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NASA NTRS1992

Laser Scanner Tests For Single-Event Upsets

Microelectronic advanced laser scanner (MEALS) is opto/electro/mechanical apparatus for nondestructive testing of integrated memory circuits, logic circuits, and other microelectronic devices. Multipurpose diagnostic system used to determine ultrafast time response, leakage, latchup, and electrical overstress. Used to simulate some of effects of heavy ions accelerated to high energies to determine susceptibility of digital device to single-event upsets.

Kim, Quiesup↗

NASA NTRS2006

Elimination of Potential Electrical Stress During EMC (CS01) Testing

This viewgraph presentation reviews possible ways to eliminate electrical stress during Electromagneticic Compatibility (EMC) testing. The presentation reviews tests that have had problems due to electrical stress. On December 5, 1995 Cassini Radar instrument failed a functional test in preparation for EMC conducted susceptibility (CSO 1 ) testing. The instrument power supply did not turn on as required, and failure occurred prior to injection of CS test stimulus. A investigation of the failure was conducted. A PSPICE simulation of Cassini Radar 30V line using the EMC test setup was performed; the result of the simulation was an oscillation on the 30V input of the power supply. In another case: on December 28, 1999 an oscillation occurred on the input power line of the SlRTF Infrared Array Camera (IRAC) while preparing to perform CSOI testing, Resulted in damage to flight hardware. Subsequent to failure, JPL provided GSFC history and corrective action from Cassini Radar CSOI test failure GSFC implemented the same corrective action as JPL, except that the value of the resistor connected across the isolation transformer primary winding is 2.5 ohms instead of 50 ohms. Three recommendations are made: (1) Make EMC test community aware of the problem and potential solutions by presenting papers at major environmental test conferences (2) Include warnings and safeguards in EMC test requirements and procedures (3) Try to convince EMC test equipment suppliers to design a CSOl test fixture similar to fixture shown in the diagram

Cassini radar↗

DOE OSTI2025

Strain-induced lead-free morphotropic phase boundary

Enhanced susceptibilities in ferroelectrics often arise near phase boundaries between competing ground states. While chemically-induced phase boundaries have enabled ultrahigh electrical and electromechanical responses in lead-based ferroelectrics, precise chemical tuning in lead-free alternatives, such as (K,Na)NbO 3 thin films, remains challenging due to the high volatility of alkali metals. Here, we demonstrate strain-induced morphotropic phase boundary-like polymorphic nanodomain structures in chemically simple, lead-free, epitaxial NaNbO 3 thin films. Combining ab initio simulations, thin-film epitaxy, scanning probe microscopy, synchrotron X-ray diffraction, and electron ptychography, we reveal a labyrinthine structure comprising coexisting monoclinic and bridging triclinic phases near a strain-induced phase boundary. The coexistence of energetically competing phases facilitates field-driven polarization rotation and phase transitions, giving rise to a multi-state polarization switching pathway and large enhancements in dielectric susceptibility and tunability across a broad frequency range. Our results open new possibilities for engineering lead-free thin films with enhanced functionalities for next-generation applications.

