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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↗

Roadmap on thermodynamics and thermal metamaterials

Thermal metamaterials represent a transformative paradigm in modern physics, synergizing thermodynamic principles with metamaterial engineering to master heat flow at will. As next-generation technologies demand multi-scale thermal control, this field urgently requires systematic frameworks to unify its multidisciplinary advances. Curated through a global collaboration involving over 50 specialists across 25 subdisciplines, this review primarily summarizes two decades of advancements, ranging from theoretical breakthroughs to functional implementations. The review reveals groundbreaking innovations in heat manipulation through the exploration of both classical and non-classical transport regimes, topological thermal control mechanisms, and quantum-informed phonon engineering strategies. By bridging physical insights like non-Hermitian thermal dynamics and valleytronic phonon transport with cutting-edge applications, we demonstrate paradigm-shifting capabilities: environment-adaptive thermal cloaks, AI-optimized metamaterials, and nonlinear thermal circuits enabling heat-based computation. Experimental milestones include 3D thermal null media with reconfigurable invisibility and thermal designs breaking classical conductivity limits. Here, this collaborative effort establishes an indispensable roadmap for physicists, highlighting pathways to quantum thermal management, entropy-controlled energy systems, and topological devices. As thermal metamaterials transition from laboratory marvels to technological cornerstones, this work provides the foundational lexicon and design principles for the coming era of intelligent thermal matter.

heat conduction control↗

Physical Behavior of Quantum Metamaterials (Final Report)

We are on the cusp of creating artificial quantum matter through engineered structures that mimic natural atoms and create new electronic and electromagnetic behavior not observed in nature. My objective is to explore new quantum states of matter through creation of engineered quantum meta-atoms and their arrangement into structures that create qualitatively new types of quantum coherent behavior, especially in terms of their interaction with electromagnetic fields. The technical approach involves assembly of superconducting quantum devices that are nominally identical and strongly interacting with each other, and with a bath of microwave photons, and measuring their emergent behavior through their electromagnetic response. The results will give fundamental insights into the nature of condensed matter and specific outcomes include investigation of proposed but un-realized states of matter, emergent quantum phenomena, and controlled super-radiant behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Embedded 3D printing of isotropically enhanced lattice structure with programmable elasticity via three-dimensional fiber alignment

Engineered composites with fiber orientation in a complete three-dimensional (3D) context are highly desired for maximizing structural performance as they mimic the well-organized fiber arrangement in natural composites. However, most fabrication techniques lack the capability for through-plane (z-axis) alignment, limiting the possibility for structural design and performance optimization. In this study, we present an embedded 3D printing approach that enables complete 3D fiber alignment, including region-specific alignment control along the through-plane direction. Our method utilizes the extrusion and suspension of composite inks within a supporting matrix. By regionally adjusting the ink extrusion rate and nozzle translation rate, we locally manipulated the fiber arrangement within the composite 3D architecture. Here, we demonstrate that the 3D alignment of carbon fibers in a structural composite significantly enhances both mechanical properties and thermal conductivity in the in-plane and through-plane directions. Furthermore, by strategically arranging regional fiber orientations within micro-architected materials, we fabricated metamaterial engineered composites with programmable anisotropy ratio and directional moduli.

36 MATERIALS SCIENCE↗

Nonlocal elastic metasurfaces: Enabling broadband wave control via intentional nonlocality

