Theory of hard magnetic soft materials to create magnetoelectricity

Materials that generate electrical signals upon exposure to a well-controlled stimuli are high desirable. In that context, magnetoelectrics are unusual in the sense that the stimulus may be applied remotely (and wirelessly) without recourse to any physical contact. Wireless energy harvesting, remotely triggered biomedical agents, soft robots among others are some of the applications of such materials. The magnetoelectric property however is somewhat elusive in natural materials and artificial composites designed to exhibit this effect are invariably hard materials, require a pre-existing magnetic field and only exhibit a non-trivial coupling at high frequencies. Our recent experiments (presented elsewhere) demonstrated a facile route to create highly deformable soft magnetoelectric materials predicated on the concept of programmable hard magnetic soft materials with embedded immobile electric charges (electrets). In this work, we offer a nonlinear theoretical framework to both understand the emergent magnetoelectric effect in this class of soft materials as well as to design novel structures and devices with tailored functionality. Specifically, we are able to show that mechanical strain convects residual electrical and magnetic field states to mediate an unprecedented strong magnetoelectric coupling that is independent of the applied external magnetic field and retains its potency at low frequencies. We analytically solve simple illustrative examples to establish insights and present a finite element approach to handle complexities that may be otherwise intractable. The predictions of our theory agree very well with published experiments.