials display rich and myriad types of magnetic, electronic, and structural ordering, often with these ordering modes either competing with one another or 'intertwining', that is, reinforcing one another. Low dimensional quantum materials, influenced strongly by competing interactions and/or geometric frustration, are particularly susceptible to such ordering phenomena and thus offer fertile ground for understanding the consequent emergent collective quantum phenomena. Such is the case of the quasi-2D materials R4Ni3O10(R=La, Pr), in which intertwined charge-and spin-density waves (CDW and SDW) on the Ni sublattice have been identified and characterized. Not unexpectedly, these density waves are largely 2D as a result of weak coupling between planes, compounded with magnetic frustration. In the case of R=Pr, however, we show here that exchange coupling between the transition metal and rare earth sublattices upon cooling overcomes both obstacles, leading to a dimensional crossover into a fully 3D ordered and coupled SDW state on both sublattices, as an induced moment on notionally nonmagnetic Pr3+ opens exchange pathways in the third dimension. In the process, the structure of the SDW on the Ni sublattice is irreversibly altered, an effect that survives reheating of the material until the underlying CDW melts. This 'bootstrapping' mechanism linking incommensurate SDWs on the two sublattices illustrates a new member of the multitude of quantum states that low-dimensional magnets can express, driven by coupled orders and modulated by frustrated exchange pathways., Comment: 48 pages including supplementary, 6 figures, 19 supplementary figures

We use europium doped single crystalline NaYF$_4$ nanorods for probing the electric and magnetic contributions to the local density of optical states (LDOS). Reciprocically, we determine intrinsic properties of the emitters (oscillator strength, quantum yield) by comparing their measured and simulated optical responses in front of a mirror. We first experimentally determine the specifications of the nanoprobe (orientation and oscillator strength of the electric and magnetic dipoles moments) and show significant orientation sensitivity of the branching ratios associated with electric and magnetic transitions. In a second part, we measure the modification of the LDOS in front of a gold mirror in a Drexhage's experiment. We discuss the role of the electric and magnetic LDOS on the basis of numerical simulations, taking into account the orientation of the dipolar emitters. We demonstrate that they behave like degenerated dipoles sensitive to polarized partial LDOS.

Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic at the same time but for different crystallographic axes. We show that inducing competition of anisotropic interactions of orthogonal irreducible representations represents a general route to obtain new exotic magnetic states. We demonstrate it here by observing the emergence of a continuously tunable 12-layer spatial spin modulation when distorting the square lattice planes in the quasi-2D antiferromagnetic Sr2IrO4 under in situ shear strain. This translation-symmetry-breaking phase is a result of an unusual strain activated anisotropic interaction which is at the 4th order and competing with the inherent quadratic anisotropic interaction. Such a mechanism of competing anisotropy is distinct from that among the ferromagnetic, antiferromagnetic, and/or the Dzyaloshinskii-Moriya interactions, and it could be widely applicable and highly controllable in low dimensional magnets.

$RE$NiO$_3$ is a negative charge transfer energy system and exhibits a temperature-driven metal-insulator transition (MIT), which is also accompanied by a bond disproportionation (BD) transition. In order to explore how hole doping affects the BD transition, we have investigated the electronic structure of single-crystalline thin films of Nd$_{1-x}$Ca$_x$NiO$_3$ by synchrotron based experiments and {\it ab-initio} calculations. For a small value of $x$, we find that the doped holes are localized on one or more Ni sites around the dopant Ca$^{2+}$ ions, while the BD state for the rest of the lattice remains intact. The effective charge transfer energy ($\Delta$) increases with Ca concentration and the formation of BD phase is not favored above a critical $x$, suppressing the insulating phase. Our present study firmly demonstrates that the appearance of BD mode is essential for the MIT and settles a long-standing debate about the role of structural distortions for the MIT of the $RE$NiO$_3$ series., Comment: 4 Figures

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.

