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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

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↗
DOE OSTI2025

Spin density wave and van Hove singularity in the kagome metal CeTi 3 Bi 4

Kagome metals with van Hove singularities near the Fermi level can host intriguing quantum phenomena such as chiral loop currents, electronic nematicity, and unconventional superconductivity. However, to our best knowledge, unconventional magnetic states driven by van Hove singularities–like spin-density waves–have not been observed experimentally in kagome metals. Here, we report the magnetic and electronic structure of the layered kagome metal CeTi 3 Bi 4 , where Ti kagome electronic structure interacts with a magnetic sublattice of Ce 3+ J eff = 1/2 moments. Neutron diffraction reveals an incommensurate spin-density wave ground state of the Ce 3+ moments, coexisting with commensurate antiferromagnetic order across most of the temperature-field phase diagram. The commensurate component is preferentially suppressed by thermal fluctuations and magnetic field, yielding a rich phase diagram involving an intermediate single-Q spin-density wave phase. First-principles calculations and angle-resolved photoemission spectroscopy identify van Hove singularities near the Fermi level, with the observed magnetic propagation vectors connecting their high density of states, strongly suggesting a van Hove singularity-assisted spin-density wave. These findings establish kagome metals LnTi 3 Bi 4 as a model platform where the characteristic electronic structure of the kagome lattice plays a pivotal role in magnetic order.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Superfluid condensate fraction and pairing wave function of the unitary Fermi gas

The unitary Fermi gas is a many-body system of two-component fermions with zero-range interactions tuned to infinite scattering length. Despite much activity and interest in unitary Fermi gas and its universal properties, there have been great difficulties in performing accurate calculations of the superfluid condensate fraction and pairing wave function. In this paper, we present auxiliary-field lattice Monte Carlo simulations using a lattice interaction which accelerates the approach to the continuum limit, thereby allowing for robust calculations of these difficult observables. As a benchmark test, we compute the ground-state energy of 33 spin-up and 33 spin-down particles. As a fraction of the free Fermi gas energy $E_{\text{FG}}$, we find $E_0/E_{\text{FG}}$ = 0.369(2), 0.372(2), using two different definitions of the finite-system energy ratio, in agreement with the latest theoretical and experimental results. We then determine the condensate fraction by measuring off-diagonal long-range order in the two-body density matrix. We find that the fraction of condensed pairs is α = 0.43(2). Further, we also extract the pairing wave function and find the pair correlation length to be $ζ_pk_F$ = 1.8(3)ℏ, where $k_F$ is the Fermi momentum. Provided that the simulations can be performed without severe sign oscillations, the methods we present here can be applied to superfluid neutron matter as well as more exotic $\textit{P}$-wave and $\textit{D}$-wave superfluids.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2023

A Machine Learning–Based Approach to Time-series Wave Identification in the Solar Wind

The Wind spacecraft has yielded several decades of high-resolution magnetic field data, a large fraction of which displays small-scale structures. In particular, the solar wind is full of wavelike fluctuations that appear in both the field magnitude and its components. The nature of these fluctuations can be tied to the properties of other structures in the solar wind, such as shocks, that have implications for the time evolution of the solar wind. As such, having a large collection of wave events would facilitate further study of the effects that these fluctuations have on solar wind evolution. Given the large volume of magnetic field data available, machine learning is the most practical approach to classifying the myriad small-scale structures observed. To this end, a subset of Wind data is labeled and used as a training set for a multibranch 1D convolutional neural network aimed at classifying circularly polarized wave modes. Using this algorithm, a preliminary statistical study of 1 yr of data is performed, yielding about 300,000 wave intervals out of about 5,000,000 solar wind intervals. The wave intervals come about more often in the fast solar wind and at higher temperatures, and the number of waves per day is highly periodic. This machine learning–based approach to wave detection has the potential to be a powerful, inexpensive way to catalog waves throughout decades of spacecraft data.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Convergence of nuclear effective field theory with perturbative pions

The classic paper by Fleming, Mehen, and Stewart (FMS) cast doubts on the convergence of spin-triplet nucleon-nucleon partial wave scattering amplitudes when following the proposal of Kaplan, Savage, and Wise to construct nuclear effective field theory (EFT) around the unitary fermion limit with perturbative pion exchange. FMS identified the subclass of iterated one-pion exchange potential graphs as the cause of this poor convergence, which they showed persisted in the chiral limit. Theoretical tools are developed in this work to compute these Feynman graphs analytically to high order in all angular momentum channels simultaneously, examining the amplitudes computed to seven loops in the $\textit{L = J}$ channels and three loops in the coupled $\textit{L = J}$ ± 1 channels. One finds that there is nothing pathological about the perturbative expansion of a 1/$r^3$ potential in general and that the expansion converges satisfactorily in all partial waves except those with the lowest angular momentum, particularly the $^3P_0$ and the coupled $^3S_1 - ^3D_1$ channels. The results corroborate work by Birse, which suggests possible avenues to explore for improving the range of validity of the EFT expansion.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Spectra of magnetic fields from electroweak symmetry breaking

