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Magnetostriction

Magnetostriction is a fundamental property of ferromagnetic materials that causes them to undergo a change in shape or dimensions when exposed to a magnetic field, effectively converting magnetic energy into mechanical strain. This reversible deformation, typically on the order of parts per million in common materials like iron and nickel, arises from the alignment of internal magnetic domains with the applied field. Discovered in 1842 by James Prescott Joule during experiments on iron samples, the effect—often termed the Joule effect—marks the interplay between magnetism and mechanics in solids.^[1]^[2] The underlying mechanism of magnetostriction involves spin-orbit coupling, where the magnetization process induces anisotropic strain through the rotation of magnetic domains and lattice distortions at the atomic level. In ferromagnetic crystals, the saturation magnetostrictive strain \lambda_s is defined as the relative change in length \Delta l / l upon reaching magnetic saturation, with positive values indicating elongation along the field direction and negative values contraction. The inverse effect, known as the Villari effect, occurs when mechanical stress alters the material's magnetic permeability, highlighting the bidirectional magnetoelastic coupling. Notable advancements include the development of "giant" magnetostrictive materials in the 1970s, such as Terfenol-D (Tb_0.3Dy_0.7Fe₂), which exhibit strains up to 2000 ppm at room temperature due to rare-earth elements enhancing magnetoelastic interactions. More recent developments include giant magnetostriction in ultrathin Fe-Mn-Ga alloys without rare-earth elements, as reported in 2025.^[1]^[2]^[3] Magnetostriction finds diverse applications across engineering and biomedicine, leveraging its high energy density and rapid response times. In industrial settings, it powers ultrasonic transducers, sonar systems, and vibration dampers, while in transformers, it contributes to audible humming from core expansions at twice the line frequency. Emerging biomedical uses include wireless sensors for implant monitoring and microactuators for tissue engineering, where Fe-Ga alloys stimulate cell growth in bone repair with strains around 350 ppm. These applications underscore magnetostriction's role in precision control, though challenges like material brittleness and energy efficiency continue to drive research into novel alloys.^[1]^[4]^[2]

Fundamentals

Definition and Principles

Magnetostriction is the phenomenon observed in ferromagnetic and ferrimagnetic materials wherein their dimensions change in response to an applied magnetic field. This effect stems from the intrinsic coupling between the material's magnetic and elastic properties, resulting in deformation that accompanies changes in magnetization. The magnetostrictive strain is quantified as

\lambda = \frac{\Delta L}{L},

where \Delta L is the change in length along a specified direction and L is the original length.^[5] The basic principles of magnetostriction arise from magnetoelastic coupling, a interaction at the atomic level where spin-orbit effects link electron spins to the crystal lattice, altering the material's shape as magnetization varies. In these materials, magnetic domains—regions of aligned atomic moments—exist in a demagnetized state; an external magnetic field H induces alignment of these domains through growth, rotation, or reorientation, which in turn generates mechanical strain via the magnetoelastic interaction. The magnetization M thus serves as the intermediary, with the strain proportional to changes in M.^[6]^[7] Magnetostriction encompasses distinct forms, including volume magnetostriction, which produces an isotropic change in the material's overall volume, and linear (or Joule) magnetostriction, an anisotropic effect causing elongation or contraction primarily along the direction of the applied field. The saturation magnetostriction \lambda_s represents the maximum achievable strain when the material reaches full magnetic saturation. Typical strains range from $10^{-6} to $10^{-3}, with corresponding stress equivalents up to several MPa, influenced by the material's elastic modulus. For example, nickel displays a negative \lambda_s \approx -30 \times 10^{-6}, while iron exhibits a negative value on the order of -7 \times 10^{-6}.^[5]^[8]^[6]

