Structural distortion-induced magnetoelastic locking in Sr(2)IrO(4) revealed through nonlinear optical harmonic generation

Extraordinary phase transition revealed in a van der Waals antiferromagnet

While the surface-bulk correspondence has been ubiquitously shown in topological phases, the relationship between surface and bulk in Landau-like phases is much less explored. Theoretical investigations since 1970s for semi-infinite systems have predicted the possibility of the surface order emerging at a higher temperature than the bulk, clearly illustrating a counterintuitive situation and greatly enriching phase transitions. But experimental realizations of this prediction remain missing. Here, we demonstrate the higher-temperature surface and lower-temperature bulk phase transitions in CrSBr, a van der Waals (vdW) layered antiferromagnet. We leverage the surface sensitivity of electric dipole second harmonic generation (SHG) to resolve surface magnetism, the bulk nature of electric quadrupole SHG to probe bulk spin correlations, and their interference to capture the two magnetic domain states. Our density functional theory calculations show the suppression of ferromagnetic-antiferromagnetic competition at the surface is responsible for this enhanced surface magnetism. Our results not only show counterintuitive, richer phase transitions in vdW magnets, but also provide viable ways to enhance magnetism in their 2D form.

Quantum spin nematic phase in a square-lattice iridate

Spin nematic is a magnetic analogue of classical liquid crystals, a fourth state of matter exhibiting characteristics of both liquid and solid1,2. Particularly intriguing is a valence-bond spin nematic3-5, in which spins are quantum entangled to form a multipolar order without breaking time-reversal symmetry, but its unambiguous experimental realization remains elusive. Here we establish a spin nematic phase in the square-lattice iridate Sr2IrO4, which approximately realizes a pseudospin one-half Heisenberg antiferromagnet in the strong spin-orbit coupling limit6-9. Upon cooling, the transition into the spin nematic phase at TC ≈ 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 phase below TN ≈ 230 K and becomes directly observable through its interference with the antiferromagnetic 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 many-body quantum entanglement in the antiferromagnetic state10,11. Taken together, our results reveal a quantum order underlying the Néel antiferromagnet that is widely believed to be intimately connected to the mechanism of high-temperature superconductivity12,13.

Mechanoresponsive Spin via Spin-Lattice Coupling in Organic Cocrystals

The response of crystal structure to external stimuli provides potential applications in the areas of detection, diagnosis, and repair. In this work, we fabricate two allotropic organic cocrystals, with different space groups and lattice parameters, with identical donor and acceptor molecules inside them. Under external stimuli, lattice vibration and electron-phonon coupling present pronounced differences in these two types of crystals, where different strengths of spin polarizations are observed. Furthermore, due to pronounced differences in coupling between lattice and spin inside the allotropic charge transfer crystals, the magnetic field presents a discrepant tunability on both transmission and fluorescence lifetimes. Through decreasing temperature or applying external electric field, the electron-phonon coupling coefficient presents a decreasing tendency, which will affect the dipole and dielectric constant in the allotropic crystals differently.

Controllable Emergent Spatial Spin Modulation in Sr_{2}IrO_{4} by In Situ Shear Strain

Symmetric anisotropic interaction can be ferromagnetic and antiferromagnetic at the same time but for different crystallographic axes. We show that the competition of anisotropic interactions of orthogonal irreducible representations can be 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-two-dimensional antiferromagnetic Sr_{2}IrO_{4} under in situ shear strain. This translation-symmetry-breaking phase is a result of an unusual strain-activated anisotropic interaction which is at the fourth 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.

Rich information on 2D materials revealed by optical second harmonic generation

Two-dimensional (2D) materials have brought a spectacular revolution in fundamental research and industrial applications due to their unique physical properties of atomically thin thickness, strong light-matter interaction, unity valley polarization and enhanced many-body interactions. To fully explore their exotic physical properties and facilitate potential applications in electronics and optoelectronics, an effective and versatile characterization method is highly demanded. Among the many methods of characterization, optical second harmonic generation (SHG) has attracted broad attention because of its sensitivity, versatility and simplicity. The SHG technique is sufficiently sensitive at the atomic scale and therefore suitable for studies on 2D materials. More importantly, it has the capacity to acquire abundant information ranging from crystallographic, and electronic, to magnetic properties in various 2D materials due to its sensitivity to both spatial-inversion symmetry and time-reversal symmetry. These advantages accompanied by its characteristics of non-invasion and high throughput make SHG a powerful tool for 2D materials. This review summarizes recent experimental developments of SHG applications in 2D materials and also provides an outlook of potential prospects based on SHG.

