Magnetoelectric nanoparticles could sense brain magnetic fields, simulation study finds

A computational study published in Bioelectronic Medicine suggests that resonant core–shell magnetoelectric nanoparticles could, in principle, act as tiny wireless sensors for the weak magnetic fields produced by brain activity. The work, led by Giulia Caiani and colleagues at institutions including the Istituto di Ricerche Farmacologiche Mario Negri and the Fondazione IRCCS Istituto Neurologico Carlo Besta in Milan, models a single nanoparticle made of a magnetostrictive cobalt ferrite core wrapped in a piezoelectric barium titanate shell and asks whether its mechanical resonance could be shifted measurably by neural-level magnetic signals. The simulations show a maximum sensitivity of 2.59 Hz per nanotesla for a nanoparticle with a 50-nanometre core diameter when held under a static bias magnetic field of 1000 oersted, the highest value among the core sizes tested.

The study is explicitly a proof of concept carried out entirely in silico, using finite-element simulations in COMSOL Multiphysics 6.3 rather than laboratory measurements. No noise modelling was included, so the simulations do not establish a limit of detection, and the authors note that real sensing would likely involve clusters of interacting nanoparticles rather than a single isolated one. Even so, the modelling points to a sensing mechanism that would not require cryogenic cooling, implanted electronics or batteries, since the nanoparticles emit an electromagnetic signal at their resonance frequency that could in principle be picked up by an external receiving antenna tuned to the gigahertz range.

The physics underlying the proposal is the delta-E effect, a change in the Young’s modulus of a magnetostrictive material that arises when magnetic domains reorient during magnetization. In the cobalt ferrite core, this means the material’s stiffness depends on the magnetic field it experiences. Because the nanoparticle’s electromechanical resonance frequency depends on that stiffness, a change in the surrounding magnetic field translates into a measurable shift in the frequency at which the particle resonates. The authors quantify this effect by tracking the resonance frequency as the bias field varies, and they compute a relative stiffness change of 1.94 percent for the 50-nanometre-core particle.

To build a credible model, the team first characterized the nanoparticle’s magnetic behaviour. The cobalt ferrite core was described with the Jiles–Atherton hysteresis model, with parameters tuned to reproduce the magnetization loop of a cobalt ferrite–barium titanate nanoparticle synthesized in a previous experimental study. The modelled particle has a 50-nanometre core and a 15-nanometre-thick barium titanate shell, and the surrounding environment was simulated as a cylindrical domain extending well beyond the particle itself. When the model was driven to magnetic saturation with a static field of 15 kilo-oersted, the magnetoelectric coefficient, a measure of how efficiently the particle converts magnetic input into electric potential, came out at 22.9 millivolts per centimetre per oersted at a bias of 12 kilo-oersted, a value the authors describe as consistent with published literature on similar nanoparticles.

The next step was to find where the particle naturally resonates. Eigenfrequency simulations, linearized around a static bias of 1000 oersted, revealed six resonant modes in the gigahertz range for each core diameter tested, which ranged from 25 to 250 nanometres. The first resonant mode turned out to be weak, producing a magnetoelectric coefficient below 1 millivolt per centimetre per oersted, while the second mode reached values on the order of volts per centimetre per oersted, roughly two orders of magnitude above the off-resonance condition. The team therefore focused on this second mode for all subsequent analysis. For the 50-nanometre-core particle, the dominant resonance sits near 36.135 gigahertz, where the simulations show a sharp peak in core strain, core magnetization and the electric potential on the outer shell, indicating efficient conversion of magnetic excitation into electrical output at that frequency.

Core diameter proved to be a powerful tuning knob. As the core grows larger, the resonance frequency falls exponentially, asymptotically approaching about 10 gigahertz with a characteristic decay length of 69 nanometres, meaning that a change in core diameter of that scale produces a 37 percent drop in resonant frequency relative to the initial value above the asymptote. Larger cores also showed higher quality factors, which correspond to narrower resonance peaks and therefore greater selectivity in detecting small frequency shifts. This tunability matters because gigahertz-frequency electromagnetic waves are strongly absorbed by biological tissue, with attenuation the authors cite as exceeding 100 decibels, a recognized obstacle for in vivo use. Shifting the resonance toward lower gigahertz frequencies by enlarging the core could reduce that attenuation, and the authors suggest that synthesis strategies such as cationic substitutions or specific processing methods could push frequencies down further.