While elastic metasurfaces offer a remarkable and very effective approach to the subwavelength control of stress waves, their use in practical applications is severely hindered by intrinsically narrow band performance. In applications to electromagnetic and photonic metamaterials, some success in extending the operating dynamic range was obtained by using nonlocality. However, while electronic properties in natural materials can show significant nonlocal effects, even at the macroscales, in mechanics, nonlocality is a higher-order effect that becomes appreciable only at the microscales. This study introduces the concept of intentional nonlocality as a fundamental mechanism to design passive elastic metasurfaces capable of an exceptionally broadband operating range. The nonlocal behavior is achieved by exploiting nonlocal forces, conceptually akin to long-range interactions in nonlocal material microstructures, between subsets of resonant unit cells forming the metasurface. These long-range forces are obtained via carefully crafted flexible elements, whose specific geometry and local dynamics are designed to create remarkably complex transfer functions between multiple units. The resulting nonlocal coupling forces enable achieving phase-gradient profiles that are functions of the wavenumber of the incident wave. The identification of relevant design parameters and the assessment of their impact on performance are explored via a combination of semianalytical and numerical models. The nonlocal metasurface concept is tested, both numerically and experimentally, by embedding a total-internal-reflection design in a thin-plate waveguide. Results confirm the feasibility of the intentionally nonlocal design concept and its ability to achieve a fully passive and broadband wave control.

36 MATERIALS SCIENCE↗

Cyclically symmetric radially self-similar phononic pseudocrystal isolator for broadband, ultrasonic vibration bandstop filtering

A 2D phononic pseudocrystal isolator exhibiting cyclic symmetry and radial self-similarity is measured and demonstrated to block a wide range of ultrasonic vibration. Measurements of longitudinal and shear wave blocking effects are made and compared with computational results. The use of the bandgap edge ratio is recommended for quantifying suppression in very-wide-bandgap materials. In conclusion, the upper-to-lower suppression edge frequency ratios of 3–4 are remarkably large for shear waves and even larger for longitudinal waves upper-to-lower suppression ratio (13 at 5 dB), such that 92.5% of frequencies in that range experience ≥ 5 dB of suppression.

Acoustic metamaterial↗

Effect of heating/cooling dynamics in the hysteresis loop and tunable IR emissivity of VO 2 thin films

We experimentally investigate the semiconductor-to-metal transition (SMT) in vanadium dioxide thin films using an infrared thermographic technique. During the semiconductor to metal phase change process, VO 2 optical properties dynamically change and infrared emission undergoes a hysteresis loop due to differences between heating and cooling stages. The shape of the hysteresis loop was accurately monitored under different dynamic heating/cooling rates. In order to quantify and understand the effects of different rates, we used a numerical modelling approach in which a VO 2 thin layer was modeled as metamaterial. The main experimental findings are interpreted assuming that both the rate of formation and shape of metallic inclusions are tuned with the heating/cooling rate. The structural transition from monoclinic to tetragonal phases is the main mechanism for controlling the global properties of the phase transition. However, our experimental results reveal that the dynamics of the heating/cooling process can become a useful parameter for further tuning options and lays out a macroscopic optical sensing scheme for the microscopic phase change dynamics of VO 2 . Our study sheds light on phase-transition dynamics and their effect on the infrared emission spectra of VO 2 thin films, therefore enabling the heating/cooling rate to be an additional parameter to control infrared emission characteristics of thermal emitters. The hysteresis loop represents the phase coexistence region, thus being of fundamental importance for several applications, such as the operation of radiative thermal logic elements based on phase transition materials. For such applications, the phase transition region is shifted for heating and cooling processes. We also show that, depending on the way the phase change elements are heated, the temperature operation range will be slightly modified.