Organic Multiferroic Magnetoelastic Complexes

The design of crystal structures aids the discovery of interesting physical phenomena in organic crystals. In this work, the optimization of the coronene-tetracyanoquinodimethane (TCNQ) structure generates non-degenerate energy levels of spin-up and spin-down electrons after charge transfer, producing spontaneous spin polarization, leading to pronounced ferromagnetism. The deformed crystal lattice can significantly affect the saturation magnetization of organic ferromagnets to present a remarkable magnetoelastic coupling. Furthermore, the magnetic-field-induced lattice shrinkage of the ferromagnetic crystals supports a spin-lattice-interaction-dependent magnetoelastic coupling. This concept of organic magnetoelastic coupling will pave the way for the rapid mechanical control of spin polarization in organic multiferroic magnetoelastic materials.

Enhancement of the spin-orbit coupling by strong electronic correlations in transition metal and light actinide compounds

A simple variational argument is presented which indicates that the spin-orbit coupling in itinerant systems can be enhanced by strong electronic correlations. The importance of the enhancement in the formation of the giant magnetic anisotropy found in the metallic paramagnetic and magnetically ordered states of compounds containing transition metal and light actinide elements (such as tetragonal Sr2RhO4, Sr2IrO4, the cubic uranium monochalcogenides and tetragonal URu2Si2) is discussed.

Unveiling the Fine Structural Distortion of Atomically Thin Bi2 O2 Se by Third-Harmonic Generation

Bismuth oxyselenide (Bi₂ O₂ Se), a new type of 2D material, has recently attracted increased attention due to its robust bandgap, stability under ambient conditions, and ultrahigh electron mobility. In such complex oxides, fine structural distortion tends to play a decisive role in determining the unique physical properties, such as the ferrorotational order, ferroelectricity, and magnetoelasticity. Therefore, an in-depth investigation of the fine structural symmetry of Bi₂ O₂ Se is necessary to exploit its potential applications. However, conventional techniques are either time consuming or requiring tedious sample treatment. Herein, a noninvasive and high-throughput approach is reported for characterizing the fine structural distortion in 2D centrosymmetric Bi₂ O₂ Se by polarization-dependent third-harmonic generation (THG). Unprecedentedly, the divergence between the experimental results and the theoretical prediction of the perpendicular component of polarization-dependent THG indicates a fine structural distortion, namely, a <1.4° rotation of the oxygen square in the tetragonal (Bi₂ O₂ ) layers. This rotation breaks the intrinsic mirror symmetry of 2D Bi₂ O₂ Se, eventually reducing the symmetry from the D_4h to the C_4h point group. The results demonstrate that THG is highly sensitive to even fine symmetry variations, thereby showing its potential to uncover hidden phase transitions and interacting polarized sublattices in novel 2D material systems.

Towards electrical-current control of quantum states in spin-orbit-coupled matter

Novel materials, which often exhibit surprising or even revolutionary physical properties, are necessary for critical advances in technologies. Simultaneous control of structural and physical properties via a small electrical current is of great significance both fundamentally and technologically. Recent studies demonstrate that a combination of strong spin-orbit interactions and a distorted crystal structure in magnetic Mott insulators is sufficient to attain this long-desired goal. In thistopical review, we highlight underlying properties of this class of materials and present two representative antiferromagnetic Mott insulators, namely, 4d-electron based Ca2RuO4and 5d-electron based Sr2IrO4, as model systems. In essence, a small, applied electrical current engages with the lattice, critically reducing structural distortions, which in turn readily suppresses the antiferromagnetic and insulating state and subsequently results in emergent new states. While details may vary in different materials, at the heart of these phenomena are current-reduced lattice distortions, which, via spin-orbit interactions, dictate physical properties. Electrical current, which joins magnetic field, electric field, pressure, light, etc as a new external stimulus, provides a new, key dimension for materials research, and also pose a series of intriguing questions that may provide the impetus for advancing our understanding of spin-orbit-coupled matter. ThisTopical Reviewprovides a brief introduction, a few hopefully informative examples and some general remarks. It is by no means an exhaustive report of the current state of studies on this topic.

