Magnetic ordering and physical stability of X2Mn1+xSn1-x (X = Ru, Os, Co, Rh, Ni, Pd, Cu, and Ag) Heusler alloys from a first-principles study

The magnetic ordering and its effect on the physical stability of X2Mn1+xSn1-x (0 <= x <= 0.5, and X = Ru, Os, Co, Rh, Ni, Pd, Cu, and Ag) Heusler alloys are investigated systematically by the use of first-principles method. It is found that the ferromagnetic (FM) coupling between Mn on Mn sublattice (Mn-1) and Mn on Sn sublattice (Mn-2) is favorable over the antiferromagnetic (AFM) coupling for X with the number of valence electrons [N-v(X)] of 8 and 9, and vice versa for X with N-v(X) = 10 and 11, originated from the competition of the exchange interactions between X-Mn-2 and Mn-1-Mn-2. In comparison with the FM Mn-1-Mn-2 coupling, the AFM coupling decreases significantly the shear elastic constant C' but increases slightly C-44, which results in increasing elastic anisotropy (A = C-44/C') and consequently may facilitate the tetragonal shear lattice deformation. The hybridization of the minority electronic states between X d and Sn p plays a dominant role on the orientation of the magnetic coupling. The smaller change of the density of states in the Fermi level, induced by the lattice distortion for C', corresponds to the softer C' as well as the larger A in the AFM state than the FM one.