Bulk single-crystal relaxor-ferroelectrics, like Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), are widely known for their large piezoelectricity. This is attributed to polarization rotation which is facilitated by the presence of various crystal symmetries for compositions near a morphotropic phase boundary (MPB). Relaxor-ferroelectric thin films, which are necessary for low-voltage applications, suffer a reduction in their piezoelectric response due to clamping by the passive substrate. To understand the microscopic behavior of this adverse phenomenon, we employ AC electric field driven in-operando synchrotron x-ray diffraction (XRD) on patterned device structures to investigate the piezoelectric domain behavior under an electric field for both a clamped (001) PMN-PT thin film on Si and a (001) PMN-PT membrane released from its substrate. In the clamped film, the substrate inhibits the field induced rhombohedral (R) to tetragonal (T) phase transition resulting in a reversible R to Monoclinic (M) transition with a reduced longitudinal piezoelectric coefficient d33 < 100 pm/V. Releasing the film from the substrate results in recovery of the R to T transition and results in a d33 > 1000 pm/V. Using diffraction with spatial mapping, we find that lateral constraints imposed by the boundary between active and inactive material also inhibits the R to T transition. Phase-field calculations on both clamped and released PMN-PT thin films simulate our experimental findings. Resolving the suppression of thin film piezoelectric response is critical to their application in piezo-driven technologies.

Rare-earth doped nanocrystals possess optical transitions with significant either electric or magnetic dipole characters. They are of strong interest for understanding and engineering light-matter interactions at the nanoscale with numerous applications in nanophotonics. Here, we study the $^5$D$_0\rightarrow ^7$F$_1$ transition dipole vector in individual NaYF$_4$:Eu$^{3+}$ nanorod crystals by Fourier and confocal microscopies. {Single crystalline host matrix leads to narrow emission lines at room temperature that permit to separate Stark sublevels resulting from the crystal field splitting}. We observe a fully magnetic transition and {low variability} of the transition dipole orientation over several single nanorods. We estimate the proportion of the dipole transitions for the Stark sublevels. We also determine an effective altitude of the rod with respect to the substrate. The narrow emission lines characteristic of NaYF$_4$:Eu$^{3+}$ ensure well-defined electric or magnetic transitions, and are thus instrumental for probing locally their electromagnetic environment by standard confocal microscopy.

We report a La2CuO4-like interlayer antiferromagnetic order in Sr2IrO4 films with large orthorhombic distortion (> 1.5%). The biaxial lattice strain in epitaxial heterostructures of Sr2IrO4/Ca3Ru2O7 lowers the crystal symmetry of Sr2IrO4 from tetragonal (C4) to orthorhombic (C2), guiding the Ir 5d Jeff = 1/2 pseudospin moment parallel to the elongated b-axis via magnetic anisotropy. From resonant X-ray scattering experiments, we observed an antiferromagnetic order in the orthorhombic Sr2IrO4 film whose interlayer stacking pattern is inverted from that of the tetragonal Sr2IrO4 crystal. This interlayer stacking is similar to that of the orthorhombic La2CuO4, implying that the asymmetric interlayer exchange interaction along a and b-directions exceeds the anisotropic interlayer pseudo-dipolar interaction. Our result suggests that strain-induced distortion can provide a delicate knob for tuning the long-range magnetic order in quasi-two-dimensional systems by evoking the competition between the interlayer exchange coupling and the pseudo-dipolar interaction., Comment: 5 pages, 4 figures

The quasi-static strain (QSS) is the product generated by the lattice thermal expansion after ultrafast photo-excitation and the effects of thermal and QSS are inextricable. Nevertheless, the two phenomena with the same relaxation timescale should be treated separately because of their different fundamental actions to the ultrafast spin dynamics. By employing ultrafast Sagnac interferometry and magneto-optical Kerr effect, we quantitatively prove the existence of QSS, which has been disregarded, and decouple two effects counter-acting each other. Through the magnetoelastic energy analysis, rather we show that QSS in ferromagnets plays a governing role on ultrafast spin dynamics, which is opposite to what have been known on the basis of thermal effect. Our demonstration provides an essential way of analysis on ultrafast photo-induced phenomena., Comment: 6 pages, 4 figures in Manuscript, 8 pages, 4 figures in Supplementary word file

