A unified structural framework for modulation and nanotwinning in Ni–Mn–Ga alloys

P. Veřtát1, L. Straka1, H. Seiner2, M. Klicpera3, M. Zelený4, J. Luštinec1, O. Fabelo5, O. Heczko1

1 FZU – Institute of Physics of the Czech Academy of Sciences, Prague, Czechia

 2Institute of Thermomechanics of the Czech Academy of Sciences, Prague, Czechia

3Faculty of Mathematics and Physics, Charles University, Prague, Czechia

4Faculty of Mechanical Engineering, Institute of Materials Science and Engineering, Brno University of Technology, Brno, Czechia

5Institut Laue-Langevin, Grenoble, France

vertat@fzu.cz

Magnetically induced reorientation in Ni–Mn–Ga-based single crystals represents a unique paradigm of material deformation, where the crystal microstructure is manipulated through magnetically driven twin boundary motion, resulting in a giant magnetic-field-induced strain. The extraordinary mobility of twin boundaries in its martensitic phases, particularly high in the five-layered modulated martensite [1], fundamentally relies on the complex structure. Traditionally, the Ni–Mn–Ga martensite structure has been viewed through two contrasting descriptions: traditional continuous wave modulation [2] and discrete adaptive (nano)twinning [3]. Recently, we have built a unified structural framework that seamlessly bridges both distinct perspectives.

Using single-crystal neutron and X-ray diffraction, we tracked the structural evolution with temperature in several off-stoichiometric Ni–Mn–Ga alloys. We revealed that the modulation is anharmonic—evidenced by an unusually rich spectrum of high-order satellite reflections—and evolves continuously from a commensurate five-layered state near the martensitic transformation to an incommensurate state upon cooling [4]. Importantly, this evolution is accompanied by dramatic changes in shear stability: the shear elastic constant exhibits anomalous behaviour, indicating an extraordinary softness to the forces perpendicular to the modulation vector. Near the martensitic transformation, Ni–Mn–Ga is one of the most anisotropic metallic materials ever reported [5].

By mapping the diffraction-validated, complex anharmonic modulation onto a discrete basal-plane stacking sequence, we demonstrate that the evolving incommensurability naturally produces periodic nanodomains. Furthermore, upon cooling, the incommensurate modulation locks into various stable long-period commensurate states, whose orthorhombic unit cells simultaneously incorporate the a/b-nanotwin boundaries [6].

Since subtle dynamic shifts in the modulation phase project directly onto discrete microstructural changes in Ni–Mn–Ga, our findings also suggest that phasons—collective acoustic-like excitations in incommensurate crystals—can mediate the microstructural rearrangements with minimal required energy. Ultimately, our work not only resolves the long-standing modulation-nanotwinning duality, but also points towards the phason-driven lattice dynamics as a potentially crucial ingredient in the fundamental mechanism underlying the exceptional twin-boundary mobility in Ni–Mn–Ga-based functional materials.

1. O. Heczko, V. Kopecký, A. Sozinov, L. Straka, Appl. Phys. Lett. 103, (2013) 072405.

2. T. Janssen, A. Janner, A. Looijenga-Vos, P.M. de Wolff, in International Tables for Crystallography, Volume C: Mathematical, physical and chemical tables, (Springer, Dordrecht), 2006, pp. 907-955.

3. A.G. Khachaturyan, S.M. Shapiro, S. Semenovskaya, Phys. Rev. B. 43, (1991) 10832-10843.

4. P. Veřtát, M. Klicpera, O. Fabelo, O. Heczko, L. Straka, Scr. Mater. 252, (2024) 116251.

5. K. Repček, P. Stoklasová, T. Grabec, P. Sedlák, J. Olejňák, M. Vinogradova, A. Sozinov, P. Veřtát, L. Straka, O. Heczko, H. Seiner, Adv. Mater. 36, (2024), 2406672.

6. P. Veřtát, M. Zelený, A. Sozinov, M. Klicpera, O. Fabelo, R. Chulist, M. Vinogradova, P. Sedlák, H. Seiner, O. Heczko, L. Straka, ArXiv:2503.04379 (2025) (under review in Acta Mater.).

This work was supported by the Ferroic Multifunctionalities project, supported by the Ministry of Education, Youth, and Sports of the Czech Republic [Project No. CZ.02.01.01/00/22_008/0004591], co-funded by the European Union.