Thermal hysteresis is recognized as one of the main drawbacks for cyclical applications of magnetocaloric and ferromagnetic shape memory materials with first order transformations. As such, the challenge is to develop strategies that improve the compatibility between the phases involved in the transitions and study its influence on thermal hysteresis. With this purpose, we explore the thermal, structural and magnetic properties of the Ni2Mn1-xCuxGa0.84Al0.16 Heusler alloys. The alloys present a thermal hysteresis reduction of ~60% when the Cu content in the compound varies from x = 0.10 to x = 0.25, with a minimum hysteresis width of 6 K being achieved. We applied the geometric non-linear theory of martensite to address the phase compatibility, quantified by the parameter lambda2, the middle eigenvalue of the transformation stretch tensor, and found that the minimum of hysteresis is associated with a better crystallographic compatibility (lambda2 closer to 1) between the austenite and martensite phases. In addition, we show that the valley-like properties of hysteresis found in the Ni2Mn1-xCuxGa0.84Al0.16 compounds is present in several other alloys in the literature. These results provide new pathways to understand as well as to masters the phase compatibility and ultimately achieve a low thermal hysteresis in multifunctional Heusler alloys.
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