Optimize Ferromagnetic Resonance for Spintronics Applications
MAR 7, 20269 MIN READ
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Ferromagnetic Resonance Background and Spintronic Goals
Ferromagnetic resonance emerged as a fundamental phenomenon in the 1940s when physicists first observed the resonant absorption of electromagnetic radiation by ferromagnetic materials under applied magnetic fields. This discovery laid the groundwork for understanding spin dynamics in magnetic systems, where the precession of magnetic moments around an effective magnetic field creates characteristic resonance frequencies. The phenomenon occurs when the frequency of applied microwave radiation matches the natural precession frequency of magnetization, leading to energy absorption and spin excitation.
The evolution of FMR research has been driven by the quest to understand and manipulate spin-dependent transport phenomena. Early investigations focused on bulk magnetic materials, revealing the relationship between magnetic anisotropy, exchange interactions, and resonance linewidth. As material science advanced, researchers began exploring thin films and multilayer structures, discovering that reduced dimensionality significantly affects magnetic properties and spin dynamics.
The emergence of spintronics as a distinct field in the late 20th century transformed FMR from a characterization tool into a critical optimization target. Spintronics exploits both the charge and spin degrees of freedom of electrons, promising revolutionary advances in information processing, storage, and quantum technologies. Unlike conventional electronics that relies solely on charge transport, spintronic devices manipulate spin currents and magnetic states to achieve enhanced functionality.
Contemporary spintronic applications demand precise control over FMR characteristics to enable efficient spin injection, detection, and manipulation. The primary technical objectives include minimizing Gilbert damping parameters to reduce energy dissipation during spin precession, achieving ultrafast switching speeds for high-frequency applications, and maintaining coherent spin states over extended periods. These requirements necessitate materials with low magnetic damping, high spin polarization, and tunable magnetic anisotropy.
Modern research targets encompass developing novel magnetic heterostructures that exhibit tailored FMR properties, engineering interfacial effects to enhance spin-orbit coupling, and creating hybrid systems that integrate ferromagnetic resonators with superconducting or semiconducting components. The ultimate goal involves realizing practical spintronic devices such as spin-transfer torque oscillators, magnonic crystals, and quantum spin processors that leverage optimized FMR characteristics for superior performance compared to conventional electronic counterparts.
The evolution of FMR research has been driven by the quest to understand and manipulate spin-dependent transport phenomena. Early investigations focused on bulk magnetic materials, revealing the relationship between magnetic anisotropy, exchange interactions, and resonance linewidth. As material science advanced, researchers began exploring thin films and multilayer structures, discovering that reduced dimensionality significantly affects magnetic properties and spin dynamics.
The emergence of spintronics as a distinct field in the late 20th century transformed FMR from a characterization tool into a critical optimization target. Spintronics exploits both the charge and spin degrees of freedom of electrons, promising revolutionary advances in information processing, storage, and quantum technologies. Unlike conventional electronics that relies solely on charge transport, spintronic devices manipulate spin currents and magnetic states to achieve enhanced functionality.
Contemporary spintronic applications demand precise control over FMR characteristics to enable efficient spin injection, detection, and manipulation. The primary technical objectives include minimizing Gilbert damping parameters to reduce energy dissipation during spin precession, achieving ultrafast switching speeds for high-frequency applications, and maintaining coherent spin states over extended periods. These requirements necessitate materials with low magnetic damping, high spin polarization, and tunable magnetic anisotropy.
Modern research targets encompass developing novel magnetic heterostructures that exhibit tailored FMR properties, engineering interfacial effects to enhance spin-orbit coupling, and creating hybrid systems that integrate ferromagnetic resonators with superconducting or semiconducting components. The ultimate goal involves realizing practical spintronic devices such as spin-transfer torque oscillators, magnonic crystals, and quantum spin processors that leverage optimized FMR characteristics for superior performance compared to conventional electronic counterparts.
Market Demand for Advanced Spintronic Devices
The global spintronic devices market is experiencing unprecedented growth driven by the increasing demand for energy-efficient computing solutions and next-generation memory technologies. Traditional silicon-based electronics face fundamental limitations in power consumption and processing speed, creating substantial market opportunities for spintronic alternatives that leverage electron spin properties alongside charge characteristics.
