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Magnetism of mixed quaternary Heusler alloys: (Ni,T)$_{2}$MnSn (T=Cu,Pd) as a case study

The electronic properties, exchange interactions, finite-temperature magnetism, and transport properties of random quaternary Heusler Ni$_{2}$MnSn alloys doped with Cu- and Pd-atoms are studied theoretically by means of {\it ab initio} calculations over the entire range of dopant concentrations. While the magnetic moments are only weakly dependent on the alloy composition, the Curie temperatures exhibit strongly non-linear behavior with respect to Cu-doping in contrast with an almost linear concentration dependence in the case of Pd-doping. The present parameter-free theory agrees qualitatively and also reasonably well quantitatively with the available experimental results. An analysis of exchange interactions is provided for a deeper understanding of the problem. The dopant atoms perturb electronic structure close to the Fermi energy only weakly and the residual resistivity thus obeys a simple Nordheim rule. The dominating contribution to the temperature-dependent resistivity is due to thermodynamical fluctuations originating from the spin-disorder, which, according to our calculations, can be described successfully via the disordered local moments model. Results based on this model agree fairly well with the measured values of spin-disorder induced resistivity.