Historical Development

The discovery of magnetostriction traces back to 1842, when English physicist James Prescott Joule observed that a sample of iron underwent a small elongation when subjected to a magnetic field along its length, while contracting perpendicularly.^[9] This phenomenon, initially termed the Joule effect, represented the first empirical identification of dimensional changes in ferromagnetic materials due to magnetization.^[10] Shortly thereafter, in 1865, Italian physicist Emilio Villari noted the inverse process, where mechanical stress altered the magnetic susceptibility of iron, laying the groundwork for understanding bidirectional magnetoelastic coupling.^[11] The term "magnetostriction" was coined in 1881 by Scottish physicist James Ewing to describe this class of effects more broadly.^[10] Early 20th-century research expanded on these observations, with Japanese physicists Hantaro Nagaoka and Kotaro Honda conducting detailed measurements in the late 1890s and early 1900s on nickel, revealing its negative magnetostriction—characterized by contraction along the magnetization direction, in contrast to iron's positive response.^[12] Their work highlighted material-specific behaviors and influenced subsequent studies on alloys. By the 1930s, German physicist Richard Becker advanced theoretical frameworks, linking magnetostriction to magnetic anisotropy through models that incorporated spin-orbit interactions and crystal structure effects.^[13] Post-World War II developments in the 1940s saw magnetostriction applied practically in sonar transducers, where nickel-based devices operated at frequencies like 24 kHz for underwater detection, driven by wartime needs for antisubmarine warfare.^[14] This era spurred material refinements to address limitations such as low strain amplitudes. In the 1970s, the U.S. Naval Ordnance Laboratory pioneered rare-earth alloys, culminating in the invention of Terfenol-D (TbDyFe2), which exhibited giant magnetostriction strains up to 2000 ppm—orders of magnitude larger than nickel—enabling high-performance actuators and sensors.^[15] From 2020 to 2025, research has focused on nanomaterials and composites to enhance performance while mitigating brittleness and cost issues of bulk rare-earth materials. Advances include ferromagnetic polymer composites achieving reversible giant magnetostriction through aligned steel fibers or nanoprecipitates, yielding strains over 1000 ppm with improved flexibility.^[16] Similarly, TbDyFe/epoxy composites with spherical single crystals have demonstrated enhanced magnetostriction via optimized particle orientation, alongside explorations in Fe-Ga-based nanomaterials for damping-integrated applications.^[17] In 2025, studies demonstrated room-temperature giant magnetostriction in ultrathin Fe_xMn_1–xGa₄ films, enabling advancements in micro-nano electromechanical systems.^[3] These innovations emphasize scalable synthesis and hybrid structures for broader device integration.

Physical Mechanisms

Direct Magnetostriction

Direct magnetostriction, commonly referred to as the Joule effect, describes the change in shape or dimensions of a ferromagnetic material when subjected to an external magnetic field. This phenomenon arises primarily from the reorientation of magnetic domains under the influence of the applied field, which aligns the magnetization vector \mathbf{M} with the field direction. As domains rotate or grow, the material experiences anisotropic lattice distortions driven by magnetocrystalline anisotropy energy, where the preferred easy magnetization directions in the crystal lattice dictate the nature of the strain. The resulting strain tensor \boldsymbol{\varepsilon} is directly coupled to the magnetization, expressed as \boldsymbol{\varepsilon} = f(\mathbf{M}), reflecting the magnetoelastic interaction that minimizes the total energy of the system.^[5]^[18] In polycrystalline materials, the linear magnetostriction \lambda along the field direction follows the quadratic dependence \lambda = \frac{3}{2} \lambda_s \left( \frac{M}{M_s} \right)^2, where \lambda_s is the saturation magnetostriction constant and M_s is the saturation magnetization; this relation captures the progressive alignment from random initial states to full saturation. The Joule effect is typically volume-conserving, with the relative volume change \Delta V / V \approx 0, as the distortions are shear-like rather than isotropic expansions. The sign and magnitude of the strain depend on the crystal's easy axes—such as \langle 100 \rangle or \langle 111 \rangle in cubic ferromagnets—where alignment along these axes induces either elongation or contraction; for instance, iron displays positive magnetostriction (expansion) in certain directions due to its one-ion anisotropy, whereas nickel exhibits negative magnetostriction (contraction).^[19]^[20]^[21] Microstructural elements play a significant role in modulating the direct magnetostriction response by affecting domain dynamics. Grain boundaries impede or facilitate domain wall motion, leading to inhomogeneous strain distributions that can enhance or suppress overall deformation compared to ideal single crystals. Defects, such as dislocations or inclusions, further alter the elastic strain variations by pinning domain walls, thereby influencing the efficiency of magnetization reorientation and the resulting magnetoelastic coupling. These effects are particularly pronounced in polycrystalline or nanostructured materials, where surface proximity can amplify local strains.^[5]^[22]

Inverse Magnetostriction

Inverse magnetostriction, also known as the Villari effect, refers to the change in a ferromagnetic material's magnetic susceptibility, permeability μ, or magnetization M induced by applied mechanical stress σ. Discovered by Italian physicist Emilio Villari in 1865, this phenomenon arises from the bidirectional magnetoelastic coupling inherent in magnetostrictive materials. Under stress, magnetic domains reorient to minimize the total energy, leading to variations in magnetic induction B, often quantified by the relation ΔB/Δσ. This domain wall motion and rotation effectively alter the material's magnetic response without requiring an external magnetic field.^[23] The underlying mathematical model incorporates the magnetoelastic interaction into the material's free energy density. A key term in this energy expression is the magnetoelastic contribution, typically written as -b σ ε, where b denotes the magnetoelastic coupling constant, σ is the applied stress, and ε is the resulting strain. This term couples mechanical deformation to magnetic orientation, influencing domain configurations. The inverse effect is characterized by the piezomagnetic coefficient d, defined as d ≈ ∂M/∂σ, which by thermodynamic reciprocity equals the direct magnetostrictive coefficient ∂λ/∂H (where λ is the magnetostrictive strain and H is the magnetic field strength). In more detailed models, stress induces an effective magnetic field H_σ = (1/μ_0) [∂(3/2 σ ε)/∂M], driving magnetization toward an anhysteretic state through domain wall unpinning.^[24] Theoretically, inverse magnetostriction explains the high sensitivity of magnetic sensors to mechanical loads, as stress modulates permeability and induces magnetic anisotropy shifts that alter domain alignment. In soft magnetic materials, such as amorphous alloys or ferrites, applied stresses can produce relative permeability changes Δμ/μ exceeding 50%, highlighting the effect's scale for sensing applications. These shifts arise from stress-dependent domain reorientation, providing a basis for detecting subtle mechanical perturbations via magnetic measurements.^[25]

