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The structural and magnetic properties of functional Ni-Mn-Z (Z = Ga, In, Sn)Heusler alloys are studied by first-principles and Monte Carlo methods. The\textit{ab initio} calculations give a basic understanding of the underlyingphysics which is associated with the strong competition of ferro- andantiferromagnetic interactions with increasing chemical disorder. The resulting$d$-electron orbital dependent magnetic ordering is the driving mechanism ofmagnetostructural instability which is accompanied by a drop of magnetizationgoverning the size of the magnetocaloric effect. The thermodynamic propertiesare calculated by using the \textit{ab initio} magnetic exchange couplingconstants in finite-temperature Monte Carlo simulations, which are used toaccurately reproduce the experimental entropy and adiabatic temperature changesacross the magnetostructural transition.

First-principles calculation of the instability leading to giant inverse magnetocaloric efects