Modeling of core-shell magneto-electric nanoparticles for biomedical applications: Effect of composition, dimension, and magnetic field features on magnetoelectric response

Abstract

The recent development of core-shell nanoparticles which combine strain coupled magnetostrictive and piezoelectric phases, has attracted a lot of attention due to their ability to yield strong magnetoelectric effect even at room temperature, thus making them a promising tool to enable biomedical applications. To fully exploit their potentialities and to adapt their use to in vivo applications, this study analyzes, through a numerical approach, their magnetoelectric behavior, shortly quantified by the magnetoelectric coupling coefficient (αME), thus providing an important milestone for the characterization of the magnetoelectric effect at the nanoscale. In view of recent evidence showing that αME is strongly affected by both the applied magnetic field DC bias and AC frequency, this study implements a nonlinear model, based on magnetic hysteresis, to describe the responses of two different core-shell nanoparticles to various magnetic field excitation stimuli. The proposed model is also used to evaluate to which extent realistic variables such as core diameter and shell thickness affect the electric output. Results prove that αME of 80 nm cobalt ferrite-barium titanate (CFO-BTO) nanoparticles with a 60:40 ratio is equal to about 0.28 V/cm∙Oe corresponding to electric fields up to about 1000 V/cm when a strong DC bias is applied. However, the same electric output can be obtained even in absence of DC field with very low AC fields, by exploiting the hysteretic characteristics of the same composites. The analysis of core and shell dimension is as such to indicate that, to maximize αME, larger core diameter and thinner shell nanoparticles should be preferred. These results, taken together, suggest that it is possible to tune magnetoelectric nanoparticles electric responses by controlling their composition and their size, thus opening the opportunity to adapt their structure on the specific application to pursue.

Fig 1. MENP computational modeling.

Schematic representation of: a) the geometrical parameters of a generic core-shell MENP; b) the simulation settings in the three different analyses performed; c) the computational study workflow.

Fig 2

MENPs cores magnetization behavior. DC magnetization loops of a) CFO and b) FO core 50 nm nanoparticles.

Fig 3. Magnetoelectric effect elicited by DC magnetic field stimulation.

Distribution of (from top to bottom) surface: M (emu/g), strain ε (ppm), electric field E module (V/m), and electric potential V (mV) in 2D axisymmetric (left) CFO-BTO and (right) FO-BTO core shell nanoparticles (Ø_core = 50 nm and t_shell = 15 nm) when a high amplitude (H = M_s) magnetic field is used as stimulation.

Fig 4. Effect of core and shell size on magnetoelectric coefficient.

Trend analysis of variable core size (a and b) and shell thickness (c and d) of CFO-BTO (a and c) and FO-BTO (b and d) MENPs when stimulated with a high strength (> Ms) DC bias magnetic field directed along z on the magnetoelectric coefficient α_ME (V/cm∙Oe).

Fig 5. Magnetization of MENP under DC+AC stimulation.

Magnetization M(emu/g) (red line) of a CFO core (Ø_core = 50 nm)-BTO shell (t_shell = 15 nm) nanoparticle under a DC+AC external magnetic field (H (Oe)- blue line) directed along z. a) M(emu/g) as a function of 2 seconds DC high amplitude (H = 10 kOe) magnetic field followed by 4 seconds weak AC (f = 50 Hz, 100 Oe) magnetic field excitation. b) Magnification of Fig 5A in five AC excitation periods.