Characterization and Measurement

Magnetostrictive Hysteresis

Magnetostrictive hysteresis refers to the nonlinear, path-dependent relationship between the magnetostrictive strain and the applied magnetic field in ferromagnetic materials, manifesting as a closed loop when strain λ is plotted against the magnetic field strength H. This loop illustrates the lag in strain response during increasing and decreasing field cycles, analogous to the magnetic B-H hysteresis loop but featuring mechanical deformation as the primary output. Prominent features include the coercivity H_c, the reverse field magnitude needed to nullify the strain after reaching saturation, and the saturation strain λ_s, the peak strain value attained at high fields. Minor loops within the major loop represent partial reversals, often asymmetric, and may exhibit unique distortions such as twisted sections in certain materials like Terfenol-D due to multiple magnetic dipole equilibria.^[26] The primary causes of magnetostrictive hysteresis stem from irreversible processes in magnetic domain dynamics, including the pinning of domain walls by microstructural defects, inclusions, and internal stresses, which impede smooth wall motion under changing fields. Irreversible rotations of magnetic moments within domains further contribute to the lag, as moments do not revert precisely along the same path upon field reversal. These mechanisms lead to energy dissipation, predominantly as heat through eddy currents induced by domain wall motion and viscous damping in the material lattice; the area enclosed by the hysteresis loop directly quantifies this cyclic energy loss.^[27]^[26] Key quantitative characteristics of the loop include the remanent strain λ_r, the residual deformation persisting after the magnetic field is removed, reflecting incomplete domain relaxation. The initial magnetostrictive susceptibility χ, defined as the derivative dλ/dH near zero field, measures the material's low-field responsiveness and slope of the loop's initial branch. Temperature exerts a profound influence on these properties, with hysteresis amplitude and coercivity increasing as temperature decreases below the Curie point, where ferromagnetic ordering persists; above this point, the effect vanishes as the material transitions to paramagnetism.^[26]^[28] Variations in hysteresis loops occur across material types and operating conditions. Soft magnetostrictive materials, such as certain alloys with low anisotropy, exhibit narrow loops with small H_c and minimal area, enabling efficient, low-loss operation in cyclic applications. In contrast, hard magnets display wide loops with large coercivity, signifying substantial pinning and higher energy dissipation suited for stable, permanent-like responses. For dynamic scenarios, loop shape and area show frequency dependence, with widening and increased losses at higher frequencies due to enhanced eddy current effects and rate-limited domain dynamics, critical for high-speed actuators.^[26]^[29]

Experimental Techniques

Experimental techniques for quantifying magnetostriction primarily involve precise strain measurements under controlled magnetic fields, often combined with mechanical stress to capture coupled effects. Strain gauges, attached directly to the sample surface, provide reliable detection of dimensional changes (ΔL/L) with resolutions typically around 10^{-6} m/m, suitable for bulk materials where direct contact is feasible.^[30] For higher precision, non-contact methods such as laser interferometry or capacitive sensors achieve resolutions down to 10^{-9} m/m by monitoring optical path length variations or capacitance shifts induced by sample deformation.^[31]^[32] Magnetic fields are applied using electromagnets or solenoids, generating uniform fields (H) up to 100 kA/m along the sample axis to induce saturation or directional effects.^[33] Simultaneous uniaxial stress is imposed via loading frames or clamps, allowing investigation of magnetoelastic coupling without altering field uniformity.^[34] Standard techniques include static tests following protocols like those standardized for electrical steels using single-sheet testers with optical sensors for vibration detection at resolutions of 0.01 μm/m.^[35] Dynamic measurements employ vibrating sample magnetometers (VSM) to simultaneously record magnetization (M) and strain (λ), enabling coupled M-λ hysteresis characterization.^[36] For the inverse effect, permeability bridges measure changes in magnetic permeability under applied stress, quantifying stress-induced magnetization variations.^[37] Key challenges in these measurements include maintaining temperature control up to Curie temperatures (often exceeding 700°C for ferrimagnets), where phase transitions can introduce thermal expansion artifacts requiring cryogenic or furnace-integrated setups.^[38] High-frequency AC fields (up to kHz ranges) for transducer applications demand specialized coils and fast-response sensors to capture dynamic responses without eddy current interference.^[39] Recent advances in the 2020s feature optical methods like profilometry and laser deflection for thin films, offering non-contact, sub-ppm sensitivity in nanoscale structures.^[40]^[41] These techniques briefly reference hysteresis loops to validate full-cycle strain-magnetic field dependencies but focus on practical implementation.^[33]