We characterize magnetic fields produced during electroweak symmetry breaking by nondynamical numerical simulations based on the Kibble mechanism. The generated magnetic fields were thought to have an energy spectrum ∝ k3 for small wave numbers k, but here we show that it is actually a spectrum ∝ k4 along with characteristic fluctuations in the magnetic helicity. Using scaling results from magnetohydro- dynamics simulations for the evolution and assuming that the initial magnetic field is coherent on the electroweak Hubble scale, we estimate the magnetic field strength to be ∼10−13 G on kpc scales at the present epoch for nonhelical fields. For maximally helical fields we obtain ∼10−10 G on Mpc scales. We also give scalings of these estimates for partially helical fields.

Vachaspati, Tanmay [Arizona State University]↗
DOE OSTI2024

Prototype X-ray and Gamma Detection with Cyclotron Radiation Emission Spectroscopy

Cyclotron radiation emission spectroscopy, or CRES, is a novel approach to measuring the energy of an electron. By trapping a free electron in a high magnetic field, it undergoes cyclotron motion and emits radiofrequency (RF) waves. The frequency of this RF radiation is directly related to the energy of the electron. Because many cycles of the RF emission are recorded, the energy resolution of the CRES system is on the order of a single electron volt. To make a CRES system sensitive to photons, a target gas is used to induce a photoelectric effect, producing the electron that is subsequently trapped. By adding the binding energy of the target atom, the energy of the incident photon may be reconstructed. Using a xenon target gas, photoelectric interactions dominate up to approximately 300 keV, covering not only all atomic shell X-rays of the elements, but many low-lying nuclear states as well, including key transuranic elements related to nuclear security. CRES holds the potential of maintaining single-eV resolution up to this 300-keV range, thereby surpassing current state-of-the-art detectors by a factor of 10-100. The instrumental resolution of the system is limited by the uniformity of the applied magnetic field.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2024

Celestial gluon amplitudes from the outside in

We show that, given a two-dimensional realization of the celestial OPE in self-dual Yang-Mills, we can find a scalar source around which scattering amplitudes replicate correlation functions computed from the 2D ‘gluon’ operators in a limit where a dynamic massless scalar decouples. We derive conditions on the two-dimensional three-point correlation function so that such a source exists and give two particular examples of this construction, one in which gluons are constructed from vertex operators in the semiclassical limit of Liouville theory and another in which the soft gluons arise from generalized free fields. Finally, we identify a bulk dual to the level of the boundary Kac-Moody algebra and discuss moving beyond the decoupling limit.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Identification of a nematic pair density wave state in Bi 2 Sr 2 CaCu 2 O 8+x

Electron-pair density wave (PDW) states are now an intense focus of research in the field of cuprate correlated superconductivity. PDWs exhibit periodically modulating superconductive electron pairing that can be visualized directly using scanned Josephson tunneling microscopy (SJTM). Although from theory, intertwining the d-wave superconducting (DSC) and PDW order parameters allows a plethora of global electron-pair orders to appear, which one actually occurs in the various cuprates is unknown. In this work, we use SJTM to visualize the interplay of PDW and DSC states in Bi 2 Sr 2 CaCu 2 O 8+x at a carrier density where the charge density wave modulations are virtually nonexistent. Simultaneous visualization of their amplitudes reveals that the intertwined PDW and DSC are mutually attractive states. Then, by separately imaging the electron-pair density modulations of the two orthogonal PDWs, we discover a robust nematic PDW state. Its spatial arrangement entails Ising domains of opposite nematicity, each consisting primarily of unidirectional and lattice commensurate electron-pair density modulations. Further, we demonstrate by direct imaging that the scattering resonances identifying Zn impurity atom sites occur predominantly within boundaries between these domains. This implies that the nematic PDW state is pinned by Zn atoms, as was recently proposed [Lozano et al., Phys. Rev. B 103, L020502 (2021)]. Taken in combination, these data indicate that the PDW in Bi 2 Sr 2 CaCu 2 O 8+x is a vestigial nematic pair density wave state [Agterberg et al. Phys. Rev. B 91, 054502 (2015); Wardh and Granath arXiv:2203.08250].

