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The 2022 magneto-optics roadmap

Abstract Magneto-optical (MO) effects, viz. magnetically induced changes in light intensity or polarization upon reflection from or transmission through a magnetic sample, were discovered over a century and a half ago. Initially they played a crucially relevant role in unveiling the fundamentals of electromagnetism and quantum mechanics. A more broad-based relevance and wide-spread use of MO methods, however, remained quite limited until the 1960s due to a lack of suitable, reliable and easy-to-operate light sources. The advent of Laser technology and the availability of other novel light sources led to an enormous expansion of MO measurement techniques and applications that continues to this day (see section 1). The here-assembled roadmap article is intended to provide a meaningful survey over many of the most relevant recent developments, advances, and emerging research directions in a rather condensed form, so that readers can easily access a significant overview about this very dynamic research field. While light source technology and other experimental developments were crucial in the establishment of today’s magneto-optics, progress also relies on an ever-increasing theoretical understanding of MO effects from a quantum mechanical perspective (see section 2), as well as using electromagnetic theory and modelling approaches (see section 3) to enable quantitatively reliable predictions for ever more complex materials, metamaterials, and device geometries. The latest advances in established MO methodologies and especially the utilization of the MO Kerr effect (MOKE) are presented in sections 4 (MOKE spectroscopy), 5 (higher order MOKE effects), 6 (MOKE microscopy), 8 (high sensitivity MOKE), 9 (generalized MO ellipsometry), and 20 (Cotton–Mouton effect in two-dimensional materials). In addition, MO effects are now being investigated and utilized in spectral ranges, to which they originally seemed completely foreign, as those of synchrotron radiation x-rays (see section 14 on three-dimensional magnetic characterization and section 16 on light beams carrying orbital angular momentum) and, very recently, the terahertz (THz) regime (see section 18 on THz MOKE and section 19 on THz ellipsometry for electron paramagnetic resonance detection). Magneto-optics also demonstrates its strength in a unique way when combined with femtosecond laser pulses (see section 10 on ultrafast MOKE and section 15 on magneto-optics using x-ray free electron lasers), facilitating the very active field of time-resolved MO spectroscopy that enables investigations of phenomena like spin relaxation of non-equilibrium photoexcited carriers, transient modifications of ferromagnetic order, and photo-induced dynamic phase transitions, to name a few. Recent progress in nanoscience and nanotechnology, which is intimately linked to the achieved impressive ability to reliably fabricate materials and functional structures at the nanoscale, now enables the exploitation of strongly enhanced MO effects induced by light–matter interaction at the nanoscale (see section 12 on magnetoplasmonics and section 13 on MO metasurfaces). MO effects are also at the very heart of powerful magnetic characterization techniques like Brillouin light scattering and time-resolved pump-probe measurements for the study of spin waves (see section 7), their interactions with acoustic waves (see section 11), and ultra-sensitive magnetic field sensing applications based on nitrogen-vacancy centres in diamond (see section 17). Despite our best attempt to represent the field of magneto-optics accurately and do justice to all its novel developments and its diversity, the research area is so extensive and active that there remains great latitude in deciding what to include in an article of this sort, which in turn means that some areas might not be adequately represented here. However, we feel that the 20 sections that form this 2022 magneto-optics roadmap article, each written by experts in the field and addressing a specific subject on only two pages, provide an accurate snapshot of where this research field stands today. Correspondingly, it should act as a valuable reference point and guideline for emerging research directions in modern magneto-optics, as well as illustrate the directions this research field might take in the foreseeable future.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Observation of interlayer plasmon polaron in graphene/WS 2 heterostructures

