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1. Homotopy Continuation for Feedback Linearization of Noncontact Magnetic Manipulators

   https://doi.org/10.23919/ACC45564.2020.9147681  

   Riahi, Nayereh; Tituana, Luis R.; Komaee, Arash (July 2020, 2020 American Control Conference (ACC))

   null (Ed.)

   Magnetic fields render a unique ability to control magnetic objects without a direct mechanical contact. To exploit this potential for a broad range of medical, microrobotics, and microfluidics applications, noncontact magnetic manipulators have been designed using both electromagnets and permanent magnets. By feedback control of these manipulators, magnetic objects can be precisely driven in the directions required by an application of interest. The feedback design process for these manipulators is normally complicated by their highly nonlinear nature, particularly for those utilizing permanent magnets. Yet, feedback linearization techniques can be applied to compensate for the nonlinear nature of most magnetic manipulators. This goal can be achieved by solving an underdetermined system of nonlinear algebraic equations. This paper adopts a homotopy continuation approach to solve this system of equations. It is shown by simulations that the proposed feedback linearization scheme drastically improves the control performance compared to the alternative control design methods used in prior work. 

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2. Nonlinear magnetoelectric effects in layered multiferroic composites

   https://doi.org/10.1063/5.0183351  

   Fetisov, Y K; Srinivasan, G (January 2024, Journal of Applied Physics)

   Magnetoelectric (ME) effects in a ferromagnetic and piezoelectric composite are the changes in the polarization caused by a magnetic field or the changes in the magnetization caused by an electric field. These effects are aided by the mechanical deformation in the ferroic phases caused by the combination of magnetostriction and piezoelectricity. Interest in ME effects is due to a variety of physical phenomena they exhibit, as well as their potential applications in the creation of highly sensitive magnetic field sensors and other electronic devices. Linear ME effects in structures with layers of different ferroic materials have been studied extensively. However, nonlinear ME effects, which are caused by the nonlinearity of the magnetic, dielectric, and acoustic properties of ferromagnets and piezoelectrics, are less well understood. The purpose of this review is to summarize the current state of knowledge on nonlinear ME (NLME) effects in composite heterostructures and to discuss their potential applications. The review begins by discussing the characteristics of materials that are conductive to the occurrence of NLME effects and ferromagnetic-piezoelectric materials that are most commonly used to study such effects. The review then provides details on theoretical approaches to the description of NLME effects in heterostructures and experimental methods for studying these effects. Finally, the review presents a chronological overview of the experimentally observed NLME effects in composite structures excited by low-frequency and pulsed magnetic or electric fields. The review concludes with a discussion on the potential applications of NLME effects for highly sensitive magnetic field sensors. 

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3. Discovery of an Intrinsic Antiferromagnetic Semiconductor EuSc ₂ Te ₄ With Magnetism‐Driven Nonlinear Transport

   https://doi.org/10.1002/adfm.202424231  

   Lee, Seng_Huat; Zhao, Yufei; Gluscevich, Noble; Yi, Hemian; Morgan, Zachary; Cao, Huibo; Koo, Jahyun; Wang, Yu; He, Jingyang; Gopalan, Venkatraman; et al (March 2025, Advanced Functional Materials)

   Abstract Magnetic topological materials have recently emerged as a promising platform for studying quantum geometry by the nonlinear transport in thin film devices. In this work, an antiferromagnetic (AFM) semiconductor EuSc₂Te₄ as the first bulk crystal that exhibits quantum geometry‐driven nonlinear transport is reported. This material crystallizes into an orthorhombic lattice with AFM order below 5.2 K and a bandgap of less than 50 meV. The calculated band structure aligns with the angle‐resolved photoemission spectroscopy spectrum. The AFM order preserves combined space‐time inversion symmetry but breaks both spatial inversion and time‐reversal symmetry, leading to the nonlinear Hall effect (NLHE). Nonlinear Hall voltage measured in bulk crystals appears at zero field, peaks near the spin‐flop transition as the field increases, and then diminishes as the spin moments align into a ferromagnetic order. This field dependence, along with the scaling analysis of the nonlinear Hall conductivity, suggests that the NLHE of EuSc₂Te₄ involves contributions from quantum metric, in addition to extrinsic contributions, such as spin scattering and junction effects. Furthermore, this NLHE is found to have the functionality of broadband frequency mixing, indicating its potential applications in electronics. This work reveals a new avenue for studying magnetism‐induced nonlinear transport in magnetic materials. 

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4. Networks extracted from nonlinear fMRI connectivity exhibit unique spatial variation and enhanced sensitivity to differences between individuals with schizophrenia and controls

   https://doi.org/10.1038/s44220-024-00341-y  

   Kinsey, Spencer; Kazimierczak, Katarzyna; Camazón, Pablo Andrés; Chen, Jiayu; Adali, Tülay; Kochunov, Peter; Adhikari, Bhim M; Ford, Judith; van_Erp, Theo_G M; Dhamala, Mukesh; et al (December 2024, Nature Mental Health)

   Abstract Schizophrenia is a chronic brain disorder associated with widespread alterations in functional brain connectivity. Although data-driven approaches such as independent component analysis are often used to study how schizophrenia impacts linearly connected networks, alterations within the underlying nonlinear functional connectivity structure remain largely unknown. Here we report the analysis of networks from explicitly nonlinear functional magnetic resonance imaging connectivity in a case–control dataset. We found systematic spatial variation, with higher nonlinear weight within core regions, suggesting that linear analyses underestimate functional connectivity within network centers. We also found that a unique nonlinear network incorporating default-mode, cingulo-opercular and central executive regions exhibits hypoconnectivity in schizophrenia, indicating that typically hidden connectivity patterns may reflect inefficient network integration in psychosis. Moreover, nonlinear networks including those previously implicated in auditory, linguistic and self-referential cognition exhibit heightened statistical sensitivity to schizophrenia diagnosis, collectively underscoring the potential of our methodology to resolve complex brain phenomena and transform clinical connectivity analysis. 

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5. Weighing Dirac fermions by nonlinear Hall effect

   Wang, Yang; Mambakkam, Sivakumar V.; Law, Stephanie A.; Xiao, John. Q. (March 2022, ArXivorg)

   Breaking the time-reversal symmetry on the surface of a topological insulator can open a gap for the linear dispersion and make the Dirac fermions massive. This can be achieved by either doping a topological insulator with magnetic elements or proximity-coupling it to magnetic insulators. While the exchange gap can be directly imaged in the former case, measuring it at the buried magnetic insulator/topological insulator interface remains to be challenging. Here, we report the observation of a large nonlinear Hall effect in iron garnet/Bi2Se3 heterostructures. Besides illuminating its magnetic origin, we also show that this nonlinear Hall effect can be utilized to measure the size of the exchange gap and the magnetic-proximity onset temperature. Our results demonstrate the nonlinear Hall effect as a spectroscopic tool to probe the modified band structure at magnetic insulator/topological insulator interfaces. 

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