Adaptive modulation in the $\mathrm{Ni_{2}Mn_{1.4}In_{0.6}}$ magnetic shape-memory Heusler alloy

The origin of incommensurate structural modulation in Ni-Mn based Heusler-type magnetic shape-memory alloys (MSMAs) is still an unresolved issue in spite of intense focus on it due to its role in the magnetic field induced ultrahigh strains. In the archetypal MSMA Ni$_2$MnGa, the observation of “nonuniform displacement” of atoms from their mean positions in the modulated martensite phase, premartensite phase, and charge density wave as well as the presence of phason broadening of satellite peaks has been taken in support of the electronic instability model linked with a soft acoustic phonon. We present here results of a combined high-resolution synchrotron x-ray powder diffraction (SXRPD) and neutron powder diffraction (NPD) study on Ni$_2$Mn$_{1.4}$In$_{0.6}$ using a (3+1)D superspace group approach, which reveals not only uniform atomic displacements in the modulated structure of the martensite phase with physically acceptable ordered magnetic moments in the antiferromagnetic phase at low temperatures, but also the absence of any premartensite phase and phason broadening of the satellite peaks. Our HRTEM studies and first-principles calculations of the ground state also support uniform atomic displacements predicted by powder diffraction studies. All these observations suggest that the structural modulation in the martensite phase of Ni$_2$Mn$_{1.4}$In$_{0.6}$ MSMA can be explained in terms of the adaptive phase model. The present study underlines the importance of superspace group analysis using complementary SXRPD and NPD in understanding the physics of the origin of modulation as well as the magnetic and the modulated ground states of the Heusler-type MSMAs. Our work also highlights the fact that the mechanism responsible for the origin of modulated structure in different Ni-Mn based MSMAs may not be universal and it must be investigated thoroughly in different alloy compositions