Harnessing electronic excitations involving coherent coupling to bosonic modes is essential for the design and control of emergent phenomena in quantum materials. In situations where charge carriers induce a lattice distortion due to the electron-phonon interaction, the conducting states get “dressed", which leads to the formation of polaronic quasiparticles. The exploration of polaronic effects on low-energy excitations is in its infancy in two-dimensional materials. Here, we present the discovery of an interlayer plasmon polaron in heterostructures composed of graphene on top of single-layer WS 2 . By using micro-focused angle-resolved photoemission spectroscopy during in situ doping of the top graphene layer, we observe a strong quasiparticle peak accompanied by several carrier density-dependent shake-off replicas around the single-layer WS 2 conduction band minimum. Our results are explained by an effective many-body model in terms of a coupling between single-layer WS 2 conduction electrons and an interlayer plasmon mode. It is important to take into account the presence of such interlayer collective modes, as they have profound consequences for the electronic and optical properties of heterostructures that are routinely explored in many device architectures involving 2D transition metal dichalcogenides.

36 MATERIALS SCIENCE↗

Supertwisted spirals of layered materials enabled by growth on non-Euclidean surfaces

Using curves to make twists The growth of layered materials on flat substrates usually occurs in stacked layers, although defects or a lattice mismatch can induce strains that distort the shape of subsequent layers. However, these effects are usually small and can be uncontrolled. Zhao et al. now demonstrate the possibility of synthesizing multilayers of two-dimensional materials with certain twists between the layers induced by the presence of screw dislocations in combination with curved substrate surfaces. Different twist angles are achieved by varying the amount of nonplanarity and the character (conical or hyperbolic) of the surface. Science , this issue p. 442

Science & Technology - Other Topics↗

Two-step electronic response to magnetic ordering in a van der Waals ferromagnet

The two-dimensional material Cr 2 ⁢Ge 2 ⁢Te 6 is a member of the class of insulating van der Waals (vdW) magnets. Here, using high resolution angle-resolved photoemission spectroscopy in a detailed temperature dependence study, we identify a clear response of the electronic structure to a dimensional crossover in the form of two distinct temperature scales marking onsets of modifications in the electronic structure. Specifically, we observe Te 𝑝-orbital-dominated bands to undergo changes at the Curie transition temperature 𝑇 𝐶 while the Cr 𝑑-orbital-dominated bands begin evolving at a higher temperature scale. Combined with neutron scattering, density functional theory calculations, and Monte Carlo simulations, we find that the electronic system can be consistently understood to respond sequentially to the distinct temperatures at which in-plane and out-of-plane spin correlations exceed a characteristic length scale. Finally, our findings reveal the sensitivity of the orbital-selective electronic structure for probing the dynamical evolution of local moment correlations in vdW insulating magnets.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

One-Pot Coating of Ceramic Powders by Exfoliated Boron Nitride Layers with a Dense CO 2 Medium and Ultrasound-Aided Mixing

The coating or doping of substrates by two-dimensional materials to impart superior functional properties (such as improved thermal conductivity, bacterial resistance, reduced friction) is receiving increased attention. Environmentally benign, rapid and scalable coating techniques are desirable for this purpose. Here, we report a novel process for coating alumina, silicon carbide and boron carbide substrates with hexagonal boron nitride (h-BN) layers. The process consists of two sequential steps. First, h-BN layers are exfoliated from bulk h-BN in supercritical carbon dioxide (scCO 2 ) using ultrasound-aided mixing. This step is followed by self-assembly (i.e., coating) of the exfoliated h-BN on the substrates in liquid CO 2 also aided by ultrasound. The liquid CO 2 state is achieved by simply lowering the pressure and temperature of the first step below the critical point of CO 2 (P c = 72.8 atm; T c = 31.1 °C). Scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS) micrographs clearly reveal the exfoliation of h-BN under scCO 2 conditions as well as the h-BN assembly on various substrates under liquid CO 2 conditions. X-ray diffraction patterns confirm the structural integrity of the coated h-BN layers. It was also confirmed that without a transition to the liquid CO 2 phase following exfoliation in scCO 2 , there was negligible coating of h-BN on the substrates. Researchers in the field could consider this benign process to rapidly coat or dope materials with h-BN and other 2D materials to impart improved functional properties in myriad applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Imaging Strain-Localized Single-Photon Emitters in Layered GaSe below the Diffraction Limit