Nonlinear optical response spatial self-phase modulation in MoTe2: correlations between χ(3) and mobility or effective mass

We report on an unambiguous observation of the third-order nonlinear optical effect, spatial self-phase modulation (SSPM), in a MoTe₂ dispersion. The values of the third-order nonlinear optical coefficients effectively for one-layer MoTe₂, χone-layer(3), are obtained through the SSPM method at excitation wavelengths 473, 532, 750, and 801 nm, respectively. The wind-chime model is used to explain the ring formation time. The wavelength dependence of χone-layer(3) compares well with the photo-absorption spectra. Significantly, we find a correlation between χ⁽³⁾ and the carrier mobility μ or effective mass m*, which again further supports the laser-induced ac electron coherence in 2D materials.

Recovery of photoexcited magnetic ordering in Sr2IrO4

The recovery of antiferromagnetic and lattice order of Sr₂IrO₄ upon laser excitation was measured by time-resolved x-ray diffraction on nanosecond time scales. The in situ measurements of both magnetic and lattice order parameters allow direct comparison of their time evolutions without ambiguity. We found that the magnetic order recovers with two time constants. The fast sub-nanosecond recovery is associated with the re-establishment of three dimensional antiferromagnetic order while the slow sub-nanosecond recovery agrees with the lattice cooling on tens of nanoseconds. The strong oscillating behavior of magnetic order during the long time recovery may be related to complicated dynamics of defect-pinned magnetic domains.

Fast reflective optic-based rotational anisotropy nonlinear harmonic generation spectrometer

We present a novel Rotational Anisotropy Nonlinear Harmonic Generation (RA-NHG) apparatus based primarily upon reflective optics. The data acquisition scheme used here allow for fast accumulation of RA-NHG traces, mitigating low frequency noise from laser drift, while permitting real-time adjustment of acquired signals with significantly more data points per unit angle rotation of the optics than other RA-NHG setups. We discuss the design and construction of the optical and electronic components of the device and present example data taken on a GaAs test sample at a variety of wavelengths. The RA-second harmonic generation data for this sample show the expected four-fold rotational symmetry across a broad range of wavelengths, while those for RA-third harmonic generation exhibit evidence of cascaded nonlinear processes possible in acentric crystal structures.

Fourier domain rotational anisotropy-second harmonic generation

We describe a novel scheme of detecting rotational anisotropy-second harmonic generation (RA-SHG) signals using a lock-in amplifier referenced to a fast scanning RASHG apparatus. The method directly measures the nth harmonics of the scanning frequency corresponding to SHG signal components of Cn symmetry that appear in a Fourier series expansion of a general RA-SHG signal. GaAs was used as a test sample allowing comparison of point-by-point averaging with the lock-in based method. When divided by the C_∞ signal component, the lock-in detected data allowed for both self-referenced determination of ratios of Cn components of up to 1 part in 10⁴ and significantly more sensitive measurement of the relative amount of different Cn components when compared with conventional methods.

Determination of the local structure of Sr2-xMxIrO4 (M = K, La) as a function of doping and temperature

The local structure of correlated spin-orbit insulator Sr2-xMxIrO4 (M = K, La) has been investigated by Ir L3-edge extended X-ray absorption fine structure measurements. The measurements were performed as a function of temperature for different dopings induced by substitution of Sr with La or K. It is found that Ir-O bonds have strong covalency and they hardly show any change across the Néel temperature. In the studied doping range, neither Ir-O bonds nor their dynamics, measured by their mean square relative displacements, show any appreciable change upon carrier doping, indicating the possibility of nanoscale phase separation in the doped system. On the other hand, there is a large increase of the static disorder in Ir-Sr correlation, larger for K doping than La doping. Similarities and differences with respect to the local lattice displacements in cuprates are briefly discussed.

