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Recently, broken symmetry within crystals has been igniting tremendous research interest since it can be utilized to effectively manipulate the propagation of photons. In particular, low-symmetry Bravais crystals can support hyperbolic shear polaritons (HShPs), holding great promise for technological upgrading on the emerging research area of spinoptics. Herein, an Otto-type multilayer structure consisting of KRS5 prism, sensing medium, and monoclinic β-Ga2O3 crystal is designed to ameliorate the photonic spin Hall effect (PSHE). The surface of β-Ga2O3 is the monoclinic (010) plane (x-y plane). We show that giant spin Hall shifts with three (or two) orders of magnitude of the incident wavelength are obtained in the in-plane (or transverse) directions. The azimuthal dispersions of photonic spin Hall shifts present non‐mirror‐symmetric patterns at tuning the rotation angle of β-Ga2O3 around the z axis in plane. All of these exotic optical properties are closely correlated with the broken crystal lattice symmetry and the incurred excitation of HShPs in monoclinic β-Ga2O3 crystal. By virtue of the remarkably enhanced PSHE, our proposed Otto-type multilayer structure shows a superior biosensing performance in which the maximum sensitivity is two orders of magnitude larger than previously reported PSHE biosensors based on two-dimensional materials. In addition, the optimized physical and structural parameters including the incident angle, excitation wavelength, azimuth angle and doping concentration of β-Ga2O3, thickness and refractive index of sensing medium are also investigated and given. This work unequivocally confirms the strong influence of crystal symmetry on the PSHE, shedding important insights into understanding the rich modulation of spin-orbit interaction of light via shear polaritons and therefore facilitating potential applications in photoelectronic devices. 

Previously, the infrared permittivity tensor of monoclinic β-Ga 2 O 3 crystals has been determined using ellipsometry reflection measurements from two differently oriented monoclinic β-Ga 2 O 3 crystals with surfaces parallel to (010) and (−201). The (010) surface places the crystallographic a-c plane in the table of the instrument. The permittivity tensor consists of four complex values, and in order to compute it, four or more combinations of measurements are required at selected table rotations and incidence angles. However, the (010) orientation also places the transverse optical (TO) modes with Au symmetry parallel to the z-axis of the instrument, and we find that these modes are not fully excited and, hence, not measurable due to underlying selection rules. This makes additional measurements on surfaces other than (010) necessary. The second orientation has been the (−201) crystal, which places the crystallographic b axis in the plane of the table to access the transverse Au phonons. In prior work, the overall tensor has been determined by combining measurements of the two crystal orientations [Schubert et al., Phys. Rev. B 93, 125209 (2016)]. The goal of the work here is to find single crystal orientations for which all TO modes can be determined from measurements. The use of a set of measurements employed for such a single crystal is inextricably linked to the choice of incidence angles and table rotations. Consequently, determining suitable angles for these is linked to the selection of a crystal orientation, which is, therefore, an integral part of the overall goal. The TO contribution to the permittivity strongly dominates at or near the TO mode wavenumber resonances and, therefore, are used in this work to identify suitable orientations for a single crystal. Any such crystal orientation will also provide measurements useful to compute permittivity across the entire measured wavenumber range. In principle, any crystal orientation that does not place the direction of any TO mode at or near the z-axis may be suitable due to the underlying physics and mathematics of the problem. We discuss which of these measurement parameters contain the most sensitivity for the (111) orientation. For accuracy, we seek the best or very good orientations. Our investigation follows a previously demonstrated approach where at a single wavelength, the full tensor of an orthorhombic absorbing crystal was obtained from a low-symmetry surface of stibnite [Schubert and Dollase, Opt. Lett. 27, 2073 (2002)]. We discuss which of these measurement parameters contain the most sensitivity for the (111) orientation. The methods presented here will also be useful for other monoclinic materials as well as other materials of different crystal structures, including orthorhombic and triclinic materials. 

We report the effect of remote surface optical (RSO) phonon scattering on carrier mobility in monolayer graphene gated by ferroelectric oxide. We fabricate monolayer graphene transistors back-gated by epitaxial (001) Ba 0.6 Sr 0.4 TiO 3 films, with field effect mobility up to 23 000 cm 2  V −1  s −1 achieved. Switching ferroelectric polarization induces nonvolatile modulation of resistance and quantum Hall effect in graphene at low temperatures. Ellipsometry spectroscopy studies reveal four pairs of optical phonon modes in Ba 0.6 Sr 0.4 TiO 3 , from which we extract RSO phonon frequencies. The temperature dependence of resistivity in graphene can be well accounted for by considering the scattering from the intrinsic longitudinal acoustic phonon and the RSO phonon, with the latter dominated by the mode at 35.8 meV. Our study reveals the room temperature mobility limit of ferroelectric-gated graphene transistors imposed by RSO phonon scattering. 

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. 

