Flexomagnetic Effects in Nanostructured Materials

Flexomagnetism refers to the coupling between gradients of mechanical strain and magnetic polarisation, a higher-order phenomenon that becomes prominent at the nanoscale. Unlike bulk piezomagnetic responses, flexomagnetic effects emerge from strong strain gradients in structures such as beams, films and particles with characteristic dimensions below a few hundred nanometres. Theoretical treatments often invoke nonlocal strain-gradient elasticity to capture size-dependent behaviour and draw analogies with flexoelectricity in dielectrics. Experimental realisations include nanoindentation under magnetic bias, buckling tests on nanobeams and dynamic resonance measurements. Advances in fabrication—ranging from focused-ion-beam milling to self-assembled multilayers—have enabled precise control of geometry and defect distribution, while high-resolution magnetic and mechanical probes have quantified local flexomagnetic coefficients. The interplay of flexomagneticity with piezomagnetism, magnetostriction and thermal fields offers routes to tunable sensors, energy harvesters and adaptive resonators. Globally, this research underpins next-generation micro-electro-mechanical systems in areas such as biomedical devices, environmental sensing and information storage. Progress hinges on integrated modelling, innovative metrology and the design of multifunctional nanocomposites, pointing to a rapidly evolving field at the intersection of mechanics, magnetism and materials science.

Research from Nature Portfolio

Recent studies have shown that magnetomechanical nanoindentation on nickel single crystals can isolate flexomagnetic contributions to mechanical properties. In a pioneering experiment, indentation hardness and apparent Young’s modulus were measured both with and without an applied magnetic field, revealing a flexomagnetic-driven modulus increase of about 31 % and a hardness reduction of around 7 %. The work elucidates how strain-gradient-induced magnetic polarisation interacts with dislocations, providing a quantitative benchmark for flexomagnetic coupling coefficients and guiding the design of magnetic field-tunable microscale devices.

Flexomagnetic Effects in Nanostructured Materials publication trend

The graph below shows the total number of articles in flexomagnetic effects in nanostructured materials across all publications each year (not limited to Nature Index journals).

Technical terms

Flexomagnetism: Magnetisation induced by gradients of mechanical strain, significant at nanometre scales.

Piezomagnetism: Linear coupling between uniform mechanical strain and magnetic polarisation.

Strain gradient: Spatial variation of strain within a material, central to size-dependent effects.

Nonlocal strain-gradient elasticity: Continuum theory extending classical elasticity to include strain gradient terms for nanoscale modelling.

Nanoindentation: Technique for probing local mechanical properties by pressing a sharp tip into a material surface under controlled loading.

References

1. Magnetic Field Tunable Small-scale Mechanical Properties of Nickel Single Crystals Measured by Nanoindentation Technique. Scientific Reports (2014).
2. Effect of Axial Porosities on Flexomagnetic Response of In-Plane Compressed Piezomagnetic Nanobeams. Symmetry (2020).
3. Thermal buckling of functionally graded piezomagnetic micro- and nanobeams presenting the flexomagnetic effect. Continuum Mechanics and Thermodynamics (2021).
4. On dynamic modeling of piezomagnetic/flexomagnetic microstructures based on Lord–Shulman thermoelastic model. Archive of Applied Mechanics (2022).