Nanoscale strain control of exciton funneling is an increasingly critical tool for the scalable production of single photon emitters (SPEs) in two-dimensional materials. However, conventional far-field optical microscopies remain constrained in spatial resolution by the diffraction limit and thus can provide only a limited description of nanoscale strain localization of SPEs. Here, we quantify the effects of nanoscale heterogeneous strain on the energy and brightness of GaSe SPEs on nanopillars with correlative cathodoluminescence, photoluminescence, and atomic force microscopy, supported by density functional theory simulations. We report the strain-localized SPEs have a broad range of emission wavelengths from 620 to 900 nm. We reveal substantial strain-controlled SPE wavelength tunability over a ~100 nm spectral range and 2 orders of magnitude enhancement in the SPE brightness at the pillar center due to Type-I exciton funneling. In addition, we show that radiative biexciton cascade processes contribute to observed CL photon superbunching. Also, the GaSe SPEs show excellent stability, where their properties remain unchanged after electron beam exposure. Importantly, we anticipate that this comprehensive study on the nanoscale strain control of two-dimensional SPEs will provide key insights to guide the development of truly deterministic quantum photonics.

2D materials↗

Prediction of room-temperature multiferroicity in strained MoCr 2 S 6 monolayer

The contrasting d-orbital occupation required for ferroelectricity vs ferromagnetism makes it difficult for their coexistence in two-dimensional materials, especially at high temperature. To resolve this intrinsic contradiction, we propose a layered MoCr 2 S 6 multiferroics by alloying magnetic Cr element into the ferroelectric 1T phase of the MoS 2 matrix. First-principles calculations disclose that a spontaneous symmetry breaking, depending on the Mo atom displacement, leads to a robust ferroelectricity, which coexists with a ferromagnetic order originated from two neighboring Cr atoms. The effect can be further enhanced by tensile strain to bring about a room-temperature multiferroicity. Our results shed new light on the fundamental understanding of multiferroics and display promising applications in spintronics and multistate data storage.

2D materials↗

Solving the Bethe-Salpeter equation on a subspace: Approximations and consequences for low-dimensional materials

It is well known that the ambient environment can dramatically renormalize the quasiparticle gap and exciton binding energies in low-dimensional materials, but the effect of the environment on the energy splitting of the spin-singlet and spin-triplet exciton states is less understood. A prominent effect is the renormalization of the exciton binding energy and optical strength (and hence the optical spectrum) through additional screening of the direct Coulomb term describing the attractive electron-hole interaction in the kernel of the Bethe-Salpeter equation. The repulsive exchange interaction responsible for the singlet-triplet splitting, on the other hand, is unscreened within formal many-body perturbation theory. However, Benedict argued that in practical calculations restricted to a subspace of the full Hilbert space, the exchange interaction should be appropriately screened by states outside of the subspace, the so-called S approximation [L. X. Benedict, Phys. Rev. B 66, 193105 (2002)PRBMDO0163-182910.1103/PhysRevB.66.193105]. Here, we systematically explore the accuracy of the S approximation for different confined systems, including a molecule and heterostructures of semiconducting and metallic layered materials. We show that the S approximation is actually exact in the limit of small exciton binding energies (i.e., small direct term) and can be used to significantly accelerate convergence of the exciton energies with respect to the number of empty states, provided that a particular effective screening consistent with the conventional Tamm-Dancoff approximation is employed. We further find that the singlet-triplet splitting in the energy of the excitons is largely unaffected by the external dielectric environment for most quasi-two-dimensional materials.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Beyond the Anderson rule: importance of interfacial dipole and hybridization in van der Waals heterostructures

