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Resonant ultrasound spectroscopy and magnetic susceptibility experiments havebeen used to characterize strain coupling phenomena associated with structuraland magnetic properties of the shape-memory Heusler alloy seriesNi$_{50+x}$Mn$_{25-x}$Ga$_{25}$ ($x=0$, 2.5, 5.0, and 7.5). All samples exhibita martensitic transformation at temperature $T_M$ and ferromagnetic ordering attemperature $T_C$, while the pure end member ($x=0$) also has a premartensitictransition at $T_{PM}$, giving four different scenarios: $T_C>T_{PM}>T_M$,$T_C>T_M$ without premartensitic transition, $T_C\approx T_M$, and $T_C<T_M$.Fundamental differences in elastic properties i.e., stiffening versussoftening, are explained in terms of coupling of shear strains with threediscrete order parameters relating to magnetic ordering, a soft mode and theelectronic instability responsible for the large strains typical of martensitictransitions. Linear-quadratic or biquadratic coupling between these orderparameters, either directly or indirectly via the common strains, is then usedto explain the stabilities of the different structures. Acoustic losses areattributed to critical slowing down at the premartensite transition, to themobility of interphases between coexisting phases at the martensitic transitionand to mobility of some aspect of the twin walls under applied stress down tothe lowest temperatures at which measurements were made.

Strain and order-parameter coupling in Ni-Mn-Ga Heusler alloys from resonant ultrasound spectroscopy