Materials and Properties

Types of Magnetostrictive Materials

Magnetostrictive materials are broadly classified into several categories based on their composition and structure, each exhibiting distinct strain responses under magnetic fields. Traditional ferromagnetic metals, such as nickel, iron, and cobalt, represent the earliest explored class, with relatively modest saturation magnetostriction coefficients (\lambda_s) that make them suitable for basic applications despite limitations in strain magnitude.^[11] Nickel displays a negative \lambda_s \approx -41 ppm, leading to contraction upon magnetization, while iron exhibits a small negative \lambda_s \approx -9 ppm in polycrystalline form, resulting in minimal dimensional change.^[42]^[43] Cobalt, in contrast, shows a larger negative \lambda_s \approx -52 ppm but is limited by its brittleness, which restricts practical use in high-stress environments.^[43] Alloys like permalloy (Ni-Fe compositions, e.g., 80% Ni-20% Fe) achieve near-zero magnetostriction (typically <5 ppm), enabling low-strain applications such as magnetic shielding and sensor cores where dimensional stability is critical.^[44] Rare-earth alloys, particularly those based on Laves-phase intermetallics, offer "giant" magnetostriction due to strong magnetoelastic coupling from 4f electron contributions. Terfenol-D, with the composition Tb_{0.3}Dy_{0.7}Fe_2, achieves \lambda_s up to 2000 ppm at room temperature, enabling significant strains for actuators, though its brittleness and high cost pose challenges.^[2] Galfenol (Fe_{1-x}Ga_x alloys, typically x \approx 0.17-0.19) provides moderate \lambda_s \approx 300-350 ppm with excellent ductility (tensile strength ~500 MPa), making it advantageous for dynamic, high-cycle applications like vibration control.^[45]^[2] Other types include amorphous ribbons, such as Metglas (Fe-based alloys like Fe_{40}Ni_{38}Mo_4B_{18}), which exhibit high magnetic permeability (>10,000) and tunable magnetostriction around 50 ppm, ideal for flexible sensors and transformers.^[46] Composites and thin films incorporate magnetostrictive particles (e.g., Terfenol-D in polymer matrices) to enhance flexibility and reduce brittleness, achieving strains up to 1000 ppm while maintaining processability for microdevices.^[47] Ferrimagnetic spinel ferrites, such as CoFe_2O_4 or NiFe_2O_4, display weaker effects with \lambda_s typically 100-300 ppm in polycrystalline forms, suitable for low-strain, high-frequency applications due to their electrical insulation and moderate anisotropy.^[48] Material selection hinges on key properties: the magnitude of \lambda_s for desired strain levels, Curie temperature T_c exceeding room temperature (e.g., >300°C for Terfenol-D) to ensure operational stability, and mechanical strength to withstand cyclic loading without fracture.^[49]^[45] Emerging nanomaterials, including Fe nanowires fabricated via template methods post-2015, show promise for enhanced magnetostriction through shape anisotropy, potentially exceeding 100 ppm in nanoscale configurations for biomedical and flexible electronics.^[50]

