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Quantum Saturation of Magnetoelectric Coupling in Fe₃O₄ Nanoparticles

Abstract

We report magnetoelectric coupling in nanoparticle assemblies that persists to temperatures over 300 times lower than in previous studies. The ME response saturates at low temperature, revealing a quantum plateau of the coupling. A field dependence analysis shows a crossover from quadratic to linear behavior, captured by a phenomenological expansion C(B,T) ≃ C₀(T) + a₁(T) B + a₂(T) B². The magnitude of the extracted quadratic coefficient, |a₂(T)|, follows a power law |a₂(T)| ∼ T^-α with α ≈ 1.15, indicating proximity to a quantum critical regime. The observed saturation reflects a new intrinsic energy scale, distinct from finite-size or extrinsic effects. These results establish nanoparticle assemblies as a new platform for studying quantum magnetoelectric phenomena.

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