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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 ab initio calculations give a basic understanding of the underlying physics which is associated with the strong competition of ferroand antiferromagnetic interactions with increasing chemical disorder. The resulting d-electron orbital dependent magnetic ordering is the driving mechanism of magnetostructural instability which is accompanied by a drop of magnetization governing the size of the magnetocaloric effect. The thermodynamic properties are calculated by using the ab initio magnetic exchange coupling constants in finite-temperature Monte Carlo simulations, which are used to accurately reproduce the experimental entropy and adiabatic temperature changes across the magnetostructural transition. PACS numbers: 75.50.-y, 75.10.-b, 75.30.SgFollowing the concepts of Hume-Rothery the influence of composition on martensitic and magnetic transformation temperatures is commonly condensed as a dependency of electrons per atom (e/a-ratio) [1]. Experiment and first-principles calculations, however, reveal that the Z element in Ni-Mn-Z Heusler alloys (Z = Ga, In, Sn) also affects the transformation temperatures substantially [2]. Moreover, recent experiments on samples with identical composition but different heat treatment indicate that chemical disorder also plays an important role [3][4][5]. Here, we use first-principles calculations to identify the influence of chemical disorder on the magnetic exchange parameters and derive guidelines for a further systematic improvement of magnetocaloric materials [6].Besides the magnetocaloric effect (MCE) in Gd and other alloys at room temperature [7,8], the metamagnetic Ni-Mn based Heusler materials [9,10], have attracted much interest recently [11,12]. In these alloys the metamagnetic features are responsible for magnetic glass behavior and frustration due to chemical disorder [13][14][15] as well as unusual magnetization behavior under an external magnetic field such as a large jump of the magnetization ∆M (T m ) at the martensitic/magnetostructural transformation temperature T m [16]. This gives rise to the large inverse MCE of the materials [9,10,17,18]. The MCE can be influenced when Ni is substituted in part by Co: It is strongly enhanced in the case of In-based intermetallics [19,20] (with adiabatic temperature change ∆T ad = −6 K in 2 T field [20]) while in the case of Ga the MCE is turned from direct to inverse by decoupling T m and Curie temperature T C [21] (with ∆T ad = −1.6 K in 1.9 T field [22,23]).Chemical disorder in the Mn-rich Heusler alloys is responsible for competing magnetic interactions (ferromagnetic versus antiferromagnetic) because the extra Mn atoms occupy lattice sites of the Z-sublattice which interact antiferromagnetically with the Mn atoms on the Y-sublattice due to RKKY-type interactions. This competition of magnetic interactions leads to the characteristic drop of magnetization curves at T m , wh...