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Canted antiferromagnetic order and spin dynamics in the honeycomb-lattice compound Tb 2 Ir 3 Ga 9

Here, single-crystal neutron diffraction, inelastic neutron scattering, bulk magnetization measurements, and first-principles calculations are used to investigate the magnetic properties of the honeycomb lattice Tb 2 Ir 3 Ga 9 . While the R ln 2 magnetic contribution to the low-temperature entropy indicates a J eff = 1 / 2 moment for the lowest-energy crystal-field doublet, the Tb 3 + ions form a canted antiferromagnetic structure below 12.5 K. Due to the Dzyaloshinskii-Moriya interactions, the Tb moments in the a b plane are slightly canted towards b with a canted moment of 1.22 μ B per formula unit. A minimal x x z spin Hamiltonian is used to simultaneously fit the spin-wave frequencies along the high-symmetry directions and the field dependence of the magnetization along the three crystallographic axes. Long-range magnetic interactions for both in-plane and out-of-plane couplings up to the second nearest neighbors are needed to account for the observed static and dynamic properties. The z component of the exchange interactions between Tb moments is larger than the x and y components. This compound also exhibits bond-dependent exchange with negligible nearest-neighbor exchange coupling between moments parallel and perpendicular to the 4 f orbitals. Despite the J eff = 1 / 2 moments, the spin Hamiltonian is denominated by a large in-plane anisotropy K z ~ – 1 meV . DFT calculations confirm the antiferromagnetic ground state and the substantial interplane coupling at larger Tb-Tb distances.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Interference in nonlinear Compton scattering using a Schrödinger-equation approach

The interference between Compton scattering and nonlinear Compton scattering from a two-color field in the X-ray regime is theoretically examined for bound electrons. Here, the underlying phase shifts are analyzed using a perturbative approach in the incoming classical field. The perturbative approach is bench marked with a non-perturbative approach in the classical field. The interference for different combinations of linear polarization of the two fields is examined when the Compton and the nonlinear Compton scattered waves have the same wave vector and polarization. Only two cases exhibit interference. When there is interference, the calculations reveal an intrinsic phase difference between the Compton scattered wave function and the nonlinear Compton scattered wave function of either 0 or pi depending on the scattering angle.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

3D printing of High Precision Radiation Filters for next generation Cosmic Background (CMB) studies (Final Report)

The terahertz (THz) spectral range is the part of the electromagnetic spectrum between 0.1–10 THz or 0.03–3 mm wavelength. For a long period, the terahertz band was relatively unexplored due to the unavailability of cost-effective and powerful sources. Due to the evolution of these devices in the mid-1980s, however, terahertz radiation has attracted much more attention. Since this part of the spectrum is between the infrared (IR) and microwave frequency ranges, the development of waveguides, filters, polarizers, lenses, and other optical components. Since terahertz waves to penetrate most dielectric materials offers the possibility of many applications. Since terahertz radiation can pass through organic tissue without causing damage, and it can be safely applied for biomedical applications. Radio astronomy and wireless communication are also fields with great interest in this spectral range. For example, terahertz waves could be used to detect cold bodies and debris in space or to increase data transmission using the larger bandwidth of the terahertz band.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

A magnon band analysis of GdRu 2 Si 2 in the field-polarized state

Understanding the formation of skyrmions in centrosymmetric materials is a problem of fundamental and technological interest. GdRu 2 Si 2 is a candidate material that hosts a variety of multi-Q magnetic phases, including in zero-field. Here, inelastic neutron scattering is used to measure the spin excitations in the field-polarized phase of GdRu 2 Si 2 . Linear spin wave theory and a method of interaction invariant path analysis are used to derive a Hamiltonian accounting for the spectra. The Hamiltonian, dominated by bilinear (Ruderman-Kittel-Kasuya-Yosida) Heisenberg exchange, compares favorably to ab initio calculations. Dipolar interactions are a secondary energy scale to consider, with J D.D ~ 0.05 J RKKY . However, it is shown that in the field-polarized phase the dipolar interactions ‘self screen’ so that their effect is largely suppressed. No specific evidence for higher-order exchange is found. These aspects are discussed in the context of the lower field multi-Q states and the anisotropy of the system.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Spin waves and high-frequency response in layered superconductors with helical magnetic structure

Here, we evaluate the spin-wave spectrum and dynamic susceptibility in a layered superconductor with helical interlayer magnetic structure. We especially focus on the structure in which the moments rotate 90 degrees from layer to layer realized in the iron pnictide RbEuFe 4 As 4 . While in nonmagnetic superconductors low-frequency magnetic field decays on the distance of the order of the London penetration depth, spin waves mediate its propagation to much larger distances limited by external dissipation mechanisms. The spin-wave spectrum in superconductors is strongly renormalized due to the long-range electromagnetic interactions between the oscillating magnetic moments. This leads to strong enhancement of the frequency of the mode coupled with uniform field and this enhancement exists only within a narrow range of the c-axis wave vectors of the order of the inverse London penetration depth. The key feature of materials like RbEuFe 4 As 4 is that this uniform mode corresponds to the maximum frequency of the spin-wave spectrum with respect to the c-axis wave vector. As a consequence, the high-frequency surface resistance acquires a very distinct asymmetric feature spreading between the bare and renormalized frequencies. Finally, we also consider excitation of spin waves with the Josephson effect in a tunneling contact between helical-magnetic and conventional superconductors and study the interplay between the spin-wave features and geometrical cavity resonances in the current-voltage characteristics.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Upper-Hybrid Waves Driven by Meandering Electrons Around Magnetic Reconnection X Line