The challenge of spin-orbit-tuned ground states in iridates: a key issues review

Effects of spin-orbit interactions in condensed matter are an important and rapidly evolving topic. Strong competition between spin-orbit, on-site Coulomb and crystalline electric field interactions in iridates drives exotic quantum states that are unique to this group of materials. In particular, the 'J _eff  =  ½' Mott state served as an early signal that the combined effect of strong spin-orbit and Coulomb interactions in iridates has unique, intriguing consequences. In this Key Issues Review, we survey some current experimental studies of iridates. In essence, these materials tend to defy conventional wisdom: absence of conventional correlations between magnetic and insulating states, avoidance of metallization at high pressures, 'S-shaped' I-V characteristic, emergence of an odd-parity hidden order, etc. It is particularly intriguing that there exist conspicuous discrepancies between current experimental results and theoretical proposals that address superconducting, topological and quantum spin liquid phases. This class of materials, in which the lattice degrees of freedom play a critical role seldom seen in other materials, evidently presents some profound intellectual challenges that call for more investigations both experimentally and theoretically. Physical properties unique to these materials may help unlock a world of possibilities for functional materials and devices. We emphasize that, given the rapidly developing nature of this field, this Key Issues Review is by no means an exhaustive report of the current state of experimental studies of iridates.

Electrical Control of Structural and Physical Properties via Strong Spin-Orbit Interactions in Sr_{2}IrO_{4}

Electrical control of structural and physical properties is a long-sought, but elusive goal of contemporary science and technology. We demonstrate that a combination of strong spin-orbit interactions (SOI) and a canted antiferromagnetic Mott state is sufficient to attain that goal. The antiferromagnetic insulator Sr_{2}IrO_{4} provides a model system in which strong SOI lock canted Ir magnetic moments to IrO_{6} octahedra, causing them to rigidly rotate together. A novel coupling between an applied electrical current and the canting angle reduces the Néel temperature and drives a large, nonlinear lattice expansion that closely tracks the magnetization, increases the electron mobility, and precipitates a unique resistive switching effect. Our observations open new avenues for understanding fundamental physics driven by strong SOI in condensed matter, and provide a new paradigm for functional materials and devices.

Time-reversal symmetry breaking hidden order in Sr2(Ir,Rh)O4

Layered 5d transition iridium oxides, Sr₂(Ir,Rh)O₄, are described as unconventional Mott insulators with strong spin-orbit coupling. The undoped compound, Sr₂IrO₄, is a nearly ideal two-dimensional pseudospin-1/2 Heisenberg antiferromagnet, similarly to the insulating parent compound of high-temperature superconducting copper oxides. Using polarized neutron diffraction, we here report a hidden magnetic order in pure and doped Sr₂(Ir,Rh)O₄, distinct from the usual antiferromagnetic pseudospin ordering. We find that time-reversal symmetry is broken while the lattice translation invariance is preserved in the hidden order phase. The onset temperature matches that of the odd-parity hidden order recently highlighted using optical second-harmonic generation experiments. The novel magnetic order and broken symmetries can be explained by the loop-current model, previously predicted for the copper oxide superconductors.

Tunable high-performance microwave absorption for manganese dioxides by one-step Co doping modification

The frequencies of microwave absorption can be affected by the permanent electric dipole moment which could be adjusted by modifying the crystal symmetry of the microwave absorbing materials. Herein, we corroborate this strategy experimentally and computationally to the microwave absorption of manganese dioxides. Nanosized Co-doped cryptomelane (Co-Cryp) was successfully synthesized by a one-step reaction. The introduction of Co(III) induced a change of crystal symmetry from tetragonal to monlclinic, which could lead to an increase of its permanent electric dipole moment. As a result, the frequencies of maximum microwave absorption were regulated in the range of 7.4 to 13.9 GHz with a broadened bandwidths. The results suggested that microwave absorption of manganese dioxides can be tailored with Co doping to expand their potential uses for abatement of various microwave pollutions.

High-speed measurement of rotational anisotropy nonlinear optical harmonic generation using position-sensitive detection

We present a method of performing high-speed rotational anisotropy nonlinear optical harmonic generation experiments at rotational frequencies of several hertz by projecting the harmonic light reflected at different angles from a sample onto a stationary position-sensitive detector. The high rotational speed of the technique, 10(3) to 10(4) times larger than existing methods, permits precise measurements of the crystallographic and electronic symmetries of samples by averaging over low frequency laser-power, beam-pointing, and pulse-width fluctuations. We demonstrate the sensitivity of our technique by resolving the bulk fourfold rotational symmetry of GaAs about its [001] axis using second-harmonic generation.