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The stability of the nonmodulated martensitic phase, the austenitic Fermisurface and the phonon dispersion relations for ferromagnetic Ni$_2$MnGa arestudied using density functional theory. Exchange-correlation effects areconsidered with various degrees of precision, starting from the simplest localspin density approximation (LSDA), then adding corrections within thegeneralized gradient approximation (GGA) and finally, including the meta-GGAcorrections within the strongly constrained and appropriately normed (SCAN). Wediscuss a simple procedure to reduce a possible overestimation of magnetizationand underestimation of nesting vector in SCAN by parametrically decreasingself-interaction corrections.

Electronic structure beyond the generalized gradient approximation for Ni$_2$MnGa