In this work, based on limited experimental magnetocaloric data for Ni–Co–Mn–Al Heusler alloys, we present a theoretical study to predict a composition with higher magnetocaloric properties. By analogy with Ni–Co–Mn–(In, Sn) alloys exhibiting a large magnetization change across the structural transformation, we suppose that the addition of 10 at. % Co in Ni–Mn–Al would yield a similar trend. Our approach is based on the combination of ab initio calculations and Monte Carlo simulations within the framework of the Potts–Blume–Emery–Griffiths model. It follows from ab initio calculations that Co addition modifies the exchange interactions and enhances the ferromagnetism in austenite, while for martensite, the ferromagnetism is substantially suppressed due to the strongest antiferromagnetic Mn–Mn interactions. Thermo-magnetization curves and magnetocaloric properties under magnetic fields of 0.5 and 2 T are simulated by the Monte Carlo method assuming the ab initio exchange-interaction parameters. A large change in magnetization of approximately 100 A m2kg1, leading to a giant magnetocaloric effect (ΔTad7 K) across the martensite–austenite transformation, is predicted.

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