Data storage applications represent the largest current market segment for spintronic devices, with magnetic random-access memory (MRAM) technologies gaining significant traction in enterprise and automotive sectors. The automotive industry particularly drives demand for non-volatile memory solutions that can withstand extreme temperatures and provide instant-on capabilities for advanced driver assistance systems and autonomous vehicle applications.
The computing sector demonstrates growing interest in spintronic processors and logic devices that promise dramatic reductions in power consumption compared to conventional CMOS technologies. Quantum computing applications further expand market potential, as spintronic components offer promising pathways for qubit implementation and quantum information processing systems.
Telecommunications infrastructure modernization creates additional demand for high-frequency spintronic devices capable of operating in millimeter-wave and terahertz frequency ranges. The deployment of 5G networks and preparation for 6G technologies require advanced RF components with superior performance characteristics that optimized ferromagnetic resonance can provide.
Healthcare and biomedical applications emerge as promising market segments, with spintronic sensors offering enhanced sensitivity for magnetic resonance imaging systems and portable diagnostic devices. The miniaturization potential of spintronic components aligns well with trends toward wearable health monitoring technologies and implantable medical devices.
Industrial automation and Internet of Things applications drive demand for low-power, high-reliability spintronic sensors and processing units. The ability to operate in harsh electromagnetic environments while maintaining precision makes spintronic devices attractive for industrial control systems and smart manufacturing applications.
Market growth faces challenges including manufacturing scalability, cost competitiveness with established silicon technologies, and the need for specialized fabrication facilities. However, increasing investment in research and development, coupled with growing awareness of energy efficiency requirements, continues to fuel market expansion and technological advancement in the spintronic device sector.
Data storage applications represent the largest current market segment for spintronic devices, with magnetic random-access memory (MRAM) technologies gaining significant traction in enterprise and automotive sectors. The automotive industry particularly drives demand for non-volatile memory solutions that can withstand extreme temperatures and provide instant-on capabilities for advanced driver assistance systems and autonomous vehicle applications.
The computing sector demonstrates growing interest in spintronic processors and logic devices that promise dramatic reductions in power consumption compared to conventional CMOS technologies. Quantum computing applications further expand market potential, as spintronic components offer promising pathways for qubit implementation and quantum information processing systems.
Telecommunications infrastructure modernization creates additional demand for high-frequency spintronic devices capable of operating in millimeter-wave and terahertz frequency ranges. The deployment of 5G networks and preparation for 6G technologies require advanced RF components with superior performance characteristics that optimized ferromagnetic resonance can provide.
Healthcare and biomedical applications emerge as promising market segments, with spintronic sensors offering enhanced sensitivity for magnetic resonance imaging systems and portable diagnostic devices. The miniaturization potential of spintronic components aligns well with trends toward wearable health monitoring technologies and implantable medical devices.
Industrial automation and Internet of Things applications drive demand for low-power, high-reliability spintronic sensors and processing units. The ability to operate in harsh electromagnetic environments while maintaining precision makes spintronic devices attractive for industrial control systems and smart manufacturing applications.
Market growth faces challenges including manufacturing scalability, cost competitiveness with established silicon technologies, and the need for specialized fabrication facilities. However, increasing investment in research and development, coupled with growing awareness of energy efficiency requirements, continues to fuel market expansion and technological advancement in the spintronic device sector.
Current FMR Optimization Challenges in Spintronics
Ferromagnetic resonance optimization in spintronics faces significant challenges that stem from the complex interplay between magnetic materials, device architectures, and operational requirements. The primary obstacle lies in achieving precise control over magnetic damping parameters while maintaining high spin polarization efficiency. Current spintronic devices struggle with excessive energy dissipation during FMR processes, leading to reduced device performance and limited operational bandwidth.
Material-related challenges represent a critical bottleneck in FMR optimization. The inherent magnetic anisotropy of ferromagnetic materials often conflicts with the desired resonance characteristics for spintronic applications. Traditional ferromagnetic materials exhibit broad linewidths and high damping constants, which severely limit the quality factor of resonance modes. Additionally, interface effects between ferromagnetic layers and adjacent materials introduce unwanted magnetic inhomogeneities that broaden resonance peaks and reduce signal clarity.
