A Thermo-Magneto-Mechanical Model for Ferromagnetic Shape Memory Thin Film Actuators Available to Purchase

The last decade has witnessed the discovery of materials combining shape memory behavior with ferromagnetic properties (FSMAs), see, e.g., James & Wuttig¹, James et al.². These materials feature the so-called giant magnetostrain effect, which, in contrast to conventional magnetostriction, is due to the motion of martensite twins. It was first observed in NiMn₂Ga single crystals, Ullakko et al.³, but later discovered in polycrystals as well, see Ullakko⁴. This effect has motivated the development of a new class of active materials transducers, which combine intrinsic sensing capabilities with superior actuation speed and improved efficiency when compared to conventional shape memory alloys. The effect has also been found in thin films, Rumpf et al.⁵, and this technology is currently being developed intensively in order to pave the way for applications in micro- and nanotechnology. As an example, Kohl et al.^6,7, recently proposed a novel actuation mechanism based on NiMnGa thin film technology, which makes use of both the ferromagnetic transition and the martensitic transformation allowing the realization of an almost perfect antagonism in a single component part. The implementation of the mechanism led to the award-winning development of an optical microscanner⁸. Possible applications in nanotechnology arise, e.g., by combination of smart NiMnGa actuators with scanning probe technologies. The key aspect of Kohl’s device is the fact that it employs electric heating for actuation, which requires a thermo-magneto-mechanical model for analysis. The research presented in this paper aims at the development of a model that simulates this particular material behavior. It is based on ideas originally developed for conventional shape memory alloy behavior, (Mueller & Achenbach⁹, Achenbach¹⁰, Seelecke¹¹, Seelecke & Mueller¹²) and couples it with a simple expression for the nonlinear temperature-and position-dependent effective magnetic force. This early and strongly simplified version does not account for a full coupling between SMA behavior and ferromagnetism yet, and does not incorporate the hysteretic character of the magnetization phenomena either. It can however be used to explain the basic actuation mechanism and highlight the role of coupled magnetic and martensitic transformation with respect to the actuator performance. In particular will we be able to develop guidelines for desirable alloy compositions, such that the resulting transition temperatures guarantee optimized actuator performance.