Mechanical and Constitutive Behaviors

Magnetostrictive materials demonstrate a variation in elastic modulus under applied magnetic fields, known as the ΔE effect, which stems from magnetoelastic coupling and can alter the Young's modulus by up to 30% in alloys like FeCoSiB.^[51] This effect is particularly pronounced in giant magnetostrictive materials such as Terfenol-D, where the modulus decreases with increasing field strength due to domain reorientation, impacting actuator performance and requiring careful modeling for dynamic applications.^[52] Under cyclic loading, these materials undergo fatigue, with crack propagation accelerated by combined magnetic and mechanical stresses; for instance, in cracked giant magnetostrictive alloys, the stress intensity factor influences fatigue life, often reduced under high fields but extended by constant bias fields that can increase cycles to failure by orders of magnitude.^[53]^[54] Microstructure plays a critical role in mechanical behavior, as grain size refinement lowers coercivity and enhances domain wall motion, thereby improving magnetostrictive responsiveness in materials like Nd₂Fe₁₄B-based alloys; finer grains near the single-domain limit reduce pinning and hysteresis losses, though excessive refinement can introduce defects that degrade fatigue resistance.^[55]^[56] Constitutive models for magnetostrictive materials often incorporate hysteresis via extensions of the Jiles-Atherton framework, which couples anhysteretic magnetization with pinning mechanisms to predict both magnetic and strain responses under preload; this approach accurately captures butterfly loops in Terfenol-D and Galfenol, with parameters tuned for stress-dependent behavior.^[57] A simpler quadratic model approximates saturation magnetostriction as \lambda = \lambda_s \left( \frac{M}{M_s} \right)^2, augmented by higher-order terms to account for anhysteretic rotation and minor loops, providing good fits for low-to-moderate fields in polycrystalline samples. Stress influences these models through the piezomagnetic coefficient d_{33}, which quantifies how compressive or tensile loads alter strain output, peaking at optimal biases in TbDyFe alloys.^[59] Advanced constitutive relations address nonlinear magnetoelastic coupling via equations like \sigma = c (\varepsilon - \lambda(M)), where \sigma is stress, c the elastic stiffness, \varepsilon total strain, and \lambda(M) field-dependent magnetostriction, enabling prediction of coupled dynamics in transducers.^[60] To achieve linear operation, bias fields are optimized around the point of maximum d_{33}, typically 100-200 kA/m for Terfenol-D stacks, minimizing nonlinearity and enhancing bandwidth in actuators.^[61] Compressive prestress aligns magnetic domains transverse to the rod axis, boosting peak strain by up to 90% at 50 MPa in polycrystalline variants, though excessive stress induces saturation.^[62] High-strain alloys like Terfenol-D suffer from brittleness, with tensile strengths limited to 25-50 MPa, restricting applications to compressive modes and necessitating composites for durability.^[63] Temperature rises induce demagnetization, shifting anisotropy and significantly reducing the modulus between 20-80°C in soft magnetostrictives, while Curie temperatures around 380°C in rare-earth alloys limit operational range.^[64] Recent models from the 2020s for multiferroic composites incorporate strain-mediated coupling in heterostructures, such as Fe₃O₄/BaTiO₃, predicting reversible magnetic modulation via nonlinear magnetoelastic terms for low-energy logic gates.^[65]

Applications

Actuators and Transducers

Magnetostrictive actuators leverage the direct magnetostriction effect in materials like Terfenol-D to generate linear or rotary motion for precision positioning applications. Terfenol-D stacks can achieve strains exceeding 1000 parts per million (ppm), enabling displacements on the order of millimeters in compact devices, while delivering blocked forces greater than 10 kN in larger configurations suitable for structural control.^[2]^[66] These actuators are particularly valued in precision engineering for their high force density and rapid response times, often outperforming piezoelectric alternatives in low-frequency, high-load scenarios. For instance, Terfenol-D-based linear actuators provide sub-micrometer resolution over strokes up to several centimeters, making them ideal for adaptive optics and vibration isolation systems.^[67] In underwater acoustics, magnetostrictive actuators serve as sonar projectors, converting electrical signals into mechanical vibrations for sound wave generation. Originating from World War II-era designs using nickel-based magnetostrictive transducers on surface ships and submarines, these devices evolved into modern high-power projectors for submarine communication and detection, operating at frequencies below 10 kHz with power outputs exceeding kilowatts.^[68] The robustness of magnetostrictive materials under high pressure and corrosion in marine environments has sustained their use, with contemporary systems incorporating Terfenol-D for enhanced efficiency and bandwidth. Magnetostrictive transducers exploit the inverse effect for energy conversion, primarily in ultrasonic applications such as welding and non-destructive testing (NDT). These devices generate high-amplitude vibrations at frequencies ranging from 20 kHz for plastic welding to several hundred kHz for guided wave flaw detection in metals, where the transducer's rod expands and contracts to drive a horn or probe.^[69] In adaptive structures, magnetostrictive transducers enable active vibration control by counteracting structural resonances in real time, as seen in aerospace components where they dampen aeroelastic flutter.^[23] Key design considerations for magnetostrictive actuators and transducers include incorporating bias magnets to linearize the response and mitigate hysteresis-induced nonlinearity. Permanent magnets provide a static field that shifts the operating point to the steepest portion of the magnetostriction curve, enabling bidirectional motion without "double-frequency" artifacts.^[61] For high-power operation, cooling systems are essential to dissipate heat from magnetic hysteresis losses, which can raise temperatures above 100°C and degrade performance; water-cooled enclosures maintain efficiency in continuous-duty cycles.^[70] Overall efficiency, defined as \eta = \frac{P_{\text{mech}}}{P_{\text{elec}}} where P_{\text{mech}} is mechanical output power and P_{\text{elec}} is electrical input power, reaches up to 50% in resonant configurations, balancing energy conversion with thermal management.^[71] Historically, magnetostrictive delay lines emerged in the late 1940s as acoustic memory storage for early computers, using nickel wires to propagate torsional pulses for data retention in systems like the EDSAC prototype.^[72] In modern applications, post-2010 advancements have integrated magnetostrictive thin films into MEMS actuators, enabling micro-scale motion for biomedical devices and optical switches with displacements up to 10 μm under low magnetic fields.^[73] These evolutions highlight the transition from bulk sonar and computing components to compact, high-precision micro-actuators.