Thermal stability presents another formidable challenge in FMR optimization. Spintronic devices operating at elevated temperatures experience significant shifts in resonance frequencies due to temperature-dependent magnetic properties. The thermal fluctuations cause variations in magnetic anisotropy fields and saturation magnetization, making it difficult to maintain consistent FMR characteristics across different operating conditions. This thermal sensitivity particularly affects the reliability of spin-transfer torque devices and magnetic tunnel junctions.
Device scaling limitations pose substantial constraints on FMR optimization efforts. As spintronic devices shrink to nanoscale dimensions, the magnetic volume becomes insufficient to maintain stable resonance modes. Edge effects and shape anisotropy become dominant factors that alter the expected FMR behavior, making it challenging to predict and control resonance characteristics in miniaturized devices. The reduced magnetic volume also increases susceptibility to external magnetic field fluctuations.
Frequency bandwidth restrictions represent a significant technical hurdle for broadband spintronic applications. Current FMR optimization techniques struggle to achieve wide operational frequency ranges while maintaining high resonance quality. The trade-off between resonance sharpness and bandwidth coverage limits the versatility of spintronic devices in high-frequency applications such as microwave signal processing and magnetic field sensing.
Integration complexity with existing semiconductor technologies creates additional optimization challenges. The magnetic materials used in spintronic devices often require specialized processing conditions that are incompatible with standard CMOS fabrication processes. This incompatibility necessitates complex hybrid integration approaches that can introduce parasitic effects and degrade FMR performance, making it difficult to achieve optimal resonance characteristics in practical device implementations.
Material-related challenges represent a critical bottleneck in FMR optimization. The inherent magnetic anisotropy of ferromagnetic materials often conflicts with the desired resonance characteristics for spintronic applications. Traditional ferromagnetic materials exhibit broad linewidths and high damping constants, which severely limit the quality factor of resonance modes. Additionally, interface effects between ferromagnetic layers and adjacent materials introduce unwanted magnetic inhomogeneities that broaden resonance peaks and reduce signal clarity.
Thermal stability presents another formidable challenge in FMR optimization. Spintronic devices operating at elevated temperatures experience significant shifts in resonance frequencies due to temperature-dependent magnetic properties. The thermal fluctuations cause variations in magnetic anisotropy fields and saturation magnetization, making it difficult to maintain consistent FMR characteristics across different operating conditions. This thermal sensitivity particularly affects the reliability of spin-transfer torque devices and magnetic tunnel junctions.
Device scaling limitations pose substantial constraints on FMR optimization efforts. As spintronic devices shrink to nanoscale dimensions, the magnetic volume becomes insufficient to maintain stable resonance modes. Edge effects and shape anisotropy become dominant factors that alter the expected FMR behavior, making it challenging to predict and control resonance characteristics in miniaturized devices. The reduced magnetic volume also increases susceptibility to external magnetic field fluctuations.
Frequency bandwidth restrictions represent a significant technical hurdle for broadband spintronic applications. Current FMR optimization techniques struggle to achieve wide operational frequency ranges while maintaining high resonance quality. The trade-off between resonance sharpness and bandwidth coverage limits the versatility of spintronic devices in high-frequency applications such as microwave signal processing and magnetic field sensing.
Integration complexity with existing semiconductor technologies creates additional optimization challenges. The magnetic materials used in spintronic devices often require specialized processing conditions that are incompatible with standard CMOS fabrication processes. This incompatibility necessitates complex hybrid integration approaches that can introduce parasitic effects and degrade FMR performance, making it difficult to achieve optimal resonance characteristics in practical device implementations.
Existing FMR Optimization Solutions
01 Ferromagnetic resonance measurement apparatus and methods
Devices and methods for measuring ferromagnetic resonance properties of materials, including apparatus configurations with magnetic field generators, microwave sources, and detection systems. These systems enable precise characterization of magnetic materials by analyzing their resonance behavior under applied magnetic fields and electromagnetic radiation. The measurement techniques can be used for material analysis, quality control, and research applications.- Ferromagnetic resonance measurement apparatus and methods: Devices and methods for measuring ferromagnetic resonance properties of materials, including apparatus configurations with magnetic field generators, microwave sources, and detection systems. These systems enable precise characterization of magnetic materials by analyzing their resonance behavior under varying magnetic field conditions and microwave frequencies.