We have carried out neutron diffraction and small angle neutron scattering measurements on a high quality single crystal of the cubic lacunar spinel multiferroic, GaV$_4$S$_8$, as a function of magnetic field and temperature to determine the magnetic properties for the single electron that is located on the tetrahedrally coordinated V$_4$ molecular unit. Our results are in good agreement with the structural transition at 44 K from cubic to rhombohedral symmetry where the system becomes a robust ferroelectric, while long range magnetic order develops below 13 K in the form of an incommensurate cycloidal magnetic structure, which can transform into a N\'eel-type skyrmion phase in a modest applied magnetic field. Below 5.9(3) K, the crystal enters a ferromagnetic phase, and we find the magnetic order parameter indicates a long range ordered ground state with an ordered moment of 0.23(1) ${\mu}_\mathrm{B}$ per V ion. Both polarized and unpolarized neutron data in the ferroelectric-paramagnetic phase have been measured to determine the magnetic form factor. The data are consistent with a model of the single spin being uniformly distributed across the V$_4$ molecular unit, rather than residing on the single apical V ion, in substantial agreement with the results of first-principles theory. In the magnetically ordered state, polarized neutron measurements are important since both the cycloidal and ferromagnetic order parameters are clearly coupled to the ferroelectricity, causing the structural peaks to be temperature and field dependent. For the ferromagnetic ground state, the spins are locked along the $[1,1,1]$ direction by a surprisingly large anisotropy.

Electronic nematicity in iron pnictide materials is coupled to both the lattice and the conducting electrons, which allows both structural and transport observables to probe nematic fluctuations and the order parameter. Here we combine simultaneous transport and x-ray diffraction measurements with in-situ tunable strain (elasto-XRD) to measure the temperature dependence of the shear modulus and elastoresistivity above the nematic transition and the spontaneous orthorhombicity and resistivity anisotropy below the nematic transition, all within a single sample of $Ba(Fe_{0.96}Co_{0.04})_{2} As_{2}$. The ratio of transport to structural quantities is nearly temperature-independent over a 74 K range and agrees between the ordered and disordered phases. These results show that elasto-XRD is a powerful technique to probe the nemato-elastic and nemato-transport couplings, which have important implications to the nearby superconductivity. It also enables the measurement in the large strain limit, where the breakdown of mean field description reveals the intertwined nature of nematicity., Comment: Main text 10 pages, 4 figures

Transition metal based oxide heterostructures exhibit diverse emergent phenomena e.g. two dimensional electron gas, superconductivity, non-collinear magnetic phase, ferroelectricity, polar vortices, topological Hall effect etc., which are absent in the constituent bulk oxides. The microscopic understandings of these properties in such nanometer thick materials are extremely challenging. Synchrotron x-ray based techniques such as x-ray diffraction, x-ray absorption spectroscopy (XAS), resonant x-ray scattering (RXS), resonant inelastic x-ray scattering (RIXS), x-ray photoemission spectroscopy, etc. are essential to elucidating the response of lattice, charge, orbital, and spin degrees of freedoms to the heterostructuring. As a prototypical case of complex behavior, rare-earth nickelates (RENiO3 with RE=La, Pr, Nd, Sm, Eu, Lu) based thin films and heterostructures have been investigated quite extensively in recent years. An extensive body of literature about these systems exists and for an overview of the field, we refer the interested readers to the recent reviews Annual Review of Materials Research 46, 305 (2016) and Reports on Progress in Physics 81, 046501 (2018). In the present article, we give a brief review that concentrates on the use of synchrotron based techniques to investigate a specific set of EuNiO3/LaNiO3 superlattices, specifically designed to solve a long-standing puzzle about the origin of simultaneous electronic, magnetic and structural transitions of the RENiO3 series., Comment: Invited Review Article

We have elucidated the spin, lattice, charge and orbital coupling mechanism underlying the multiferroic character in tensile strained EuTiO3 films. Symmetry determined by oxygen octahedral tilting shapes the hybridization between the Eu 4f and Ti 3d orbitals and this inhibits predicted Ti displacement proper ferroelectricity. Instead, phonon softening emerges at low temperatures within the pseudo-cube (110) plane, orthogonal to the anticipated ferroelectric polarization symmetry. Additionally, the magnetic anisotropy is determined by orbital distortion through hybridization between the Ti 3d and typically isotropic Eu2+ 4f. This unique scenario demonstrates the critical role symmetry plays in the coupling of order parameters defining multiferroic behaviour., Comment: 11 pages, 3 figures

