Magnetic properties of Ni-Ti clusters of the lower hierarchical level

•Magnetization for quasicrystal structures of Ni51Ti49 alloy is due to emergence of Frank-Kasper (FK) clusters into them.•FK clusters appeared can be considered as some microdomains with nonzero magnetic moment.•Magnetization of clusters depends on both coordinational number of nearest atoms and positions of different atoms of the first coordinational sphere.•The increase of number of FK-12 polyhedrons in NixTiy clusters leads to the increase of the binding energy per atom for these structures.