Quantitative Measurements of Size-Dependent Magnetoelectric Coupling in Fe₃O₄ Nanoparticles

Bulk magnetite (Fe₃O₄), the loadstone used in magnetic compasses, has been known to exhibit magnetoelectric (ME) properties below ∼10 K; however, corresponding ME effects in Fe₃O₄ nanoparticles have been enigmatic. We investigate quantitatively the ME coupling of spherical Fe₃O₄ nanoparticles with uniform diameters (d) from 3 to 15 nm embedded in an insulating host, using a sensitive ME susceptometer. The intrinsic ME susceptibility (MES) of the Fe₃O₄ nanoparticles is measured, exhibiting a maximum value of ∼0.6 ps/m at 5 K for d = 15 nm. We found that the MES is reduced with reduced d but remains finite until d = ∼5 nm, which is close to the critical thickness for observing the Verwey transition. Moreover, with reduced diameter the critical temperature below which the MES becomes conspicuous increased systematically from 9.8 K in the bulk to 19.7 K in the nanoparticles with d = 7 nm, reflecting the core-shell effect on the ME properties. These results point to a new pathway for investigating ME effect in various nanomaterials.