Fe-based superconductors exhibit a diverse interplay between charge, orbital, and magnetic ordering1-4. Variations in atomic geometry affect electron hopping between Fe atoms5,6 and the Fermi surface topology, influencing magnetic frustration and the pairing mechanism through changes of orbital overlap and occupancies7-11. Here, we experimentally demonstrate a systematic approach to realize superconductivity without chemical doping in BaFe2As2, employing geometric design within an epitaxial heterostructure. We control both tetragonality and orthorhombicity in BaFe2As2 through superlattice engineering, which we experimentally find to induce superconductivity when the As-Fe-As bond angle approaches that in a regular tetrahedron. This approach of superlattice design could lead to insights into low dimensional superconductivity in Fe-based superconductors.

The spin-Hall effect describes the interconversion of charge currents and spin currents, enabling highly efficient manipulation of magnetization for spintronics. Symmetry conditions generally restrict polarizations of these spin currents to be orthogonal to both the charge and spin flows. Spin polarizations can deviate from such direction in nonmagnetic materials only when the crystalline symmetry is reduced11. Here we experimentally show control of the spin polarization direction by using a non-collinear antiferromagnet Mn$_{3}$GaN, in which the triangular spin structure creates a low magnetic symmetry state while maintaining a high crystalline symmetry. We demonstrate that epitaxial Mn3GaN/Permalloy heterostructures can generate unique types of spinHall torques at room temperature corresponding to unconventional spin polarizations collinear to spin currents or charge currents which are forbidden in any sample with two-fold rotational symmetry. Our results demonstrate an approach based on spin-structure design for controlling spinorbit torque, paving the way for further progress in the emergent field of antiferromagnetic spintronics.

Metamagnetism in antiferromagnets exhibits distinct critical behaviors and dynamics when invoking spin reversal and rotation. Here we show a 0.05% anisotropic strain suffices to in-situ modulate the metamagnetic critical field of the Mott insulator Sr2IrO4 by over 50%, enabling electrical switching of the transition. Resonant x-ray scattering and model simulation reveal that the transition is completely tuned from the spin-flop to spin-flip type as the strain introduces C4-symmetry-breaking magnetic anisotropy. Simultaneous transport study indicates the metamagnetic responses are reflected in the large elasto- and magnetoconductance, highlighting the active charge degree of freedom in the spin-orbit-coupled Mott state and its potential for spin-electronics.

The effect of compression on the magnetic ground state of Sr$_2$IrO$_4$ is studied with x-ray resonant techniques in the diamond anvil cell. The weak interlayer exchange coupling between square-planar 2D IrO$_2$ layers is readily modified upon compression, with a crossover between magnetic structures around 7 GPa mimicking the effect of an applied magnetic field at ambient pressure. Higher pressures drive an order-disorder magnetic phase transition with no magnetic order detected above 17-20 GPa. The persistence of strong exchange interactions between $\mathrm{J_{eff}}=1/2$ magnetic moments within the insulating IrO$_2$ layers up to at least 35 GPa points to a highly frustrated magnetic state in compressed Sr$_2$IrO$_4$ opening the door for realization of novel quantum paramagnetic phases driven by extended $5d$ orbitals with entangled spin and orbital degrees of freedom., Comment: 4 pages, 3 figures, see ancillary file for Supplemental Material

Heterostructure engineering provides an efficient way to obtain several unconventional phases of LaNiO3, which is otherwise paramagnetic, metallic in bulk form. In this work, a new class of short periodic superlattices, consisting of LaNiO3 and EuNiO3 have been grown by pulsed laser interval deposition to investigate the effect of structural symmetry mismatch on the electronic and magnetic behaviors. Synchrotron based soft and hard X-ray resonant scattering experiments have found that these heterostructures undergo simultaneous electronic and magnetic transitions. Most importantly, LaNiO3 within these artificial structures exhibits a new antiferromagnetic, charge ordered insulating phase. This work demonstrates that emergent properties can be obtained by engineering structural symmetry mismatch across a heterointerface., Comment: 4 Figures

Inelastic neutron scattering studies in single crystals of TbInO3 and TbIn0.95Mn0.05O3 with nearly-triangular antiferromagnetic lattice are reported. At low energies, a broad and apparently gapless continuum of magnetic excitations, located at the triangular lattice (TL) Brillouin zone boundary, is observed. The data are well described by the uncorrelated nearest-neighbor valence bonds model. At higher energies, a broad excitation branch dispersing from the TL zone boundary is observed. No signs of static magnetic order are found down to the temperatures two orders of magnitude smaller than the effective interaction energy. The fluctuating magnetic moment exceeds two thirds of the Tb3+ free-ion value and is confined to the TL plane. These observations are consistent with a TL-based spin liquid state in TbInO3.