- Magnetic recording media utilizing ferromagnetic resonance properties: Magnetic recording materials and structures designed with specific ferromagnetic resonance characteristics to improve data storage performance. These materials incorporate optimized magnetic layer compositions and configurations that enhance recording density, signal-to-noise ratio, and thermal stability through controlled ferromagnetic resonance behavior.
- Spintronic devices based on ferromagnetic resonance: Spintronic components and devices that exploit ferromagnetic resonance phenomena for information processing and storage applications. These devices utilize spin-transfer torque, magnetoresistance effects, and resonance-based switching mechanisms to achieve high-speed, low-power operation in memory and logic applications.
- Ferromagnetic resonance frequency tuning and control: Techniques and structures for adjusting and controlling the ferromagnetic resonance frequency of magnetic materials through various means including material composition modification, geometric patterning, applied bias fields, and multilayer stack engineering. These approaches enable optimization of device performance for specific frequency ranges and applications.
- Ferromagnetic resonance in thin film and multilayer structures: Magnetic thin films and multilayer heterostructures exhibiting tailored ferromagnetic resonance properties through interface engineering, layer thickness control, and material selection. These structures demonstrate enhanced resonance characteristics suitable for high-frequency applications, sensors, and microwave devices through optimized magnetic anisotropy and damping parameters.
02 Magnetic recording media with optimized ferromagnetic resonance properties
Magnetic recording media and storage devices designed with specific ferromagnetic resonance characteristics to improve performance. The materials and structures are engineered to control magnetic properties such as coercivity, anisotropy, and damping factors. These optimizations enable higher data density, faster write speeds, and improved signal-to-noise ratios in magnetic storage applications.Expand Specific Solutions03 Spin-torque oscillators utilizing ferromagnetic resonance
Devices that exploit ferromagnetic resonance phenomena in spin-torque oscillators for generating microwave signals and performing signal processing. These devices use spin-polarized currents to excite magnetic oscillations at ferromagnetic resonance frequencies. Applications include wireless communications, radar systems, and neuromorphic computing architectures.Expand Specific Solutions04 Ferromagnetic resonance-based sensors and detection systems
Sensing devices that utilize ferromagnetic resonance principles for detecting magnetic fields, measuring material properties, or identifying substances. These sensors offer high sensitivity and selectivity by monitoring changes in resonance frequency, linewidth, or amplitude. Applications span from industrial quality control to biomedical diagnostics and security screening.Expand Specific Solutions05 Multilayer magnetic structures with controlled ferromagnetic resonance
Multilayer thin film structures engineered to exhibit specific ferromagnetic resonance characteristics through careful selection of layer compositions, thicknesses, and interfaces. These structures enable tunable magnetic properties and enhanced performance in spintronic devices. The designs optimize interlayer coupling, magnetic anisotropy, and damping parameters for applications in magnetic sensors, memory devices, and microwave components.Expand Specific Solutions
Key Players in Spintronics and Magnetic Materials
The ferromagnetic resonance optimization for spintronics applications represents an emerging technology sector in the early-to-mid development stage, with significant growth potential driven by increasing demand for next-generation computing and memory devices. The market remains relatively niche but is expanding rapidly as quantum computing and neuromorphic processing gain traction. Technology maturity varies considerably across the competitive landscape, with established semiconductor giants like Intel Corp., Taiwan Semiconductor Manufacturing Co., and NEC Corp. leading in manufacturing capabilities and commercial applications. Research institutions including CEA, CNRS, Caltech, and various Asian universities (Peking University, UESTC, National University of Singapore) are driving fundamental breakthroughs in magnetic materials and spin dynamics. Government laboratories such as Naval Research Laboratory and Japan Science & Technology Agency provide critical foundational research, while specialized companies like Hengdian Group DMEGC Magnetics focus on magnetic materials production. The technology transfer organizations like Yissum and WARF bridge academic discoveries with commercial applications, indicating a maturing ecosystem ready for broader industrial adoption.
Commissariat à l´énergie atomique et aux énergies Alternatives
Technical Solution: CEA has developed comprehensive approaches to optimize ferromagnetic resonance for spintronic applications through advanced material engineering and device physics research. Their work focuses on synthetic antiferromagnetic structures and magnetic multilayers with tailored magnetic anisotropy and reduced damping parameters. CEA's research includes development of novel magnetic materials with enhanced spin-orbit coupling effects and optimized interface properties for efficient spin current generation and detection. The organization has demonstrated prototype spintronic devices including spin-torque oscillators and magnetic logic gates with precisely controlled FMR characteristics for neuromorphic computing and ultra-low power electronics applications.