42 ENGINEERING↗

Nanoparticle self-assemblies with modern complexity

Thanks to decades of tireless efforts, nanoparticle assemblies have reached at an extremely high level of controllability, sophistication, and complexity, with new insights provided by integration with graph theory, cutting-edge characterization, and machine learning (ML)-based computation and modeling, as well as with ever-diversifying applications in energy, catalysis, biomedicine, optics, electronics, magnetics, organic biosynthesis, and quantum technology. Nanoparticle assemblies can be crystalline, known as superlattices or supracrystals. Their assembly entails a transition from disorder—dispersed nanoparticles—to order, which can be achieved through classical nucleation pathways or nonclassical pathways via prenucleation precursors or particle aggregation. Further, the periodic lattices allow facile manipulations of electrons, phonons, photons, and even spins, leading to advanced device components and metamaterials. Meanwhile, aperiodic assemblies out of nanoparticles, such as gels, networks, and amorphous solids, also start to attract attentions. Despite the loss of periodicity, symmetry-lowering or symmetry-breaking three-dimensional (3D) structures emerge with unique properties, such as chiroptical activity, topological mechanical strength, and quantum entanglement. Real-space imaging such as electron microscopy and X-ray based tomography methods are utilized to characterize these complex structures, while mathematical tools such as graph theories are in need to describe such complex structures. This issue aims to provide a timely review of the efforts in this greatly broadened materials design space including experiment, simulation, theory, and applications. Nine top experts (and their teams) from four countries deliver six review papers, summarizing fundamental mechanistic understandings of nanoparticle assemblies, highlighted with the developments of state-of-the-art in situ characterization tools and ML-assisted reverse engineering, and newly emergent applications of nanoarchitectures.

36 MATERIALS SCIENCE↗

Helical Photonic Metamaterials for Encrypted Chiral Holograms

Helical structures are among the most quintessential three-dimensional (3D) forms that exhibit mirror asymmetry, a hallmark of chirality. Various structural parameters of helices directly linked to chiroptical properties highlight their importance as essential optical metamaterials for polarization-resolved sensors, imaging, and spectroscopies. However, such function-defining properties remain incompletely understood due to fabrication challenges and the lack of a relationship between structure and optical properties. Here, helical structures are analyzed parametrically, and correlations are established that are applicable to the design of chiral helical optical metamaterials. By systematically varying independent parameters—such as from single-turn to five-turn helices and from small major radii to larger ones optimized to fit the unit cell—the underlying relationships with ellipticty are revealed. In addition to theoretical modeling, the findings are experimentally validated using 3D printing and terahertz spectroscopy. The results demonstrate that optimized helical structures are mechanically tunable and exhibit unprecedented optical properties, including broadband and high-magnitude ellipticity spectra. Being embedded in soft elastomers, helical arrays can serve as soft, stretchable optical-mechanical sensors and holograms containing encoded information, such as barcodes and quick response (QR) codes. Chiral QR codes are realized using pixelated single helices with different handedness, demonstrating their potential as advanced encryption/decryption systems for security applications and chiral metaholograms.

Encrypted QR codes↗

Ultrastrong colloidal crystal metamaterials engineered with DNA

Lattice-based constructs, often made by additive manufacturing, are attractive for many applications. Typically, such constructs are made from microscale or larger elements; however, smaller nanoscale components can lead to more unusual properties, including greater strength, lighter weight, and unprecedented resiliencies. Here, solid and hollow nanoparticles (nanoframes and nanocages; frame size: ~15 nanometers) were assembled into colloidal crystals using DNA, and their mechanical strengths were studied. Nanosolid, nanocage, and nanoframe lattices with identical crystal symmetries exhibit markedly different specific stiffnesses and strengths. Unexpectedly, the nanoframe lattice is approximately six times stronger than the nanosolid lattice. Nanomechanical experiments, electron microscopy, and finite element analysis show that this property results from the buckling, densification, and size-dependent strain hardening of nanoframe lattices. Last, these unusual open architectures show that lattices with structural elements as small as 15 nanometers can retain a high degree of strength, and as such, they represent target components for making and exploring a variety of miniaturized devices.

42 ENGINEERING↗

Physics-informed neural networks for inverse problems in nano-optics and metamaterials

In this paper, we employ the emerging paradigm of physics-informed neural networks (PINNs) for the solution of representative inverse scattering problems in photonic metamaterials and nano-optics technologies. In particular, we successfully apply mesh-free PINNs to the difficult task of retrieving the effective permittivity parameters of a number of finite-size scattering systems that involve many interacting nanostructures as well as multi-component nanoparticles. Our methodology is fully validated by numerical simulations based on the finite element method (FEM). The development of physics-informed deep learning techniques for inverse scattering can enable the design of novel functional nanostructures and significantly broaden the design space of metamaterials by naturally accounting for radiation and finite-size effects beyond the limitations of traditional effective medium theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Easy axis anisotropy creating high contrast magnetic zones on magnetic tunnel junctions based molecular spintronics devices (MTJMSD)

