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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., Journal of Physics D: Applied Physics, 55 (46), ISSN:0022-3727, ISSN:1361-6463

The interactions of the excited states of a single chromophore with static and dynamic electric fields spatially varying at the atomic scale are investigated in a joint experimental and theoretical effort. In this configuration, the spatial extension of the fields confined at the apex of a scanning tunneling microscope tip is smaller than that of the molecular exciton, a property used to generate fluorescence maps of the chromophore with intramolecular resolution. Theoretical simulations of the electrostatic and electrodynamic interactions occurring at the picocavity junction formed by the chromophore, the tip, and the substrate reveal the key role played by subtle variations of Purcell, Lamb, and Stark effects. They also demonstrate that hyper-resolved fluorescence maps of the line shift and linewidth of the excitonic emission can be understood as images of the static charge redistribution upon electronic excitation of the molecule and as the distribution of the dynamical charge oscillation associated with the molecular exciton, respectively., This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Grant Agreement No. 771850) and the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie Grant Agreement No. 894434. The Labex NIE (Contract No. ANR-11-LABX-0058_NIE), the International Center for Frontier Research in Chemistry (FRC), the Spanish Ministry of Science (Project No. PID2019–107432 GB-I00), and the Department of Education of the Basque Government (Project No. IT116419) are acknowledged for financial support.

The ability to create nanometer-scale lateral p–n junctions is essential for the next generation of two-dimensional (2D) devices. Using the charge-transfer heterostructure graphene/α-RuCl3, we realize nanoscale lateral p–n junctions in the vicinity of graphene nanobubbles. Our multipronged experimental approach incorporates scanning tunneling microscopy (STM) and spectroscopy (STS) and scattering-type scanning near-field optical microscopy (s-SNOM) to simultaneously probe the electronic and optical responses of nanobubble p–n junctions. Our STM/STS results reveal that p–n junctions with a band offset of ∼0.6 eV can be achieved with widths of ∼3 nm, giving rise to electric fields of order 108 V/m. Concurrent s-SNOM measurements validate a point-scatterer formalism for modeling the interaction of surface plasmon polaritons (SPPs) with nanobubbles. Ab initio density functional theory (DFT) calculations corroborate our experimental data and reveal the dependence of charge transfer on layer separation. Our study provides experimental and conceptual foundations for generating p–n nanojunctions in 2D materials., Research at Columbia University was supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No DE-SC0019443. Plasmonic nano-imaging at Columbia University was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No DE-SC0018426. J.Z. and A.R. were supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM) EXC 2056-390715994, funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 2247, Grupos Consolidados (IT1249-19), and SFB925 “Light induced dynamics and control of correlated quantum systems”. J.Z. and A.R. would like to acknowledge Nicolas Tancogne-Dejean and Lede Xian for fruitful discussions and also acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation programme under Marie Skłodowska-Curie Grant Agreement 886291 (PeSD-NeSL). STM support was provided by the National Science Foundation via Grant DMR-2004691. C.R.-V. acknowledges funding from the European Union Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie Grant Agreement 844271. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF9069. J.Q.Y. was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. S.E.N. acknowledges support from the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Division of Scientific User Facilities. Work at University of Tennessee was supported by NSF Grant 180896.

In the framework of time-dependent density functional theory (TDDFT), the exact exchange-correlation (xc) kernel fxc(n,q,ω) determines the ground-state energy, excited-state energies, lifetimes, and the time-dependent linear density response of any many-electron system. The recently developed MCP07 xc kernel fxc(n,q,ω) of Ruzsinszky et al. [Phys. Rev. B 101, 245135 (2020)] yields excellent uniform electron gas (UEG) ground-state energies and plausible plasmon lifetimes. As MCP07 is constructed to describe fxc of the UEG, it cannot capture optical properties of real materials. To verify this claim, we follow Nazarov et al. [Phys. Rev. Lett. 102, 113001 (2009)] to construct the long-range, dynamic xc kernel, limq→0fxc(n,q,ω)=−α(ω)e2/q2, of a weakly inhomogeneous electron gas, using MCP07 and other common xc kernels. The strong wave-vector and frequency dependence of the “ultranonlocality” coefficient α(ω) is demonstrated for a variety of simple metals and semiconductors. We examine how imposing exact constraints on an approximate kernel shapes α(ω). Comparisons to kernels derived from correlated-wave-function calculations are drawn., The authors acknowledge support from the U.S. National Science Foundation under Grant No. DMR-1553022. A.D.K. acknowledges support from the U.S. Department of Energy, Basic Energy Sciences, through the Energy Frontier Research Center for Complex Materials from First Principles Grant No. DE-SC0012575; and Temple University.

