Materials Science and Engineering A 378 (2004) 52–60 Magnetically driven shape memory alloys J. Enkovaara a , A. Ayuela a,b,∗ , A.T. Zayak c , P. Entel c , L. Nordström d , M. Dube e , J. Jalkanen a , J. Impola a , R.M. Nieminen a a Laboratory of Physics, Helsinki University of Technology, Helsinki, Finland b Donostia International Physics Center (DIPC), Spain c Institute of Physics, Gerhard-Mercator University, Duisburg, Germany d Condensed Matter Theory, Uppsala University, Uppsala, Sweden e Department of Physics, McGill University, McGill, Canada Received 15 June 2003; received in revised form 17 October 2003 Abstract Significant progress has been made both in experimentation and theoretical modelling of the magnetic shape memory (MSM) effect, where magnetic field can induce strains of 10%. The theoretical models used to analyze and interpret the different experiments provide reliable information and insight into the physical changes involved in the magnetically driven shape memory alloys. The aim of this review is to discuss the presents status of the computational modelling we have done. First, the basic MSM requirements and a brief summary of the experimental results for the prototype material Ni–Mn–Ga are given. Then, in the context of atomic-scale calculations, we focus primarily on the understanding of the structural variants, magnetic anisotropy, and Curie temperatures. Finally, we discuss modelling related to mesoscopic scales where we develop a phase field model for the description of twins. © 2004 Published by Elsevier B.V. Keywords: Ferromagnetism; Shape memory; Martensitic transformation; Ternary alloys 1. Magnetic shape memory effect The phenomenon of magnetostriction where an external magnetic field can change the dimensions of the sample was observed already in 1842 by Joule. In normal ferromagnets such as Fe or Ni the strains associated with the magnetostric- tion are of the order of 10 -4 % while materials with ex- ceptionally large magnetostriction, for example Tb–Dy–Fe alloys (Terfenol-D), show strains of the order of 0.1% [1]. In contrast, MSM materials can show magnetic field induced strains of 10% [2]. Not only are the strains in the MSM ef- fect two orders of magnitude larger, but also the mechanism is different from ordinary magnetostriction. While ordinary magnetostriction is observed in structurally homogeneous samples, the MSM effect requires a special microstructure. This microstructure is provided by a martensitic transfor- mation. The martensitic transformation [3,4] is a displacive, diffusion free structural transformation from a higher ∗ Corresponding author. Tel.: +358-9451-3101; fax: +358-9451-3116. E-mail address: aay@hugo.hut.fi (A. Ayuela). symmetry structure (austenite) to a lower symmetry struc- ture (martensite) upon cooling. For example, in Ni 2 MnGa the high symmetry phase is cubic while the lower symmetry phase can be tetragonal or orthorhombic. In order to mini- mize the total shape change (and the macroscopic strain en- ergy) over the whole sample, some microstructure develops in the martensitic phase. A common way to create this kind of microstructure is twinning: because there are usually sev- eral crystallographically equivalent ways to deform the high symmetry structure, the deformation may take different di- rections in different regions of the sample. These structural domains have well defined boundaries and they are called twin variants. A schematic example of the twinning is seen in Fig. 1. Twin boundaries are often mobile which is exploited in the temperature driven shape memory effect [5]. Due to the easy movement of the twin boundaries the sample can be de- formed easily in the martensitic phase. When the material is heated back to the austenitic phase the sample will recover to its original shape, i.e. it will “remember” the shape it had be- fore cooling. Even though strains in the temperature-driven shape memory effect can be several percent, the heating 0921-5093/$ – see front matter © 2004 Published by Elsevier B.V. doi:10.1016/j.msea.2003.10.330