Modulations in martensitic Heusler alloys originate from nanotwin ordering.

Heusler alloys exhibiting magnetic and martensitic transitions enable applications like magnetocaloric refrigeration and actuation based on the magnetic shape memory effect. Their outstanding functional properties depend on low hysteresis losses and low actuation fields. These are only achieved if the atomic positions deviate from a tetragonal lattice by periodic displacements. The origin of the so-called modulated structures is the subject of much controversy: They are either explained by phonon softening or adaptive nanotwinning. Here we used large-scale density functional theory calculations on the NiMnGa prototype system to demonstrate interaction energy between twin boundaries. Minimizing the interaction energy resulted in the experimentally observed ordered modulations at the atomic scale, it explained that a/b twin boundaries are stacking faults at the mesoscale, and contributed to the macroscopic hysteresis losses. Furthermore, we found that phonon softening paves the transformation path towards the nanotwinned martensite state. This unified both opposing concepts to explain modulated martensite.