Vertical stacking of two-dimensional materials with weak van der Waals (vdW) interactions has laid the ground for breakthroughs in physics as well as in technological applications. Although vdW interactions dominate interlayer binding, interlayer electronic coupling may not be negligible and can lead to properties beyond the superposition of constituent monolayers. Here, studying heterobilayers of transition-metal dichalcogenides (MQ 2 ; M = Mo, Ni, Pt; Q = S, Se) by means of density functional theory calculations, we show two mechanisms that influence the band gaps of vdW heterostructures beyond the Anderson rule: (1) interfacial hybridization (mainly involving out-of-plane states, such as chalcogen p z -states), which leads to an upshift in the valence band maxima and accordingly a decrease in the band gap. (2) Formation of an interfacial electric dipole, resulting in an effective gap increase in type-II junctions. While the former is material specific, depending on the proximity of p z -states to each other and the valence band maxima, the latter can be generally described using a model based on the charge density decay outside the monolayers and the pristine band edge positions with respect to the vacuum level, irrespective of junction type.

36 MATERIALS SCIENCE↗

Methane Partial Oxidation over Multifunctional 2-D Materials

The objective of this research is to design, synthesize, and evaluate highly selective, active, and stable multifunctional catalysts for the low temperature (< 500 Kelvin (K)) partial oxidation of methane to methanol (MTM) with molecular oxygen: CH 4 (g) + $\frac{1}{2}$O 2 (g) → CH 3 OH(g). Methane, the primary component of natural gas, is a source of energy and economic growth as well as an environmental concern. Recent developments in horizontal drilling and enhanced extraction methods have resulted in production of an estimated 62.4 trillion m 3 of ‘stranded’, or uneconomic, natural gas. Uneconomical natural gas is often flared or vented at remote oil production sites. Leaked, flared, and/or vented gas represents a "lost opportunity”, and this research project aims to maximize the value of the resource. Conventional catalysts for MTM suffer from low methanol selectivity since they exhibit ~0.55 eV higher barrier for C-H bond activation of methane compared to methanol. Without breaking these scaling relations, methanol oxidation is orders of magnitude faster than methane oxidation and it is very challenging to envision a process with economically viable single-pass yield. Here, we chose to investigate single-atom catalysts embedded and stabilized in two-dimensional materials such as graphene (GR) and "supported" on Group VIII and IB transition metals such as nickel. The electronic atomic monolayer-metal support interaction (EAMSI) present in these systems could promote methanol selectivity by breaking the scaling relations of the C-H bond activation of methane and methanol. A density functional theory (DFT) based computational study focused on predicting families of GR-based catalysts that could be active and selective for MTM. The catalyst systems predicted by the computational study were synthesized and evaluated for the gas phase MTM under relevant conditions. Unfortunately, the experimental activity and selectivity was lower than computationally predicted. The origin for the discrepancy is likely related to difficulties in synthesizing single atom catalysts in a threecomponent catalyst system at high density and with high selectivity. Future work in our groups is thus focused on reducing the system complexity to a two-component catalyst system. Finally, a techno-economic analysis (TEA) was also conducted to identify critical bottlenecks that inhibit future commercialization.

03 NATURAL GAS↗

Nature of Magnetic Excitations in the High-Field Phase of α–RuCl 3

We present comprehensive electron spin resonance (ESR) studies of in-plane oriented single crystals of α–RuCl 3 , a quasi-two-dimensional material with honeycomb structure, focusing on its high-field spin dynamics. The measurements were performed in magnetic fields up to 16 T, applied along the [110] and [100] directions. Several ESR modes were detected. Combining our findings with recent inelastic neutron- and Raman-scattering data, we identified most of the observed excitations. Most importantly, we show that the low-temperature ESR response beyond the boundary of the magnetically ordered region is dominated by single- and two-particle processes with magnons as elementary excitations. In conclusion, the peculiarities of the excitation spectrum in the vicinity of the critical field are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Enhancing Graphene Plasmonic Device Performance via its Dielectric Environment