Mueller matrix spectroscopic ellipsometry is applied to determine anisotropic optical properties for a set of single-crystal rhombohedral structure α-(Al x Ga 1− x ) 2 O 3 thin films (0 [Formula: see text] x [Formula: see text] 1). Samples are grown by plasma-assisted molecular beam epitaxy on m-plane sapphire. A critical-point model is used to render a spectroscopic model dielectric function tensor and to determine direct electronic band-to-band transition parameters, including the direction dependent two lowest-photon energy band-to-band transitions associated with the anisotropic bandgap. We obtain the composition dependence of the direction dependent two lowest band-to-band transitions with separate bandgap bowing parameters associated with the perpendicular ([Formula: see text] = 1.31 eV) and parallel ([Formula: see text] = 1.61 eV) electric field polarization to the lattice c direction. Our density functional theory calculations indicate a transition from indirect to direct characteristics between α-Ga 2 O 3 and α-Al 2 O 3 , respectively, and we identify a switch in band order where the lowest band-to-band transition occurs with polarization perpendicular to c in α-Ga 2 O 3 whereas for α-Al 2 O 3 the lowest transition occurs with polarization parallel to c. We estimate that the change in band order occurs at approximately 40% Al content. Additionally, the characteristic of the lowest energy critical point transition for polarization parallel to c changes from M 1 type in α-Ga 2 O 3 to M 0 type van Hove singularity in α-Al 2 O 3 . 

We report on the free charge carrier properties of a two-dimensional electron gas (2DEG) in an AlN/Al x Ga 1– x N high electron mobility transistor structure with a high aluminum content ( x =  0.78). The 2DEG sheet density [Formula: see text] cm −2 , sheet mobility [Formula: see text] cm 2 /(Vs), sheet resistance [Formula: see text] [Formula: see text], and effective mass [Formula: see text] at low temperatures [Formula: see text] are determined by terahertz (THz) optical Hall effect measurements. The experimental 2DEG mobility in the channel is found within the expected range, and the sheet carrier density is in good agreement with self-consistent Poisson–Schrödinger calculations. However, a significant increase in the effective mass of 2DEG electrons at low temperatures is found in comparison with the respective value in bulk Al 0.78 Ga 22 N ([Formula: see text]). Possible mechanisms for the enhanced 2DEG effective mass parameter are discussed and quantified using self-consistent Poisson–Schrödinger calculations. 

The hot-wall metalorganic chemical vapor deposition (MOCVD) concept, previously shown to enable superior material quality and high performance devices based on wide bandgap semiconductors, such as Ga(Al)N and SiC, has been applied to the epitaxial growth of β-Ga 2 O 3 . Epitaxial β-Ga 2 O 3 layers at high growth rates (above 1 μm/h), at low reagent flows, and at reduced growth temperatures (740 °C) are demonstrated. A high crystalline quality epitaxial material on a c-plane sapphire substrate is attained as corroborated by a combination of x-ray diffraction, high-resolution scanning transmission electron microscopy, and spectroscopic ellipsometry measurements. The hot-wall MOCVD process is transferred to homoepitaxy, and single-crystalline homoepitaxial β-Ga 2 O 3 layers are demonstrated with a [Formula: see text]01 rocking curve width of 118 arc sec, which is comparable to those of the edge-defined film-fed grown ([Formula: see text]01) β-Ga 2 O 3 substrates, indicative of similar dislocation densities for epilayers and substrates. Hence, hot-wall MOCVD is proposed as a prospective growth method to be further explored for the fabrication of β-Ga 2 O 3 . 

We report the elevated temperature (22 °C [Formula: see text]  T [Formula: see text] 600 °C) dielectric function properties of melt grown single crystal ZnGa 2 O 4 using a spectroscopic ellipsometry approach. A temperature dependent Cauchy dispersion analysis was applied across the transparent spectrum to determine the high-frequency index of refraction yielding a temperature dependent slope of 3.885(2) × 10 −5  K −1 . A model dielectric function critical point analysis was applied to examine the dielectric function and critical point transitions for each temperature. The lowest energy M 0 -type critical point associated with the direct bandgap transition in ZnGa 2 O 4 is shown to red-shift linearly as the temperature is increased with a subsequent slope of −0.72(4) meV K −1 . Furthermore, increasing the temperature results in a reduction of the excitonic amplitude and increase in the exciton broadening akin to exciton evaporation and lifetime shortening. This matches current theoretical understanding of excitonic behavior and critically provides justification for an anharmonic broadened Lorentz oscillator to be applied for model analysis of excitonic contributions. 

We determine the composition dependence of the transverse and longitudinal optical infrared-active phonon modes in rhombohedral α-(Al x Ga 1− x ) 2 O 3 alloys by far-infrared and infrared generalized spectroscopic ellipsometry. Single-crystalline high quality undoped thin-films grown on m-plane oriented α-Al 2 O 3 substrates with x =  0.18, 0.37, and 0.54 were investigated. A single mode behavior is observed for all phonon modes, i.e., their frequencies shift gradually between the equivalent phonon modes of the isostructural binary parent compounds. We also provide physical model line shape functions for the anisotropic dielectric functions. We use the anisotropic high-frequency dielectric constants for polarizations parallel and perpendicular to the lattice c axis measured recently by Hilfiker et al. [Appl. Phys. Lett. 119, 092103 (2021)], and we determine the anisotropic static dielectric constants using the Lyddane–Sachs–Teller relation. The static dielectric constants can be approximated by linear relationships between those of α-Ga 2 O 3 and α-Al 2 O 3 . The optical phonon modes and static dielectric constants will become useful for device design and free charge carrier characterization using optical techniques.