Electronic properties and materials↗

DOE OSTI2025

IM3 Projected US Data Center Locations

IM3 Projected US Data Center Locations This dataset contains model projections of new data center facilities in the contiguous United States (CONUS) through 2035 using the CERF – Data Centers model. Data center locations are modeled across four data center electricity demand growth scenarios (low, moderate, high, higher) and five market gravity scenarios (0%, 25%, 50%, 75%, 100%). Projected locations are intended to be regional representations of feasible siting locations in the future to assess potential grid and water stress impacts. The data center load growth scenarios correspond with the rates outlined in EPRI (2024) and include 3.71%, 5%, 10%, and 15% annual growth of electricity demand for data centers from 2023 values in 37 states across the CONUS. Market gravity scenarios correspond to the relative importance of proximity to data center markets or high population areas compared to locational cost in the siting algorithm. 0% market gravity means that siting decisions were entirely determined by the locational cost in each feasible location. 100% market gravity means that only market proximity was considered when siting. Other scenarios have weight placed on both components where total weight always equals 100%. Locational cost is dependent on facility cooling type and corresponding electricity cost, taxes, and other factors. Facility cooling type is spatially determined where high water stress and/or areas with high summer wet bulb temperatures are assumed to operate with mechanical cooling for a higher fraction of the year rather than evaporative cooling. Feasible data center siting areas are based on geospatial suitability raster data developed with open-source information. The following areas are excluded from siting: Areas within 300 m of a federal airport runway Waterbodies Areas with slope >16% Areas susceptible to sinkholes High coastal or inland flood risk areas Local, state, and federal parks, leisure areas, and cemeteries Areas >2 km away from electric substations Areas >5 km away from a municipal water supplier service area Areas >2 km away from high-speed fiber provider service territory Protected Areas Database of the United States (PAD-US) areas Railroads, major roadways, and minor roadways Military areas and training grounds NLCD developed lands Areas >0.8 km (0.5 miles) from NLCD developed lands Because we use open-source information, proprietary information that can influence siting decisions such as individual tax agreements with cities, detailed fiber line connectivity, electric grid power capacity agreements, and others, are not currently accounted for in the modeling process. Using specific building locations and footprints in the dataset for local planning purposes is not advised. Technical Information Geospatial data is provided in geojson format using the Albers Equal Area Conic (ESRI:102003) coordinate reference system. The datasets contain the following parameters: id - unique identification number within given scenario file growth_scenario – data center demand growth scenario market_gravity_weight – market gravity weight scenario (%) region – name of region (i.e., US State) total_cost_million_usd – locational siting cost ($million) campus_size_square_ft – total land acquired for data center facility (square ft) data_center_it_power_mw – IT power of data center facility (MW) mechanical_cooling_frac – fraction of year when data center uses mechanical cooling system water_cooling_frac– fraction of year when data center uses evaporative cooling system cooling_energy_demand_mwh – total annual facility energy demand for cooling (MWh) cooling_water_demand_mgy – total annual facility water demand for cooling (MG) cooling_water_consumption_mgy – total annual facility water consumed (MG) normalized_locational_cost – normalized total locational cost score for location normalized_gravity_score – normalized market gravity score for location weighted_siting_score – total weighted siting score of locational cost and gravity score geometry – polygon geometry of facility Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License This data is made available under a CCBY4.0 License Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall (ORCID:0000000328077088)↗

NASA NTRSDate not supplied

Evaluation of Contact Separation Force Testing as a Screening Methodology for Electrical Socket Contacts

During system level testing intermittent and permanent open circuit failures of mated, crimp removable, electrical contact pairs were experienced. The root cause of the failures was determined to be low (but not zero) contact forces applied by the socket contact tines against the engaging pin. The low contact force reduces the effectiveness of the wiping action of the socket tines against the pin. The observed failure mode may be produced when insufficient wiping during mate, demate and small relative movement in use allows for the accumulation of debris or insulating films that electrically separate the contact pair. The investigation identified at least three manufacturing process control problems associated with the socket contacts that enabled shipment of contacts susceptible to developing low contact forces: (1) Improper heat treatment of the socket tines resulting in plastic rather than elastic behavior; (2) Overly thinned socket tines at their base resulting in reduced pin retention forces; (3) Insufficient screening tests to identify parts susceptible to the aforementioned failure mechanisms. The results from an extensive screening program of socket contacts utilizing the industry standard contact separation force test procedures are described herein. The investigation shows this method to be capable of identifying initially weak sockets. However, sockets whose contact retention forces may degrade during use may not be screened out by pin retention testing alone. Further investigations are required to correlate low contact retention forces with increased electrical contact resistance in the presence of insulating films that may accumulate in the use environment.

Christopher Green↗

NASA NTRS1997

Performance Comparison Between NiH2 Dry Sinter and Slurry Electrode Cells

The electrical and thermal performance of dry sinter and slurry process electrode cells manufactured for the Hubble Space Telescope (HST) batteries have been characterized for a matrix of operating conditions over the temperature range from 14 to 86 F at various charge control levels. The dry sinter process electrode cells tested are similar to the onboard HST NiH2 cells. The slurry process electrode cells were developed to be less susceptible to electrode expansion and impedance changes with life. Both cell types were impregnated by the aqueous electrochemical process. Test conditions included standard capacity tests and electrical cycling using 96-minute cycling regimens incorporating gr depth-of-discharge (DOD) cycles. The dry sinter process electrodes have higher operating capacities to 1.20V/cell, but both electrode types have similar heat dissipation for the conditions tested. The results of the testing included cyclic heat generation during a typical 96-minute cycle, operating capacity data vs. cutoff voltage to generate a temperature-compensated voltage curve, and voltage characteristics suitable to develop a voltage prediction model. Analysis of data shows differences in the discharge voltage plateaus operating conditions evaluated. This is the basis for recommended changes in the battery charge control.