Graphene plasmons provide a compelling avenue toward chip-scale dynamic tuning of infrared light. Dynamic tunability emerges through controlled alterations in the optical properties of the system defining graphene’s plasmonic dispersion. Typically, electrostatic induced alterations of the carrier concentration in graphene working in conjunction with mobility have been considered the primary factors dictating plasmonic tunability. We find here that the surrounding dielectric environment also plays a primary role, dictating not just the energy of the graphene plasmon but so too the magnitude of its tuning and spectral width. To arrive at this conclusion, poles in the imaginary component of the reflection coefficient are used to efficiently survey the effect of the surrounding dielectric on the tuning of the graphene plasmon. By investigating several common polar materials, optical phonons (i.e., the Reststrahlen band) of the dielectric substrate are shown to appreciably affect not only the plasmon’s spectral location but its tunability, and its resonance shape as well. In particular, tunability is maximized when the resonances are spectrally distant from the Reststrahlen band, whereas sharp resonances (i.e., high-Q) are achievable at the band’s edge. Overall, these observations both underscore the necessity of viewing the dielectric environment in aggregate when considering the plasmonic response derived from two-dimensional materials and provide heuristics to design dynamically tunable graphene-based infrared devices.

36 MATERIALS SCIENCE↗

Topologically derived dislocation theory for twist and stretch moiré superlattices in bilayer graphene

In this work, we develop a continuum dislocation description of twist and stretch moiré superlattices in two-dimensional material bilayers. The continuum formulation is based on the topological constraints introduced by the periodic dislocation network associated with the moiré structure. The approach is based on solving analytically for the structural distortion and displacement fields that satisfy the topological constraints and that minimize the total energy. The total energy is described by both the strain energy of each individual distorted layer and a Peierls-Nabarro-like interfacial contribution arising from stacking disregistry. The dislocation core emerges naturally within the formalism as a result of the competition between the two contributions. The approach presented here captures the structure and energetics of twist and stretch moiré superlattices of dislocations with arbitrary direction and character, without assuming an analytical solution a priori and while accounting naturally for dislocation-dislocation image interactions. In comparisons to atomistic simulations using classical potentials, the maximum structure deviation is 6%, while the maximum line energy deviation is 0.019 eV/Å. Several applications of our model are shown, including predicting the variation of structure with twist angle and describing dislocation line tension and junction energies.

36 MATERIALS SCIENCE↗

Mixed matrix membranes for post-combustion carbon capture: From materials design to membrane engineering

Mixed matrix materials (MMMs) containing nanofillers dispersed in continuous polymer matrices have emerged as an exciting and versatile platform to develop membranes with superior CO 2 /N 2 separation performance for post-combustion carbon capture. Both polymers and nanofillers can be vertically designed and engineered to combine the advantages of excellent processability (derived from polymers) and strong size-sieving ability or/and significant permanent porosity (originated from nanofillers). However, the MMMs face major challenges, such as interfacial incompatibility, particle agglomeration, and poor thin-film formability. This report provides a comprehensive yet critical review of various polymers and nanofillers (such as metal-organic frameworks, covalent organic frameworks, and two-dimensional materials) with promising CO 2 /N 2 separation properties. We exhaustively describe strategies to improve interfacial compatibility, such as in situ syntheses of polymers and nanofillers and functionalization of both components to improve adhesion. Moreover, we highlight various approaches to engineer the MMMs into thin-film composite (TFC) membranes. The review reveals the structure/property relationship in these MMMs and outlines the challenges and opportunities to realize their potential for practical applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ab Initio-Based Bond Order Potential for Arsenene Polymorphs Developed via Hierarchical Reinforcement Learning