Sensors and Energy Harvesting

Magnetostrictive sensors leverage the inverse magnetostrictive effect, also known as the Villari effect, where mechanical stress induces changes in magnetic induction (ΔB), enabling passive detection of forces and torques without requiring external power supplies.^[74] This effect allows for non-contact measurement through variations in magnetic permeability or flux, providing high sensitivity in harsh environments.^[75] Torque and force sensors based on the Villari effect are widely used in automotive and structural health monitoring applications, where applied stress alters the magnetization of the material, detectable via encircling coils.^[24] For instance, magnetostrictive torque sensors employ this principle to measure rotational forces with resolutions better than 0.1% of full scale, offering robustness against electromagnetic interference.^[76] These sensors achieve high linearity over a wide dynamic range, with sensitivities suitable for industrial applications.^[77] Magnetic field sensors utilizing magnetostriction exploit strain-induced changes in permeability for non-contact detection, where external fields modulate the material's magnetic response under controlled bias stress.^[78] This configuration enhances sensitivity to DC and AC fields, with mechanical quality factors and saturation magnetization optimizing performance for applications like structural monitoring.^[78] In biomedical contexts, such sensors enable precise navigation of catheters by tracking magnetic perturbations in real-time, facilitating minimally invasive procedures with sub-millimeter accuracy. Energy harvesting devices convert vibrational energy to electricity through the inverse magnetostrictive effect in cantilever structures, where mechanical oscillations induce magnetic flux variations that generate voltage in surrounding coils.^[79] Typical configurations use Terfenol-D or Galfenol rods bonded to beams, achieving power densities on the order of 1 mW/cm³ at resonance frequencies around 40-50 Hz.^[80] Developments in the 2010s focused on Terfenol-based generators to power wireless sensors in structural health monitoring, delivering sufficient output (up to 200 µW) for autonomous operation in remote environments.^[81] These applications benefit from magnetostrictive sensors' and harvesters' high sensitivity and self-powered nature, eliminating the need for batteries and enabling long-term deployment in inaccessible locations.^[82] However, challenges include hysteresis losses, which introduce nonlinearity and reduce energy conversion efficiency by up to 30% in dynamic cycles.^[83] Recent advances through 2025 have addressed these issues via optimized magnetoelectric composites and flexible designs, including flexible magnetic films for enhanced strain response and switching control strategies for multimodal vibrations, improving IoT integration with bandwidth and power outputs exceeding 4 mW/cm³ for low-frequency vibrations.^[79]^[84]^[85]^[86]