Nanoscale charge control is a key enabling technology in plasmonics, electronic band structure engineering, and the topology of two-dimensional materials. By exploiting the large electron affinity of α-RuCl3, we are able to visualize and quantify massive charge transfer at graphene/α-RuCl3 interfaces through generation of charge-transfer plasmon polaritons (CPPs). We performed nanoimaging experiments on graphene/α-RuCl3 at both ambient and cryogenic temperatures and discovered robust plasmonic features in otherwise ungated and undoped structures. The CPP wavelength evaluated through several distinct imaging modalities offers a high-fidelity measure of the Fermi energy of the graphene layer: EF = 0.6 eV (n = 2.7 × 1013 cm–2). Our first-principles calculations link the plasmonic response to the work function difference between graphene and α-RuCl3 giving rise to CPPs. Our results provide a novel general strategy for generating nanometer-scale plasmonic interfaces without resorting to external contacts or chemical doping., Research at Columbia was supported as part of the Energy Frontier Research Center on Programmable Quantum Materials funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under Award No. DE-SC0019443. J.Z., L.X., and A.R. were supported by the European Research Council (ERC-2015-AdG694097), the Cluster of Excellence “Advanced Imaging of Matter” (AIM) EXC 2056 - 390715994, funding by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under RTG 2247, Grupos Consolidados (IT1249-19) and SFB925 “Light induced dynamics and control of correlated quantum systems”. J.Z. acknowledges funding received from the European Union Horizon 2020 research and innovation program under Marie Sklodowska-Curie Grant Agreement 886291 (PeSD-NeSL). J.Z., L.X., and A.R. would like to acknowledge Nicolas Tancogne-Dejean for fruitful discussions and also acknowledge support by the Max Planck Institute-New York City Center for Non-Equilibrium Quantum Phenomena. The Flatiron Institute is a division of the Simons Foundation. D.G.M. acknowledges support from the Gordon and Betty Moore Foundation’s EPiQS Initiative, Grant GBMF9069. Work at ORNL was supported by the U.S. Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan, Grant JPMXP0112101001, JSPS KAKENHI Grant JP20H00354, and the CREST (JPMJCR15F3), JST. S.E.N. was supported by the Division of Scientific User Facilities of the U.S. DOE Basic Energy Sciences. M.M.F. acknowledges support from the Office of Naval Research Grant N00014-18-1-2722. D.N.B. is the Vannevar Bush Faculty ONR-VB: N00014-19-1-2630 and Moore investigator in Quantum Materials EPIQS program #9455. A.S.M acknowledges support from award 80NSSC19K1210 under the NASA Laboratory Analysis of Returned Samples program.

In narrow electron bands in which the Coulomb interaction energy becomes comparable to the bandwidth, interactions can drive new quantum phases. Such flat bands in twisted graphene-based systems result in correlated insulator, superconducting and topological states. Here we report evidence of low-energy flat bands in twisted bilayer WSe2, with signatures of collective phases observed over twist angles that range from 4 to 5.1°. At half-band filling, a correlated insulator appeared that is tunable with both twist angle and displacement field. At a 5.1° twist, zero-resistance pockets were observed on doping away from half filling at temperatures below 3 K, which indicates a possible transition to a superconducting state. The observation of tunable collective phases in a simple band, which hosts only two holes per unit cell at full filling, establishes twisted bilayer transition metal dichalcogenides as an ideal platform to study correlated physics in two dimensions on a triangular lattice., Studies of the tunable correlated states in the twisted bilayer WSe2 were supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DE-SC0019443. The synthesis of the WSe2 crystals was supported by the NSF MRSEC programme through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-1420634). The theoretical work was supported by the European Research Council (ERC-2015-AdG694097), cluster of Excellence AIM, SFB925 and Grupos Consolidados (IT1249-19). The Flatiron Institute is a division of the Simons Foundation. We acknowledge support from the Max Planck–New York Center for Non-Equilibrium Quantum Phenomena.