Arsenene, a less-explored two-dimensional material, holds the potential for applications in wearable electronics, memory devices, and quantum systems. This study introduces a bond-order potential model with Tersoff formalism, the ML-Tersoff, which leverages multireward hierarchical reinforcement learning (RL), trained on an ab initio data set. This data set covers a spectrum of properties for arsenene polymorphs, enhancing our understanding of its mechanical and thermal behaviors without the complexities of traditional models requiring multiple parameter sets. Our RL strategy utilizes decision trees coupled with a hierarchical reward strategy to accelerate convergence in high-dimensional continuous search spaces. Unlike the Stillinger-Weber approach, which demands separate formalisms for buckled and puckered forms, the ML-Tersoff model concurrently captures multiple properties of the two polymorphs by effectively representing the local environment, thereby avoiding the need for different atomic types. Here, we apply the ML model to understand the mechanical and thermal properties of the arsenene polymorphs and nanostructures. We observe an inverse relationship between the critical strain and temperature in arsenene. Thermal conductivity calculations in nanosheets show good agreement with ab initio data, reflecting a decrease in thermal conductivity attributable to increased anharmonic effects at higher temperatures. We also apply the model to predict the thermal behavior of arsenene nanotubes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Recyclable Graphene Sheets as a Growth Template for Crystalline ZnO Nanowires

Recent advances in nanoscience have opened ways of recycling substrates for nanomaterial growth. Novel materials, such as atomically thin materials, are highly desirable for the recycling substrates. In this work, we report recycling of monolayer graphene as a growth template for synthesis of single crystalline ZnO nanowires. Selective nucleation of ZnO nanowires on graphene was elucidated by scanning electron microscopy and density functional theory calculation. Growth and subsequent separation of ZnO nanowires was repeated up to seven times on the same monolayer graphene film. Raman analyses were also performed to investigate the quality of graphene structure along the recycling processes. The chemical robustness of graphene enables the repetitive ZnO nanowire growth without noticeable degradation of the graphene quality. This work presents a route for graphene as a multifunctional growth template for diverse nanomaterials such as nanocrystals, aligned nanowires, other two-dimensional materials, and semiconductor thin films.

36 MATERIALS SCIENCE↗

Achieving High-Yield Conversion of Janus Transition Metal Dichalcogenides on Diverse Substrates

Janus transition metal dichalcogenides (TMDCs) with intrinsic broken mirror symmetry and vertical dipole moment provide an additional degree of freedom to manipulate material symmetry down to atomic-layer thickness. However, despite advances in synthesis strategies, fundamental understanding of this atomic substitution process remains limited, which has impeded their implementation in advanced devices. Here, by using a room-temperature atomic-layer substitution (RT-ALS) strategy, we systematically investigate the critical factors facilitating the high-yield conversion of Janus TMDCs on diverse substrates. Combining Raman spectroscopy probes, X-ray photoelectron spectroscopy (XPS) measurements, and density functional theory (DFT) calculations, we demonstrate that substrates with enhanced electron doping or larger surface polarity substantially benefit the conversion of Janus TMDCs reaching a near-unity yield. Intriguingly, the strong affinity between Janus TMDCs and substrates (e.g., Au) brings about abnormal Raman spectroscopic phenomena. These findings highlight the significance of substrates in achieving the reliable synthesis of Janus two-dimensional materials with improved homogeneity on various substrates. In addition, this takes us one step closer to utilizing Janus TMDCs as a versatile platform in next-generation optoelectronic devices, sensors, and quantum technologies.

Doping↗

Visualization of Chiral Electronic Structure and Anomalous Optical Response in a Material with Chiral Charge Density Waves

Chiral materials have attracted significant research interests as they exhibit intriguing physical properties, such as chiral optical response, spin-momentum locking, and chiral induced spin selectivity. Recently, layered transition metal dichalcogenide 1T–TaS 2 has been found to host a chiral charge density wave (CDW) order. Nevertheless, the physical consequences of the chiral order, for example, in electronic structures and the optical properties, are yet to be explored. Here, we report the spectroscopic visualization of an emergent chiral electronic band structure in the CDW phase, characterized by windmill-shaped Fermi surfaces. Further, we uncover a remarkable chirality-dependent circularly polarized Raman response due to the salient in-plane chiral symmetry of CDW, although the ordinary circular dichroism vanishes. Chiral Fermi surfaces and anomalous Raman responses coincide with the CDW transition, proving their lattice origin. Our Letter paves a path to manipulate the chiral electronic and optical properties in two-dimensional materials and explore applications in polarization optics and spintronics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