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[PDF] study of effective methods of characterisation of magnetostriction ...
can be divided into linear magnetostriction, volume magnetostriction and form effect. Joule [16] first discovered in 1842 the fact that the ferromagnetic ...
[36]
Establishment of the standard method of magnetostriction ...
Jan 1, 2023 · Standard method of magnetostriction measurement of grain-oriented electrical steel strip and sheet by means of a single sheet tester and an optical sensor was ...
[37]
Measuring the inverse magnetostrictive effect in a thin film using a ...
Jan 30, 2014 · A method for measuring the magnetostriction of thin films using a vibrating sample magnetometer is described. We describe the design of a ...INTRODUCTION · II. METHODS · III. MEASUREMENT
[38]
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/92JB01846
[39]
High‐temperature magnetostriction of magnetite and titanomagnetites
Jan 10, 1993 · Magnetostriction of synthetic polycrystalline magnetite and titanium-rich titanomagnetites has been measured from 25°C to their Curie temperatures.Missing: challenges | Show results with:challenges
[40]
Measurement and calculation for high frequency magnetic losses of ...
Nov 14, 2023 · Therefore, according to the application range of underwater magnetostrictive transducers, the AC excitation frequency is set to 1–9 kHz, and the ...Testing system design · Experimental results and... · The modified magnetic loss...
[41]
Quantitative profilometric measurement of magnetostriction in thin ...
Jul 30, 2024 · A DC non-contact method for measuring the magnetostrictive strain in thin-films is demonstrated, achieving a state-of-the-art sensitivity.Short Communication · 2. Optical Profilometry To... · 4.4. Results<|control11|><|separator|>
[42]
Cost-effective measurement of magnetostriction in nanoscale thin ...
Jun 1, 2023 · The tip displacement is measured by monitoring the position of a reflected laser beam using two differentially coupled photodiode positioning ...
[43]
Giant magnetoelectric effect in negative magnetostrictive ...
Jan 21, 2016 · When H > 1 kOe, the magnetostriction of Ni is saturated at the value about −41 ppm. On the contrary, the magnetostriction of TbFe2 does not ...
[44]
Magnetostriction of heavily deformed Fe–Co binary alloys prepared ...
For example, pure iron possesses negative magnetostriction of about −9 ppm and cobalt shows relatively large negative magnetostriction of about −52 ... Equiatomic ...
[45]
A solution to the permalloy problem—A micromagnetic analysis with ...
Our results demonstrate that specific values of magnetostriction constants and anisotropy constants are necessary for the dramatic drop of hysteresis at 78.5% ...
[46]
Structural and magnetic properties of magnetostrictive Fe-Ga-Zr ...
Oct 5, 2023 · Rare-earth free Fe1−xGax (Galfenol) single crystals within the range of x = 0.15–0.3 showed magnetostriction with a peak value of ∼300 ppm in a ...
[47]
Improving the magnetoelectric performance of Metglas/PZT ... - NIH
The optimized ribbons had a magnetostriction of 50.6 ± 0.2 μm m−1 and magnetoelectric coefficient of 79.3 ± 1.5 μm m−1 mT−1. The optimized Metglas 2605SA1 ...
[48]
Large Magnetostriction in Terfenol-D Particulate Composites with ...
The saturation magnetostriction for a cubic polycrystal is given by λpc = 2/5λ100+3/5λ111 and is equal to 1020 ppm for Terfenol-D.
[49]
High magnetostriction and coupling coefficient for sintered cobalt ...
Aug 14, 2012 · A saturation magnetostriction of 315 ppm is obtained for this sample, much larger than that reported for cobalt ferrite powders synthesized by ...
[50]
Terfenol-D - ETREMA Products, Inc. - TdVib, LLC
Terfenol-D is an alloy comprised of Terbium, Dysprosium and Iron. Terfenol-D has the largest room temperature magnetostriction of any known material.
[51]
Preparation, characterization, and magnetic resonance imaging of ...
Oct 31, 2023 · Abstract. A facile template method was employed to synthesize Fe nanowires of different sizes, dimensions.
[52]
Influence of the delta-E effect on a surface acoustic wave resonator
Feb 15, 2019 · The Young's modulus of the FeCoSiB layer can be changed by an EMF, due to the delta-E effect and up to approximately 30% (the Young's modulus of ...
[53]
Experimental Investigation of Terfenol-D's Elastic Modulus
The variability of Young's modulus (the ▵E effect) in giant magnetostrictive Terfenol-D has a significant impact on the performance and modeling of ...
[54]
Three-point bending fatigue of cracked giant magnetostrictive ...
Jul 25, 2017 · This paper investigates the cyclic fatigue behavior in giant magnetostrictive materials with a crack under magnetic fields.
[55]
Influence of Constant Magnetic Field upon Fatigue Life of ...
It was shown that the application of the constant magnetic field of varying density led to a fold increase in the average number of cycles to destruction.
[56]
Grain Size & Coercivity Tuning in Nd2Fe14B Magnets
Sep 15, 2023 · In this work, we use high pressure hydrogen milling to reduce the average grain size in Nd 2 Fe 14 B powders towards the critical single domain regime.
[57]
Influence of the Microstructure on the Magnetic Properties of Giant ...
These additives enhance the nucleation of REFe2 grains and hinder the formation of REFe3 which is assumed to be responsible for high coercivity values.
[58]
An Improved Magnetostriction Model for Electrical Steel Sheet ...
Jan 28, 2020 · A model is established based on the improved Jiles-Atherton (JA) model by introducing the parameter k 1 , which considers the domain moment rotation.
[59]
[PDF] An Energy-Based Hysteresis Model for Magnetostrictive Transducers
The quadratic magnetostriction model is also accurate at low to moderate drivc levels but must be extended to incorporate the hysteresis and saturation present ...
[60]
The stress dependence of magnetostriction hysteresis in TbDyFe ...
piezo-magnetic coefficient, d33, reaches a maximum, as illus- trated in the inset of Fig. 1. As shown in Fig. 1, the variation tendency of magneto-.