Strengths: Strong fundamental research capabilities and government funding support. Weaknesses: Limited commercial manufacturing experience compared to industry players.
Western Digital Technologies, Inc.
Technical Solution: Western Digital has pioneered spin-orbit torque (SOT) based magnetic storage devices with optimized ferromagnetic resonance properties for next-generation hard disk drives and solid-state storage. Their technology platform utilizes heavy metal/ferromagnet bilayer structures with engineered magnetic anisotropy to achieve precise control over FMR linewidth and resonance frequency. The company has developed proprietary techniques for reducing magnetic damping through interface engineering and material composition optimization. Their spintronic read heads incorporate advanced FMR-optimized sensors that enable detection of magnetic fields with unprecedented sensitivity and speed for high-density data storage applications.
Strengths: Extensive experience in magnetic storage technologies and commercial manufacturing. Weaknesses: Primary focus on storage applications may limit broader spintronic innovation.
Core Patents in FMR-Enhanced Spintronic Systems
Devices, systems, and methods for testing samples in temporally modulated magnetic fields
PatentWO2023181037A1
Innovation
- The development of devices and systems that generate large-scale temporally modulated magnetic fields without electromagnets, allowing direct analysis of FMR signals, are compact, cost-effective, and broadband, using a rotating frame with permanent magnets and heterodyne-based demodulation for sensitive magnetic testing.
Material Safety Standards for Magnetic Devices
Material safety standards for magnetic devices in spintronic applications represent a critical framework governing the development and deployment of ferromagnetic resonance-optimized systems. These standards encompass comprehensive guidelines addressing electromagnetic field exposure limits, material biocompatibility requirements, and operational safety protocols specific to high-frequency magnetic field environments encountered in spintronic devices.
The International Electrotechnical Commission (IEC) 62311 standard establishes fundamental exposure limits for electromagnetic fields generated by magnetic devices operating in the gigahertz frequency range typical of optimized ferromagnetic resonance systems. These regulations mandate specific absorption rate (SAR) limitations and require comprehensive electromagnetic compatibility testing for devices intended for consumer or medical applications. Additionally, the IEEE C95.1 standard provides detailed guidelines for radiofrequency exposure assessment in spintronic devices utilizing enhanced ferromagnetic resonance characteristics.
Material composition safety standards focus on the toxicological evaluation of magnetic materials commonly employed in spintronic applications, including rare earth elements, transition metal alloys, and synthetic antiferromagnets. The REACH regulation framework requires extensive chemical safety assessments for novel magnetic materials, particularly those incorporating heavy metals or potentially hazardous compounds used to achieve optimal ferromagnetic resonance properties.
Operational safety protocols address the unique hazards associated with high-power magnetic field generation required for ferromagnetic resonance optimization. These include guidelines for magnetic field containment, personnel protection equipment specifications, and emergency response procedures for magnetic field exposure incidents. The standards also establish requirements for device labeling, user training, and maintenance protocols to ensure safe operation throughout the device lifecycle.
Environmental safety considerations encompass waste disposal protocols for magnetic materials, recycling requirements for rare earth elements, and environmental impact assessments for manufacturing processes. These standards ensure that the pursuit of optimized ferromagnetic resonance performance does not compromise environmental sustainability or public health safety in spintronic device development and deployment.
The International Electrotechnical Commission (IEC) 62311 standard establishes fundamental exposure limits for electromagnetic fields generated by magnetic devices operating in the gigahertz frequency range typical of optimized ferromagnetic resonance systems. These regulations mandate specific absorption rate (SAR) limitations and require comprehensive electromagnetic compatibility testing for devices intended for consumer or medical applications. Additionally, the IEEE C95.1 standard provides detailed guidelines for radiofrequency exposure assessment in spintronic devices utilizing enhanced ferromagnetic resonance characteristics.
Material composition safety standards focus on the toxicological evaluation of magnetic materials commonly employed in spintronic applications, including rare earth elements, transition metal alloys, and synthetic antiferromagnets. The REACH regulation framework requires extensive chemical safety assessments for novel magnetic materials, particularly those incorporating heavy metals or potentially hazardous compounds used to achieve optimal ferromagnetic resonance properties.