Abstract Magnetic tunnel junction-based molecular spintronics device (MTJMSD) may enable novel magnetic metamaterials by chemically bonding magnetic molecules and ferromagnets (FM) with a vast range of magnetic anisotropy. MTJMSD have experimentally shown intriguing microscopic phenomenon such as the development of highly contrasting magnetic phases on a ferromagnetic electrode at room temperature. This paper focuses on Monte Carlo Simulations (MCS) on MTJMSD to understand the potential mechanism and explore fundamental knowledge about the impact of magnetic anisotropy. The selection of MCS is based on our prior study showing the potential of MCS in explaining experimental results (Tyagi et al. in Nanotechnology 26:305602, 2015). In this paper, MCS is carried out on the 3D Heisenberg model of cross-junction-shaped MTJMSDs. Our research represents the experimentally studied cross-junction-shaped MTJMSD where paramagnetic molecules are covalently bonded between two FM electrodes along the exposed side edges of the magnetic tunnel junction (MTJ). We have studied atomistic MTJMSDs properties by simulating a wide range of easy-axis anisotropy for the case of experimentally observed predominant molecule-induced strong antiferromagnetic coupling. Our study focused on understanding the effect of anisotropy of the FM electrodes on the overall MTJMSDs at various temperatures. This study shows that the multiple domains of opposite spins start to appear on an FM electrode as the easy-axis anisotropy increases. Interestingly, MCS results resembled the experimentally observed highly contrasted magnetic zones on the ferromagnetic electrodes of MTJMSD. The magnetic phases with starkly different spins were observed around the molecular junction on the FM electrode with high anisotropy.

36 MATERIALS SCIENCE↗

A Resonant Metamaterial Line Array for Ultrasound Compressive Imaging

Abstract Acoustic metamaterials have been proposed for numerous applications including subwavelength imaging, impedance matching, and lensing. Yet, their application in compressive sensing and imaging has not been fully investigated. When metamaterials are used as resonators at certain frequencies, they can generate random radiation patterns in the transmitted waves from the transducers and received waves from a target. Compressive sensing favors such randomness inasmuch as it can increase incoherence by decreasing the amount of mutual information between any two different measurements. This study aims at assessing whether the use of resonating metamaterial unit cells in a single-layered non-optimized array between a number of ultrasound transceivers and targets can improve the sensing capacity, point-spread function of the sensing array (their beam focusing ability), and imaging performance in point-like target detection. The theoretical results are promising and can open the way for more efficient metamaterial designs with the aim of enhancing ultrasound imaging with lower number of transceivers compared to the regular systems.

Acoustics↗

Structural metamaterials comprising interpenetrating lattices

Multi-body interpenetrating lattices comprise two or more lattices that interlace or interpenetrate through the same volume without any direct physical connection to each other, wherein energy transfer is controlled by surface interactions. As a result, multifunctional or composite-like responses can be achieved by additive manufacturing of the interpenetrating lattices, even with only a single print material, with programmable interface-dominated properties. As a result, the interpenetrating lattices can have unique mechanical properties, including improved toughness, multi-stable/negative stiffness, and electromechanical coupling.

Boyce, Brad↗

Observation of maxon-like ultrasound in elastic metabeam

We observe maxon-like dispersion of ultrasonic guided waves in elastic metamaterials consisting of a rectangular beam and an array of cylindrical resonators. The pillars act as asymmetric resonators that induce a strong modal hybridization. We experimentally observe the strongly localized maxon mode with zero group velocity. Our study also demonstrates a unique feature of the maxon with a down-shifting peak frequency in space. To reveal the fundamental mechanism, we conduct comprehensive numerical studies on all frieze group symmetries and key geometric parameters.

Materials Science↗