[61]
Non-linear constitutive relations for magnetostrictive materials
In this paper, non-linear deformation behavior of magnetostrictive materials is studied and three magnetoelastic coupling constitutive models are developed.
[62]
Bias Magnetic Field of Stack Giant Magnetostrictive Actuator: Design ...
Jul 20, 2016 · Since an appropriate bias field helps these devices to operate in a region, both slope and linearity of magnetostriction are favorable and avoid ...
[63]
A thermal-induced prestress method for enhancing magnetostrictive ...
Feb 1, 2025 · By applying appropriate prestress, the initial distribution of magnetic domains in the magnetostrictive material can be aligned to the ...
[64]
Engineers guide to Terfenol-D actuators: Design, performance, and ...
Terfenol-D, a rare earth substance renowned for its remarkable magnetostrictive capabilities, is used in the field of actuators and sensors.
[65]
Temperature effects on magnetization processes and ...
Easy anisotropy direction is changed due to stress release upon heating. · Impedance changes up to 200% with moderate temperature increase to 50–80 °C.
[66]
Ultralow-energy multiferroic majority gates via magnetostrictive ...
Feb 1, 2025 · This study introduces an innovative strain clocking mechanism consisting of global strain clocking and local strain clocking for a majority logic gate.
[67]
Use of Magnetomechanical Effect for Energy Harvesting and Data ...
Apr 26, 2022 · Additionally, such actuators generate large forces, which, depending on the design and size of the device, can reach up to several hundred kN.
[68]
[PDF] Bulk motion for ultrasonic-assisted microforming using Terfenol-D
Terfenol-D is a giant magnetostrictive alloy, meaning it strains in response to a magnetic field. ... Precise position control is possible with Terfenol-D ...<|control11|><|separator|>
[69]
(PDF) A concise history of acoustics in warfare - Academia.edu
... magnetostrictive principle and was used as an active sonar on surface ships. ... The 692 submarine sonar projector mounted on submarine deck: World War II.
[70]
[PDF] ULTRASONIC NONDESTRUCTIVE TESTING - ROSA P
magnetostrictive transducers, at present, are most often used in high-power applications such as ultrasonic cleaning, welding, drilling, machining, etc.
[71]
Integrated optimized design of GMA with double water-cooling ...
Abstract: Giant magnetostrictive actuator(GMA) structure design includes magnetic design and thermal design, and they are relevant.Missing: efficiency | Show results with:efficiency
[72]
Actuation and transduction by giant magnetostrictive alloys
Given giant magnetostrictive strains (∼1200 ppm) coupled with a high transduction efficiency (>50%) and a large load bearing capability, all of which can be ...
[73]
Early British Computers
In the magnetostrictive delay line, electrical pulses were converted into stress waves which travelled down a length of (nickel) wire. The conversion from ...
[74]
Comprehensive study of magnetostriction-based MEMS magnetic ...
Nov 1, 2021 · The study is meant to explore its magnetic sensing mechanism, reaction to magnetic field direction, the separate effect of magnetic force, and ...
[75]
[PDF] MAGNETOSTRICTIVE DEVICES - U.OSU - The Ohio State University
Magnetostrictive materials convert magnetic energy to mechanical energy and vice versa. They deform when magnetized, and their magnetization changes under ...
[76]
(PDF) Galfenol-Based Devices for Magnetic Field Sensing in Harsh ...
Aug 6, 2025 · The power losses consist of hysteresis loss, classical eddy current loss, and anomalous (or excess) loss when Galfenol is excited by a dynamic ...
[77]
A high accuracy magnetostrictive linear position sensor
Preliminary results with the new sensor indicate a considerable improvement over the accuracy of standard MS sensors. Section snippets. Linear position sensors.
[78]
Constant Current Galfenol Electrodeposition on an Optical Fiber with ...
Apr 27, 2024 · These sensors are designed for measuring magnetic fields, electric current, and temperature. When a magnetostrictive material like Galfenol ...
[79]
Magnetostrictive current sensor with high sensitivity and a large ...
The sensor uses magnetostrictive composites, steel bars, and adjustable coils. It has a sensitivity of 0.391-0.418 µɛ/A and a linear range of 0-500A and 500- ...
[80]
The magnetostrictive material effects on magnetic field sensitivity for ...
Feb 9, 2012 · To obtain the high magnetic sensitivity to dc and ac magnetic field, the mechanical quality factor, the magnetic permeability and the saturation ...
[81]
Energy harvesting using a magnetostrictive transducer based on ...
Jun 1, 2023 · Switching control energy harvesting method proposed using magnetostrictive material. Large-scale kinetic to electrical energy conversion can be achieved.
[82]
Vibration energy harvesting by magnetostrictive material - IOPscience
Jun 3, 2008 · A new class of vibration energy harvester based on magnetostrictive material (MsM), Metglas 2605SC, is designed, developed and tested.
[83]
(PDF) Energy harvesting by magnetostrictive material (MsM) for ...
Aug 9, 2025 · An energy harvesting module, which powers a wireless sensor, stores excess energy in an ultracapacitor is designed on a printed circuit board ( ...
[84]
Magnetostrictive linear position sensors - Althen Sensors
MST Magnetostrictive Position Sensor · Measuring range 100 mm to 900 mm · 16 bit resolution (200 µm) · Wear- and maintenance-free.
[85]
Research on Hysteresis Modeling and Compensation Method of ...
Dec 23, 2021 · To improve the linearity and eliminate the hysteresis of such sensors, an output compensation method using a variable bias current is proposed ...Missing: challenges | Show results with:challenges
[86]
Design and Optimization of a Compact Rectangular Galfenol-Based ...
Jul 26, 2025 · Thanks to the to the refinement process, the resulting design, despite its simplicity, delivers a power density of 4.3 mW/cm3 at 40 Hz resonance ...