Spin-orbit entangled magnetic dipoles, often referred to as pseudospins, provide a new avenue to explore novel magnetism inconceivable in the weak spin-orbit coupling limit, but the nature of their low-energy interactions remains to be understood. We present a comprehensive study of the static magnetism and low-energy pseudospin dynamics in the archetypal spin-orbit Mott insulator Sr2IrO4. We find that in order to understand even basic magnetization measurements, a formerly overlooked in-plane anisotropy is fundamental. In addition to magnetometry, we use neutron diffraction, inelastic neutron scattering and resonant elastic and inelastic x-ray scattering to identify and quantify the interactions that determine the global symmetry of the system and govern the linear responses of pseudospins to external magnetic felds and their low-energy dynamics. We find that a pseudospin-only Hamiltonian is insufficient for an accurate description of the magnetism in Sr2IrO4 and that pseudospin-lattice coupling is essential. This finding should be generally applicable to other pseudospin systems with sizable orbital moments sensitive to anisotropic crystalline environments., Comment: Main text:11 pages, 12 figures Supplementary Material: 3 pages, 2 figures, 1 table

Dimensionality and symmetry play deterministic roles in the laws of Nature. They are important tools to characterize and understand quantum phase transitions, especially in the limit of strong correlations between spin, orbit, charge, and structural degrees of freedom. Using newly-developed, high-pressure resonant x-ray magnetic and charge diffraction techniques, we have discovered a quantum critical point in Cd2Os2O7 as the all-in-all-out (AIAO) antiferromagnetic order is continuously suppressed to zero temperature and, concomitantly, the cubic lattice structure continuously changes from space group Fd-3m to F-43m. Surrounded by three phases of different time reversal and spatial inversion symmetries, the quantum critical region anchors two phase lines of opposite curvature, with striking departures from a mean-field form at high pressure. As spin fluctuations, lattice breathing modes, and quasiparticle excitations interact in the quantum critical region, we argue that they present the necessary components for strongly-coupled quantum criticality in this three-dimensional compound.

Coupled transitions between distinct ordered phases are important aspects behind the rich phase complexity of correlated oxides that hinders our understanding of the underlying phenomena. For this reason, fundamental control over complex transitions has become a leading motivation of the designer approach to materials. We have devised a series of new superlattices by combining a Mott insulator and a correlated metal to form ultra-short period superlattices, which allow one to disentangle the simultaneous orderings in $RE$NiO$_3$. Tailoring an incommensurate heterostructure period relative to the bulk charge ordering pattern suppresses the charge order transition while preserving metal-insulator and antiferromagnetic transitions. Such selective decoupling of the entangled phases resolves the long-standing puzzle about the driving force behind the metal-insulator transition and points to the site selective Mott transition as the operative mechanism. This designer approach emphasizes the potential of heterointerfaces for selective control of simultaneous transitions in complex materials with entwined broken symmetries., Comment: Accepted in Phys. Rev. Lett

CaFe$_{2}$O$_{4}$ is an anisotropic $S={5\over 2}$ antiferromagnet with two competing $A$ ($\uparrow \uparrow \downarrow \downarrow$) and $B$ ($\uparrow \downarrow \uparrow \downarrow$) magnetic order parameters separated by static antiphase boundaries at low temperatures. Neutron diffraction and bulk susceptibility measurements, show that the spins near these boundaries are weakly correlated and a carry an uncompensated ferromagnetic moment that can be tuned with a magnetic field. Spectroscopic measurements find these spins are bound with excitation energies less than the bulk magnetic spin-waves and resemble the spectra from isolated spin-clusters. Localized bound orphaned spins separate the two competing magnetic order parameters in CaFe$_{2}$O$_{4}$., Comment: (main text - 5 pages, 4 figures; supplementary information - 4 pages, 6 figures, to be published in Physical Review Letters). arXiv admin note: text overlap with arXiv:1606.04243