Armantrout, J. D.↗

DOE OSTI2026

IM3 Projected US Data Center Locations

IM3 Projected US Data Center Locations This dataset contains model projections of new data center facilities in the contiguous United States (CONUS) through 2035 using the CERF – Data Centers model. Data center locations are modeled across four data center electricity demand growth scenarios (low, moderate, high, higher) and five market gravity scenarios (0%, 25%, 50%, 75%, 100%). Projected locations are intended to be regional representations of feasible siting locations in the future to assess potential grid and water stress impacts. The data center load growth scenarios correspond with the rates outlined in EPRI (2024) and include 3.71%, 5%, 10%, and 15% annual growth of electricity demand for data centers from 2023 values in 37 states across the CONUS. Market gravity scenarios correspond to the relative importance of proximity to data center markets or high population areas compared to locational cost in the siting algorithm. 0% market gravity means that siting decisions were entirely determined by the locational cost in each feasible location. 100% market gravity means that only market proximity was considered when siting. Other scenarios have weight placed on both components where total weight always equals 100%. Locational cost is dependent on facility cooling type and corresponding electricity cost, taxes, and other factors. Facility cooling type is spatially determined where high water stress and/or areas with high summer wet bulb temperatures are assumed to operate with mechanical cooling for a higher fraction of the year rather than evaporative cooling. Feasible data center siting areas are based on geospatial suitability raster data developed with open-source information. The following areas are excluded from siting: Areas within 300 m of a federal airport runway or within an airport area boundary Waterbodies Areas with slope >16% Areas susceptible to sinkholes High coastal or inland flood risk areas Local, state, and federal parks, leisure areas, and cemeteries Areas >2 km away from electric substations Areas >5 km away from a municipal water supplier service area Areas >2 km away from high-speed fiber provider service territory USGS Protected Areas Database of the United States (PAD-US) GAP status 1, 2, or 3 areas US National Parks Wetlands USFWS critical habitats BIA land areas Railroads, major roadways, and minor roadways Military areas and training grounds NLCD developed lands Areas >0.8 km (0.5 miles) from NLCD developed lands Because we use open-source information, proprietary information that can influence siting decisions such as individual tax agreements with cities, detailed fiber line connectivity, electric grid power capacity agreements, and others, are not currently accounted for in the modeling process. Using specific building locations and footprints in the dataset for local planning purposes is not advised. Technical Information Geospatial data is provided in geojson format using the Albers Equal Area Conic (ESRI:102003) coordinate reference system. The datasets contain the following parameters: id - unique identification number within given scenario file growth_scenario – data center demand growth scenario market_gravity_weight – market gravity weight scenario (%) region – name of region (i.e., US State) total_cost_million_usd – locational siting cost ($million) campus_size_square_ft – total land acquired for data center facility (square ft) data_center_it_power_mw – IT power of data center facility (MW) mechanical_cooling_frac – fraction of year when data center uses mechanical cooling system water_cooling_frac– fraction of year when data center uses evaporative cooling system cooling_energy_demand_mwh – total annual facility energy demand for cooling (MWh) cooling_water_demand_mgy – total annual facility water demand for cooling (MG) cooling_water_consumption_mgy – total annual facility water consumed (MG) normalized_locational_cost – normalized total locational cost score for location normalized_gravity_score – normalized market gravity score for location weighted_siting_score – total weighted siting score of locational cost and gravity score geometry – polygon geometry of facility Acknowledgment IM3 is a multi-institutional effort led by Pacific Northwest National Laboratory and supported by the U.S. Department of Energy's Office of Science as part of research in MultiSector Dynamics, Earth and Environmental Systems Modeling Program. License This data is made available under a CCBY4.0 License Disclaimer This material was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the United States Department of Energy, nor the Contractor, nor any or their employees, nor any jurisdiction or organization that has cooperated in the development of these materials, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness or any information, apparatus, product, software, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof, or Battelle Memorial Institute. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. PACIFIC NORTHWEST NATIONAL LABORATORYoperated byBATTELLEfor theUNITED STATES DEPARTMENT OF ENERGYunder Contract DE-AC05-76RL01830