García Martínez, Jorge Manuel et al., Comunicación presentada en el PDI Topical Workshop on MBE-Grown Graphene 2013, celebrado en Berlín el 19 y 20 de septiembre de 2013., Graphene growth on dielectric substrates has potential to enable new kinds of devices and applications. We explore graphene growth via direct depositing carbon in a MBE environment on different dielectric substrates, such as h-BN and sapphire. The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated. These results are consistent with a Van der Waals growth mode of graphene on dielectric substrates. Atomic-force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h-BN substrates. On h-BN substrates, high quality single layer growth occurs as nano-domains. The growth is governed by a high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is fairly independent of the incident flux of carbon atoms. Formation of single-layer graphene is clearly apparent in Raman spectra that display sharp optical phonon bands. We will show also results of graphene growth by MBE on sapphire, where large area growth occurs with monolayer thickness fluctuations. The successful growth of graphene on hexagonal boron-nitride flakes distributed over a large area allows the exploration of arrange of growth parameters and suggests the capability for large area growth., Work supported by ONR (N000140610138 and Graphene MURI), AFOSR (FA9550-11-1-0010), EFRC Cente fo Re-De_ning Photovoltaic E_ciency through Molecule Scale Control (award DE-SC0001085), NSF (CHE-0641523), NYSTAR, CSIC-PIF (200950I154), Spanish CAM (Q&C Light (S2009ESP-1503), Numancia 2 (S2009/ENE-1477)) and Spanish MEC (ENE2009-14481-C02-02, TEC2011-29120-C05-04, MAT2011-26534).

We have used the ratio of the integrated intensity of graphene's Raman G peak to that of the silicon substrate's first-order optical phonon peak, accurately to determine the number of graphene layers across our molecular-beam (MB) grown graphene films. We find that these results agree well both, with those from our own exfoliated single and few-layer graphene flakes, and with the results of Koh [ACS Nano 5, 269 (2011)]. We hence distinguish regions of single-, bi-, tri-, four-layer, etc., graphene, consecutively, as we scan coarsely across our MB-grown graphene. This is the first, but crucial, step to being able to grow, by such molecular-beam-techniques, a specified number of large-area graphene layers, to order. © 2013 AIP Publishing LLC., Work supported by ONR (N000140610138 and Graphene Muri), EFRC Center for Re-Defining Photovoltaic Efficiency through Molecule Scale Control (award DE-SC0001085), NSF (CHE-0641523), NYSTAR, CSIC-PIF (200950I154), Spanish CAM (Q&C Light (S2009ESP-1503), Numancia 2 (S2009/ENE-1477)), and Spanish MEC (ENE2009-14481-C02-02, TEC2011-29120-C05-04, MAT2011-26534).