We present a comprehensive temporal and spectral analysis of the long Swift GRB 120327A afterglow data to investigate the possible causes of the observed early time colour variations. We collected data from various instruments/telescopes in different bands (X-rays, ultra- violet, optical and near-infrared) and determined the shapes of the afterglow early-time light curves. We studied the overall temporal behaviour and the spectral energy distributions from early to late times. The ultra-violet, optical, and near-infrared light curves can be modelled with a single power-law component between 200 and 2e4 s after the burst event. The X-ray light curve shows a canonical steep-shallow-steep behaviour, typical of long gamma-ray bursts. At early times a colour variation is observed in the ultra-violet/optical bands, while at very late times a hint of a re-brightening is visible. The observed early time colour change can be explained as a variation in the intrinsic optical spectral index, rather than an evolution of the optical extinction., Comment: 8 pages, 4 figures, 2 tables, accepted for publication in A&A

We report the magnetic excitation spectrum as measured by inelastic neutron scattering for a polycrystalline sample of Sr$_3$CuPtO$_6$. Modeling the data by the 2+4 spinon contributions to the dynamical susceptibility within the chains, and with interchain coupling treated in the random phase approximation, accounts for the major features of the powder-averaged structure factor. The magnetic excitations broaden considerably as temperature is raised, persisting up to above 100 K and displaying a broad transition as previously seen in the susceptibility data. No spin gap is observed in the dispersive spin excitations at low momentum transfer, which is consistent with the gapless spinon continuum expected from the coordinate Bethe ansatz. However, the temperature dependence of the excitation spectrum gives evidence of some very weak interchain coupling., Comment: 9 pages, 5 figures

Resonant elastic X-ray scattering is a powerful technique for measuring multipolar order parameters. In this paper, we theoretically and experimentally study the possibility of using this technique to detect the proposed multipolar order parameters in URu$_2$Si$_2$ at the U-$L_{3}$ edge with the electric quadrupolar transition. Based on an atomic model, we calculate the azimuthal dependence of the quadrupolar transition at the U-$L_{3}$ edge. The results illustrate the potential of this technique for distinguishing different multipolar order parameters. We then perform experiments on ultra-clean single crystals of URu$_2$Si$_2$ at the U-$L_{3}$ edge to search for the predicted signal, but do not detect any indications of multipolar moments within the experimental uncertainty. We theoretically estimate the orders of magnitude of the cross-section and the expected count rate of the quadrupolar transition and compare them to the dipolar transitions at the U-$M_4$ and U-$L_3$ edges, clarifying the difficulty in detecting higher order multipolar order parameters in URu$_2$Si$_2$ in the current experimental setup., Comment: 9 pages, 4 figures, Accepted for publication in PRB

We report an experimental investigation of the two-dimensional ${J}_{\rm eff}$ = 1/2 antiferromagnetic Mott insulator by varying the interlayer exchange coupling in [(SrIrO$_3$)$_1$, (SrTiO$_3$)$_m$] ($m$ = 1, 2 and 3) superlattices. Although all samples exhibited an insulating ground state with long-range magnetic order, temperature-dependent resistivity measurements showed a stronger insulating behavior in the $m$ = 2 and $m$ = 3 samples than the $m$ = 1 sample which displayed a clear kink at the magnetic transition. This difference indicates that the blocking effect of the excessive SrTiO$_3$ layer enhances the effective electron-electron correlation and strengthens the Mott phase. The significant reduction of the Neel temperature from 150 K for $m$ = 1 to 40 K for $m$ = 2 demonstrates that the long-range order stability in the former is boosted by a substantial interlayer exchange coupling. Resonant x-ray magnetic scattering revealed that the interlayer exchange coupling has a switchable sign, depending on the SrTiO$_3$ layer number $m$, for maintaining canting-induced weak ferromagnetism. The nearly unaltered transition temperature between the $m$ = 2 and the $m$ = 3 demonstrated that we have realized a two-dimensional antiferromagnet at finite temperatures with diminishing interlayer exchange coupling., Comment: 4 figures