Mongird, Kendall (ORCID:0000000328077088)↗

NASA NTRS1975

Role of magnetic fields in physics and astrophysics; Proceedings of the Conference, Copenhagen, Denmark, June 5-7, 1974

The papers deal with the role of magnetism in astrophysics and the properties of matter in the presence of unusually large magnetic fields. Topics include a quantum-mechanical treatment of high-energy charged particles radiating in a homogeneous magnetic field, the solution and properties of the Dirac equation for magnetic fields of any strength up to 10 to the 13th power gauss, experimental difficulties encountered and overcome in generating megagauss fields, the effect of strong radiation damping for an ultrarelativistic charge in an external electromagnetic field, magnetic susceptibilities of nuclei and elementary particles, and Compton scattering in strong external electromagnetic fields. Other papers examine static uniform electric and magnetic polarizabilities of the vacuum in arbitrarily strong magnetic fields, quantum-mechanical processes in neutron stars, basic ideas of mean-field magnetohydrodynamics, helical MHD turbulence, relations between cosmic and laboratory plasma physics, and insights into the nature of magnetism provided by relativity and cosmology. Individual items are announced in this issue.

Canuto, V.↗

DOE OSTI2023

Dispersion of stored energy within a battery system at risk of failure

A method and system for dispersing stored energy in an energy storage system to delay or arrest propagation of thermal runaway and thermally-induced cascading failures. The system includes a plurality of battery sub-assemblies and DC-DC converters connected to a shared DC bus through which energy may be exchanged. The system may be interfaced to an AC power grid or DC power system through an additional power converter. The method of dispersing stored energy uses this system to charge and discharge sub-assemblies such that the system is less susceptible to propagation of thermal runaway. The method determines, based on awareness of current system state, battery types, and electrical and thermal structure, the sequence of charging and discharging actions to best inhibit thermal runaway while preserving the system's ability to perform subsequent energy redistribution.

Mueller, Jacob↗

NASA NTRS2000

Magnetic Susceptibility Effects and Lorentz Damping in Diamagnetic Fluids

A great number of crystals (semi-conductor and protein) grown in space are plagued by convective motions which contribute to structural flaws. The character of these instabilities is not well understood but is associated with density variations in the presence of residual gravity and g-jitter. Both static and dynamic (rotating or travelling wave) magnetic fields can be used to reduce the effects of convection in materials processing. In semi-conductor melts, due to their relatively high electrical conductivity, the induced Lorentz force can be effectively used to curtail convective effects. In melts/solutions with reduced electrical conductivity, such as aqueous solutions used in solution crystal growth, protein crystal growth and/or model fluid experiments for simulating melt growth, however, the variation of the magnetic susceptibility with temperature and/or concentration can be utilized to better damp fluid convection than the Lorentz force method. This paper presents a comprehensive, comparative numerical study of the relative damping effects using static magnetic fields and gradients in a simple geometry subjected to a thermal gradient. The governing equations are formulated in general terms and then simplified for the numerical calculations. Operational regimes, based on the best damping technique for different melts/solutions are identified based on fluid properties. Comparisons are provided between the numerical results and available results from experiments in surveyed literature.

Ramachandran, Narayanan↗

DOE OSTI2024

Impacts of Climate Change on the Generation Potential of Solar and Wind Energy Systems in India