Magnetic reconnection is a fundamental process in collisionless space plasma environment, and plasma waves relevant to the kinetic interactions can have a significant impact on the multiscale behavior of reconnection. Here, we present Magnetospheric Multiscale (MMS) observations during an encounter of an X line of symmetric magnetic reconnection in the magnetotail. The X line is characterized by reversals of ion and electron jets and electromagnetic fields, agyrotropic electron velocity distribution functions (VDFs), and an electron-scale current sheet. MMS observe large-amplitude nonlinear upper-hybrid (UH) waves on both sides of the neutral line, and the wave amplitudes have highly localized distribution along the normal direction. Here, the inbound meandering electrons drive the UH waves, releasing the free energy stored from the reconnection electric field along the meandering trajectories. The interaction between the meandering electrons and the UH waves may modify the balance of the reconnection electric field around the X line.

58 GEOSCIENCES↗
DOE OSTI2020

Magnetic order and fluctuations in the quasi-two-dimensional planar magnet Sr( Co 1-x Ni x ) 2 As 2

We use neutron scattering to investigate spin excitations in Sr ( Co 1 - x Ni x ) 2 As 2 , which has a c -axis incommensurate helical structure of the two-dimensional (2D) in-plane ferromagnetic (FM) ordered layers for 0.013 ≤ x ≤ 0.25 . By comparing the wave vector and energy dependent spin excitations in helical ordered Sr ( Co 0.9 Ni 0.1 ) 2 As 2 and paramagnetic SrCo 2 As 2 , we find that Ni doping, while increasing lattice disorder in Sr ( Co 1 - x Ni x ) 2 As 2 , enhances quasi-2D FM spin fluctuations. However, our band structure calculations within the combined density functional theory and dynamic mean field theory ( DFT + DMFT ) failed to generate a correct incommensurate wave vector for the observed helical order from nested Fermi surfaces. Furthermore, since transport measurements reveal increased in-plane and c -axis electrical resistivity with increasing Ni doping and associated lattice disorder, we conclude that the helical magnetic order in Sr ( Co 1 - x Ni x ) 2 As 2 may arise from a quantum order-by-disorder mechanism through the itinerant electron mediated Ruderman-Kittel-Kasuya-Yosida (RKKY) interactions.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Partial-wave decomposition of the Keldysh ionization amplitude

We present an alternative way of calculating the Keldysh amplitude, i.e., the length-gauge form of the ionization amplitude in the strong-field approximation. The amplitude is evaluated exactly by expanding it in Fourier components and partial waves. Comparisons of the semianalytic model predictions with results of ab initio numerical simulations of the time-dependent Schrödinger equation for the interaction of electrons in short-range potentials with intense laser light yield excellent agreement, for wavelengths from the single photon to the multiphoton to the tunneling regime. Specifically, for ionization from initial states with higher angular momentum quantum number, e.g., p states, a significant improvement over predictions based on the popular saddle-point approximation is found. Furthermore, the current model rate allows for interpretation of the strong-field ionization process in terms of multiphoton absorption pathways and angular momentum selection rules.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Coherent spin wave excitation with radio-frequency spin–orbit torque

Spin waves, collective perturbations of magnetic moments, are both fundamental probes for magnetic physics and promising candidates for energy-efficient signal processing and computation. Traditionally, coherent propagating spin waves have been generated by radio frequency (RF) inductive Oersted fields from current-carrying electrodes. An alternative mechanism, spin–orbit torque (SOT), offers more localized excitation through interfacial spin accumulation but has been mostly limited to DC to kHz frequencies. SOT driven by RF currents, with potentially enhanced pumping efficiency and unique spin dynamics, remains largely unexplored, especially in magnetic insulators. Here, we conduct a comprehensive theoretical and computational investigation into the generation of coherent spin waves via RF-SOT in the prototypical yttrium iron garnet. We characterize the excitation of forward volume, backward volume, and surface modes in both linear and nonlinear regimes, employing single and interdigitated electrode configurations. We reveal and explain several unique and surprising features of RF-SOT compared to inductive excitation, including higher efficiency, distinct mode selectivity, and directional symmetry, a ~ $3π/4$ phase offset, reduced anharmonic distortion in the nonlinear regime, and the absence of second harmonic generation. These insights position RF-SOT as a promising new mechanism for future magnonic and spintronic applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