García Martínez, Jorge Manuel et al., Comunicación presentada en el 17th European Molecular Beam Epitaxy Workshop (EUROMBE), celebrado en Levi (Finlandia) del 10 al 13 de marzo de 2013., Graphene growth on dielectric substrates has potential to enable new kinds of devices and applications. We explore graphene growth via direct depositing carbon in a MBE environment on different dielectric substrates, such as h-BN and sapphire. The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h-BN) flakes is demonstrated [1]. Formation of single-layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands (see Fig. 1 (a)). Atomic-force microscope images and Raman maps (Fig. 2) reveal that the graphene grown depends on the surface morphology of the h-BN substrates. On h-BN substrates, high quality single layer growth occurs as nano-domains. The growth is governed by the high mobility of the carbon atoms on the h-BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms. We will show also results of graphene growth by MBE on sapphire, where large area growth occurs with monolayer thickness fluctuations., This work is supported by ONR (N000140610138 and Graphene MURI), AFOSR (FA9550-11-1-0010), EFRC Center for Re-Defining Photovoltaic Efficiency through Molecule Scale Control (award DE-SC0001085), NSF (CHE-0641523), NYSTAR, CSIC-PIF (200950I154), Spanish CAM (Q&C Light (S2009ESP-1503), Numancia 2 (S2009/ENE-1477)) and Spanish MEC (ENE2009-14481-C02-02, TEC2011-29120-C05-04, MAT2011-26534).

Jorge M. Garcia...et al., The growth of single layer graphene nanometer size domains by solid carbon source molecular beam epitaxy on hexagonal boron nitride (h‐BN) flakes is demonstrated. Formation of single‐layer graphene is clearly apparent in Raman spectra which display sharp optical phonon bands. Atomic‐force microscope images and Raman maps reveal that the graphene grown depends on the surface morphology of the h‐BN substrates. The growth is governed by the high mobility of the carbon atoms on the h‐BN surface, in a manner that is consistent with van der Waals epitaxy. The successful growth of graphene layers depends on the substrate temperature, but is independent of the incident flux of carbon atoms., This work is supported by ONR (N000140610138 and Graphene MURI), AFOSR (FA9550‐11‐1‐ 0010), EFRC Center for Re‐Defining Photovoltaic Efficiency through Molecule Scale Control (award DE‐SC0001085), NSF (CHE‐0641523), NYSTAR, CSIC‐PIF (200950I154), Spanish CAM (Q&C Light (S2009ESP‐1503), Numancia 2 (S2009/ENE‐1477)) and Spanish MEC (ENE2009‐14481‐C02‐02, TEC2011‐29120‐C05‐04, MAT2011‐26534).

Ulrich Wurstbauer et al., We demonstrate the growth of graphene nanocrystals by molecular beam methods that employ a solid carbon source, and that can be used on a diverse class of large area dielectric substrates. Characterization by Raman and Near Edge X-ray Absorption Fine Structure spectroscopies reveal a sp2 hybridized hexagonal carbon lattice in the nanocrystals. Lower growth rates favor the formation of higher quality, larger size multi-layer graphene crystallites on all investigated substrates. The surface morphology is determined by the roughness of the underlying substrate and graphitic monolayer steps are observed by ambient scanning tunneling microscopy., This work is supported by ONR (N000140610138 and Graphene Muri),AFOSR (FA9550-11-1-0010),EFRC Center for Re-De ning Photovoltaic E ciency through Molecule Scale Control (award de-sc0001085), NSF (CHE-0641523), NYSTAR, CSIC-PIF (200950I154), Spanish CAM (Q&C Light (S2009ESP-1503), Numancia 2 (S2009/ENE- 1477)) and Spanish MICINN (TEC2008-06756-C03-01,TEC2011-29120-C05-04, MAT2011- 26534).

Highly oriented [1 1 0] Bi2Te3 films were obtained by pulsed electrodeposition. The structure, composition, and morphology of these films were characterized. The thermoelectric figure of merit (zT), both parallel and perpendicular to the substrate surface, were determined by measuring the Seebeck coefficient, electrical conductivity, and thermal conductivity in each direction. At 300 K, the in-plane and out-of-plane figure of merits of these Bi2Te3 films were (5.6 ± 1.2)·10−2 and (10.4 ± 2.6)·10−2, respectively., The authors would like to acknowledge partial financial support from ERC StG NanoTEC 240497, National Project No. MAT2011-27911, CONSOLIDER nanotherm, and Intramural Infante 201550E072. M.M.R acknowledges JAE PhD grant from CSIC and the European Social Fund. T.B.T. gratefully acknowledge funding from the US Departament of Energy, Office of Basic Energy Science through the S3TEC Energy Frontiers Research Center.