Low-carbon energy sources like wind and solar are essential for decarbonizing the electricity sector. In addition, the cost of electricity generated from these sources has plummeted over the last decade. Therefore, these energy sources are poised to take a significant share of the total installed capacity soon. However, they are susceptible to the impacts of climate change as their generation potential depends on the weather conditions. Estimating the installed capacity requirements of solar and wind energy to decarbonize the power sector without accounting for these possible changes in generation potential could lead to missing out on the set climate goals and meeting future electricity demand. This study evaluates the effect of climate change on the generation potential of wind and solar energy systems in India for two future periods, 2050 and 2070, under two climate scenarios or Shared Socioeconomic Pathway (SSP): SSP245 and SSP585. Almost all regions show a decrease, and most regions show a significant decline (>5%) in the generation potential of solar Photovoltaic (PV) as compared to 2010 levels under both climate scenarios and future periods. The changes in the generation potential of wind energy are more significant (>10%), and the majority of regions show a decline in generation potential. Southwestern and central regions show an increase in wind generation potential for 2070 as compared to 2050 levels under the SSP245 scenario and the SSP585 scenario, respectively.

climate change↗

DOE OSTI2021

Experimental evidence that zinc impurities pin pair-density-wave order in La 2-x Ba x CuO 4

Both Zn doping and c-axis magnetic fields have been observed to increase the spin stripe order in La 2-x Ba x CuO 4 with x close to 1/8. For x = 0.095, the applied magnetic field also causes superconducting layers to decouple, presumably by favoring pair-density-wave order that consequently frustrates interlayer Josephson coupling. Here we show that introducing 1% Zn also leads to an initial onset of two-dimensional (2D) superconductivity, followed by 3D superconductivity at lower temperatures, even in zero field. Overall, we infer that the Zn pins pair-density-wave order locally, establishing the generality of such behavior.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Physical properties of the layered $\mathcal{f}$-electron van der Waals magnet Ce 2 Te 5

Here. we report a detailed study of the magnetic, transport, and thermodynamic properties of Ce 2 Te 5 single crystals, a layered $\mathcal{f}$-electron van der Waals magnet. Four consecutive transitions at ~5.2, 2.1, 0.9, and 0.4 K were observed in the ac-plane electrical resistivity $\rho(T)$, which were further confirmed in specific heat $C_\text{p}(T)$ measurements. Analysis of the magnetic susceptibility $\chi(T)$, the magnetic-field variation of $\rho(T)$, and the increase of the first transition temperature ($T_c$ ~ 5.2 K) with applied magnetic field indicates ferromagnetic order, while the decrease of the other transitions with field suggests different states with dominant antiferromagnetic interactions below $T_2$ ~ 2.1 K, $T_3$ ~ 0.9 K, and $T_4$ = 0.4 K. Critical behavior analysis around Tc that gives critical exponents $\beta$ = 0.31(2), $\gamma$ = 0.99(2), $\delta$ = 4.46(1), and $T_c$ = 5.32(1) K indicates that Ce 2 Te 5 shows a three-dimensional magnetic critical behavior. Moreover, the Hall resistivity ρxy indicates that Ce2Te5 is a multiband system with a relatively high electron mobility ~2900 cm 2 V –1 s –1 near $T_c$, providing further opportunities for future device applications.

36 MATERIALS SCIENCE↗

NASA NTRS2000

Process of changing the refractive index of a composite containing a polymer and a compound having large dipole moment and polarizability and applications thereof

Fused ring bridge, ring locked dyes that form thermally stable photorfractive compositions. The fused ring bridge structures are .pi.-conjugated bonds in benzene-, naphthalene- or anthracene-derived fused ring systems that connect donor and acceptor groups. The donor and acceptor groups contribute to a high molecular dipole moment and linear polarizability anisotropy. The polarization characteristics of the dye molecules are stabilized since the bonds in the fused ring bridge are not susceptible to rotation, reducing the opportunity for photoisomerization. The dyes are compatible with polymeric compositions, including thermoplastics. The dyes are electrically neutral but have charge transport, electronic and orientational properties such that upon illumination of a composition containing the dye, the dye facilitates refractive index modulation and a photorefractive effect that can be utilized advantageously in numerous applications such as in optical quality devices and biological imaging.

Marder, Seth R.↗

NASA NTRS2002

Thermally stable molecules with large dipole moments and polarizabilities and applications thereof

Disclosed are fused ring bridge, ring-locked dyes that form thermally stable photorefractive compositions. The fused ring bridge structures are .pi.-conjugated bonds in benzene-, naphthalene- or anthracene-derived fused ring systems that connect donor and acceptor groups. The donor and acceptor groups contribute to a high molecular dipole moment and linear polarizability anisotropy. The polarization characteristics of the dye molecules are stabilized since the bonds in the fused ring bridge are not susceptible to rotation, reducing the opportunity for photoisomerization. The dyes are compatible with polymeric compositions, including thermoplastics. The dyes are electrically neutral but have charge transport, electronic and orientational properties such that upon illumination of a composition containing the dye, the dye facilitates refractive index modulation and a photorefractive effect that can be utilized advantageously in numerous applications such as in optical quality devices and biological imaging.