Operational safety protocols address the unique hazards associated with high-power magnetic field generation required for ferromagnetic resonance optimization. These include guidelines for magnetic field containment, personnel protection equipment specifications, and emergency response procedures for magnetic field exposure incidents. The standards also establish requirements for device labeling, user training, and maintenance protocols to ensure safe operation throughout the device lifecycle.
Environmental safety considerations encompass waste disposal protocols for magnetic materials, recycling requirements for rare earth elements, and environmental impact assessments for manufacturing processes. These standards ensure that the pursuit of optimized ferromagnetic resonance performance does not compromise environmental sustainability or public health safety in spintronic device development and deployment.
Energy Efficiency Considerations in Spintronic Design
Energy efficiency represents a critical design parameter in spintronic devices, particularly when optimizing ferromagnetic resonance for practical applications. The inherent advantage of spintronics lies in its potential to achieve ultra-low power consumption compared to conventional charge-based electronics, making energy considerations paramount in device architecture and material selection.
Power dissipation in spintronic systems primarily occurs through several mechanisms during ferromagnetic resonance operations. Gilbert damping constitutes the dominant energy loss channel, where magnetic precession energy converts to heat through spin-lattice interactions. Minimizing the Gilbert damping parameter while maintaining stable resonance conditions requires careful material engineering and interface optimization. Additionally, eddy current losses in metallic ferromagnetic layers contribute significantly to overall power consumption, necessitating the use of thin film geometries and high-resistivity materials.
Voltage-controlled magnetic anisotropy emerges as a promising approach for energy-efficient spintronic design. By utilizing electric fields rather than magnetic fields or spin-polarized currents to manipulate magnetic states, this technique can reduce switching energy by several orders of magnitude. The magnetoelectric coupling at ferromagnetic-dielectric interfaces enables precise control of resonance frequencies with minimal power input, making it particularly attractive for low-power applications.
Thermal management considerations become increasingly important as device dimensions shrink and operating frequencies increase. Heat generation during ferromagnetic resonance can lead to temperature-dependent shifts in magnetic parameters, affecting device reliability and performance consistency. Implementing effective heat dissipation strategies through substrate selection, thermal interface materials, and device layout optimization ensures stable operation while maintaining energy efficiency.
Material selection plays a crucial role in achieving optimal energy performance. Perpendicular magnetic anisotropy materials, such as CoFeB-MgO heterostructures, offer reduced switching energies compared to in-plane magnetized systems. Furthermore, the development of low-damping ferromagnetic materials with high spin polarization enables efficient spin current generation and detection while minimizing energy losses during resonance excitation and relaxation processes.
Power dissipation in spintronic systems primarily occurs through several mechanisms during ferromagnetic resonance operations. Gilbert damping constitutes the dominant energy loss channel, where magnetic precession energy converts to heat through spin-lattice interactions. Minimizing the Gilbert damping parameter while maintaining stable resonance conditions requires careful material engineering and interface optimization. Additionally, eddy current losses in metallic ferromagnetic layers contribute significantly to overall power consumption, necessitating the use of thin film geometries and high-resistivity materials.
Voltage-controlled magnetic anisotropy emerges as a promising approach for energy-efficient spintronic design. By utilizing electric fields rather than magnetic fields or spin-polarized currents to manipulate magnetic states, this technique can reduce switching energy by several orders of magnitude. The magnetoelectric coupling at ferromagnetic-dielectric interfaces enables precise control of resonance frequencies with minimal power input, making it particularly attractive for low-power applications.
Thermal management considerations become increasingly important as device dimensions shrink and operating frequencies increase. Heat generation during ferromagnetic resonance can lead to temperature-dependent shifts in magnetic parameters, affecting device reliability and performance consistency. Implementing effective heat dissipation strategies through substrate selection, thermal interface materials, and device layout optimization ensures stable operation while maintaining energy efficiency.
Material selection plays a crucial role in achieving optimal energy performance. Perpendicular magnetic anisotropy materials, such as CoFeB-MgO heterostructures, offer reduced switching energies compared to in-plane magnetized systems. Furthermore, the development of low-damping ferromagnetic materials with high spin polarization enables efficient spin current generation and detection while minimizing energy losses during resonance excitation and relaxation processes.
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