Present publication gives a detailed theoretical concept and also presents the relevant experimental results concerning the effect of the magnetostatic coupling between the twin layers on the magnetic-field-controlled strain response during the mechanical cycling in magnetic field in Ni-Mn-Ga. We also discuss the physical mechanism of this effect using our latest model developments. Simultaneously we give the most important information about the main structural, magnetic and mechanical properties related to a family of nonstoichiometric Ni-Mn-Ga alloys with different crystal structures. We specially emphasize the fact that the main magnetic and magneto-mechanical properties of MSMA_s are strictly dependent on the details of twin and also fine internal magnetic domain microstructure within the twin bands. These magnetic domains was not expected and usually not taken into account in many early models of MSMA_s. Here we show that their presence may essentially modify the magnetization behavior and field dependence of magnetic driving forces at the twin boundaries in these materials.

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