Marder, Seth R.↗

DOE OSTI2020

Nonlinear waves in a thin dielectric film on the surface of a topological insulator

Based on the dispersion relation for a wave localised in a thin film of a nonlinear dielectric, which is located on the surface of a topological insulator, we have derived a system of equations that describes the propagation of a surface wave. It is shown that the longitudinal and transverse tangential components of the electric field vector are related due to the nonlinearity of the film and change periodically during propagation. It is found that the rotation period of this vector is determined by the axion charge of the topological dielectric and the nonlinear susceptibility of the thin film. (paper)

36 MATERIALS SCIENCE↗

NASA NTRS1995

Electromagnetic compatibility and the all-electric airplane

NASA is studying the feasibility of installing 'all-electric' controls in future commercial aircraft, replacing the current hydraulic and pneumatic systems. Planes utilizing such equipment should weigh less and be cheaper to maintain, but might also be susceptible to interference from undesired external electromagnetic fields. Possible sources of these extraneous signals include radio and television broadcasters, two-way communications stations, and radar installations of all kinds. One way to reduce the hazard would be to use fiber-optic cables to carry signals from the cockpit to the various points of use, a concept known as 'fly-by-light' or FBL. However, electrical circuits (PBW, or 'power-by-wire') would still be required at both ends of the cables to perform control functions, so the possibility of harmful interference would remain. Computer models for two different antennas were created in order to find the magnitude of the electric fields which would be generated in the airspace around them while in the transmit mode. The first antenna was a horizontal 'rhombic' used by the Voice of America (VOA) for long-distance short-wave broadcasting. The second antenna was a multi-element 'log-periodic dipole array' (LPDA) of a type often used for two-way radio communications. For each case, a specified amount of power was applied in the computer model, and the resulting electric field intensity was predicted at a variety of locations surrounding the antenna. This information will then be used to calculate the levels of interference which could occur inside an airplane flying in the vicinity of these radiation emitters.

Christman, Al↗

DOE OSTI2024

Charge Conservation beyond Uniformity: Spatially Inhomogeneous Electromagnetic Response in Periodic Solids

Nonlinear electromagnetic response functions have reemerged as a crucial tool for studying quantum materials, due to recently appreciated connections between optical response functions, quantum geometry, and band topology. Most attention has been paid to responses to spatially uniform electric fields, relevant to low-energy optical experiments in conventional solid state materials. However, magnetic and magnetoelectric phenomena are naturally connected by responses to spatially varying electric fields due to Maxwell’s equations. Furthermore, in the emerging field of moiré materials, characteristic lattice scales are much longer, allowing spatial variation of optical electric fields to potentially have a measurable effect in experiments. In order to address these issues, we develop a formalism for computing linear and nonlinear responses to spatially inhomogeneous electromagnetic fields. Starting with the continuity equation, we derive an expression for the second-quantized current operator that is manifestly conserved and model independent. Crucially, our formalism makes no assumptions on the form of the microscopic Hamiltonian and so is applicable to model Hamiltonians derived from tight-binding or calculations. We then develop a diagrammatic Kubo formalism for computing the wave vector dependence of linear and nonlinear conductivities, using Ward identities to fix the value of the diamagnetic current order by order in the vector potential. We apply our formula to compute the magnitude of the Kerr effect at oblique incidence for a model of a moiré-Chern insulator and demonstrate the experimental relevance of spatially inhomogeneous fields in these systems. We further show how our formalism allows us to compute the (orbital) magnetic multipole moments and magnetic susceptibilities in insulators. Turning to nonlinear response, we use our formalism to compute the second-order transverse response to spatially varying transverse electric fields in our moiré-Chern insulator model, with an eye toward the next generation of experiments in these systems. Published by the American Physical Society 2024

Physics↗