To assess sensitivity, the team swept the static bias field from 0 to 15 kilo-oersted and tracked how the resonance frequency moved. For the 50-nanometre-core particle, the resonance frequency dropped from about 36.277 gigahertz near zero bias to a minimum of 35.916 gigahertz at 2.6 kilo-oersted, the field at which the piezomagnetic coefficient, describing how easily magnetic domains rotate, is highest. Beyond that point the frequency rose again and saturated at very high fields, reaching 36.27 gigahertz at 40 kilo-oersted. The total maximum resonance frequency shift across that range was 361 megahertz. Taking the derivative of the frequency-versus-field curve gave the sensitivity, and for every core size tested the maximum occurred at a bias of 1 kilo-oersted. The values were 1.81, 2.59, 2.26, 1.79, 1.45 and 1.10 Hz per nanotesla for core diameters of 25, 50, 100, 150, 200 and 250 nanometres respectively, with the 50-nanometre particle the clear winner.

With the optimal working point identified, the team then simulated what happens when a neural magnetic field is added on top of the bias. Under the simplifying assumption that the neural field and the bias field are aligned in the same direction, the external field was varied from 0 to 80 oersted in steps of 5 oersted, a range chosen in line with a previous study of resonant magnetoelectric sensors. A 5-oersted change in the external field produced a resonance frequency shift of approximately 1.4 megahertz in the modelled nanoparticle. The authors note that a 1-nanotesla change in the static magnetic field causes a shift of roughly 2 hertz, a magnitude they point out is in line with the order of the magnetic field near an axon reported in earlier experimental work. Resolving shifts of a few hertz, they argue, would require a highly selective resonant antenna with a narrow detection bandwidth centred on the nanoparticle’s natural resonance frequency.

The broader context is that biomagnetic sensing, whether magnetoencephalography for the brain or magnetocardiography for the heart, currently depends on superconducting quantum interference devices that achieve femtotesla sensitivity but demand bulky, expensive instrumentation operating in magnetically shielded and temperature-controlled environments. Magnetoelectric materials have attracted attention as room-temperature, low-power alternatives with detection limits in the picotesla-per-root-hertz range at low frequencies, but most work so far has involved millimetre-scale structures such as resonators, cantilevers and delay lines. Magnetoelectric nanoparticles themselves have mainly been studied for brain stimulation, nano-electroporation and targeted drug delivery, and in vivo animal studies have shown they can be injected intravenously without surgery. Using them as nanoscale sensors of spontaneous neural magnetic activity via the delta-E effect, the authors say, has not been investigated before and represents a novel direction.

Several limitations temper the promise. The study is deterministic and excludes noise, so no limit of detection can be stated yet; a full noise model is planned for future work. The analysis covers a single nanoparticle, whereas realistic sensing would involve clusters whose mutual interactions, and whose variability in size and morphology from synthesis, could shift resonant frequencies and alter magnetoelectric responses in ways that are not yet modelled. The resonance frequencies found, in the tens of gigahertz, sit in a regime where tissue absorption is severe, although the authors argue that antenna technology operating in the low gigahertz range, such as implantable brain–computer interfaces and wireless pacemakers already described in the literature, makes external detection of the emitted signal plausible. The authors also note that the delta-E effect is attenuated at high frequencies due to stiffening of the Young’s modulus, which is why the resonance shifts they observe occur under magnetic field strengths in the kilo-oersted range. As a theoretical groundwork, the study establishes that the delta-E effect can in principle be exploited at the nanoscale and that structural parameters such as core diameter and bias field can be tailored for specific applications, but translating these simulations into working sensors will require experimental validation, noise analysis and a better understanding of how nanoparticles behave when deployed together in biological tissue.

Subject of Research: Computational modelling of resonant core–shell magnetoelectric nanoparticles as wireless nanoscale sensors of neural magnetic fields via the delta-E effect

Article Title: Resonant core–shell magnetoelectric nanoparticles as sensors of neural magnetic activity: a computational study

Article References: Caiani, G., Chiaramello, E., Ravazzani, P., & Fiocchi, S. (2026). Resonant core–shell magnetoelectric nanoparticles as sensors of neural magnetic activity: a computational study. Bioelectronic Medicine, 12(1), Article 1. https://doi.org/10.1186/s42234-025-00198-1

Image Credits: AI Generated

DOI: 10.1186/s42234-025-00198-1

Keywords: magnetoelectric nanoparticles, delta-E effect, biomagnetic sensing, cobalt ferrite, barium titanate, neural magnetic fields, computational modelling, COMSOL simulation, electromechanical resonance, core–shell nanoparticles, magnetoencephalography, wireless sensors