What Is Magnetoelasticity?

Magnetoelasticity is a branch of continuum mechanics and materials physics that describes the bidirectional coupling between the magnetic state and the mechanical deformation state of a solid. A magnetoelastic material changes its shape when its magnetization changes, and conversely, changes its magnetic properties when it is mechanically strained. The field draws on classical elasticity theory, micromagnetics, and thermodynamics, and is directly relevant to the design of magnetic sensors, actuators, and resonant devices built from ferromagnetic and ferrimagnetic materials. The coupling is most pronounced in transition metal alloys and rare-earth compounds with strong spin-orbit interaction, and absent or negligible in diamagnetic and most paramagnetic materials.

Magnetoelasticity encompasses both the intrinsic coupling encoded in a material's free energy and the macroscopic deformation patterns that result when domains rearrange under applied fields or stresses. The field is sometimes called magnetomechanics when the emphasis is on force and strain, and magnetostriction when the emphasis is on dimensional change.

Joule Magnetostriction and the Villari Effect

Joule magnetostriction, described by James Prescott Joule in 1842, is the elongation or contraction a ferromagnetic body experiences along the direction of an applied magnetic field. It arises because magnetic domain boundaries shift and domains rotate to align with the field, changing the average spacing between atomic planes. The fractional length change, denoted lambda (the magnetostrictive coefficient), is typically on the order of 10 to 100 parts per million (ppm) for iron and nickel, but reaches 1500 to 2000 ppm in Terfenol-D (Tb0.3Dy0.7Fe2), a rare-earth compound developed at the Naval Ordnance Laboratory in the 1970s. The nonlinear magneto-mechanical coupling in ferromagnetic materials is well captured by models that combine micromagnetics with elastic strain fields. The inverse process, the Villari effect, describes a change in magnetization produced by applied mechanical stress, and forms the basis of magnetostrictive stress sensors.

Magneto-Mechanical Coupling and Domain Dynamics

At the microscale, magnetoelastic coupling arises from spin-orbit interaction: the electron orbits responsible for magnetization are also responsible for the electrostatic repulsion between neighboring atoms, so rotating spins changes interatomic distances. Domain walls, the boundaries between regions of uniform magnetization, move under applied stress or field, and their motion is the primary carrier of both the magnetostrictive strain and the associated hysteresis losses. The coupling is quantified by magnetoelastic coupling coefficients that appear in the free-energy expansion alongside the magnetic anisotropy energy and the exchange energy. High magnetoelastic coupling makes a material useful as an actuator; low hysteresis makes it useful as a sensor. Magnetostriction and magnetoelasticity in heterogeneous and nanostructured materials follow different scaling laws than bulk materials because domain sizes become comparable to sample dimensions.

Magnetoelastic Resonance and Sensing

Magnetoelastic resonators are thin strips or ribbons of amorphous ferromagnetic alloys, typically iron-based metallic glasses, that vibrate at characteristic mechanical resonant frequencies that shift with applied stress, temperature, or surface loading. Because the resonant frequency is detected magnetically, no electrical connection to the sensor is required, enabling wireless, passive sensing schemes. Viscosity, mass loading, and pressure can all be measured by monitoring the resonant frequency of a remotely interrogated strip. The principles and applications of magneto-elastic resonance have been reviewed in detail, covering biosensors, structural health monitoring, and food-safety inspection devices. MEMS-scale magnetoelastic structures produced by sputtering or electrodeposition extend the technology to the micrometer length scale.

Applications

Magnetoelasticity has applications in a range of fields, including:

• Linear and rotary actuators using Terfenol-D or Galfenol (Fe-Ga alloys) in precision positioning and ultrasonic transduction
• Torque and stress sensors embedded in shafts and structural members without electrical contact
• Wireless biochemical sensors that detect viscosity, mass loading, or specific binding events
• Energy harvesting devices that convert ambient mechanical vibration into electrical power through the Villari effect
• Magnetostrictive sonar transducers and underwater acoustic projectors