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Magnetostructural correlations in antiperovskite manganese nitrides were investigated systematically for stoichiometric and solid solution Mn3Cu1−xAxN (A = Co, Ni, Zn, Ga, Ge, Rh, Pd, Ag, In, Sn or Sb). This class of nitrides is attracting great attention because of their giant negative thermal expansion, which is achieved by doping Ge or Sn into the A site as a relaxant of the sharp volume contraction on heating (spontaneous volume magnetostriction ωs) because of the magnetovolume effects. The physical background of large ωs and mechanism of how the volume contraction becomes gradual with temperature are central concerns for the physics and applications of these nitrides. An entire dataset of thermal expansion, crystal structure and magnetization demonstrates that the cubic triangular antiferromagnetic state is crucial for large ωs. The intimate relationship between ωs and the magnetic structure is discussed in terms of geometrical frustration related to the Mn6N octahedron and magnetic stress concept. The results presented herein also show that ωs depends on the number of d electrons in the A atom, suggesting the important role of the d orbitals of the A atom. Not all the dopants in the A site, but the elements that disturb the cubic triangular antiferromagnetic state, are effective in broadening the volume change. This fact suggests that instability neighboring the phase boundary is related to the broadening. The relation between the gradual volume change and the local structure anomaly is suggested by recent microprobe studies. [ABSTRACT FROM AUTHOR]