Due to its magnetostructural phase transition (the structural phase transition and the magnetic phase transition are strongly coupled together and occur simultaneously),Mn-based Heusler alloys exhibit attractive physical effects,such as ferromagnetic shape memory effect,magnetostrain effect,magnetocaloric effect,magnetoresistance effect,and exchange bias effect.These effects are receiving increasing attentions from the applications in actuating,sensing,magnetic cooling,heat pump,and energy conversion.However,Mn-based Heusler alloys display these potentially useful magnetic effects only in the vicinity of the magnetostructural transformation temperature.Therefore,from the application point of view,being able to tune the magnetostructural transformation temperature and the magnetism simultaneously is highly desirable.Recently,our group has developed a new Mn-based Heusler alloy (Mn2NiSn) with magnetostructural phase transition.Considering that the magnetostructural transformation temperature of Mn50Ni41Sn9 alloy is relatively high (278 K) and its magnetism is relatively weak (19.5 emu/g at 5 K,1 emu/g=1 Am2kg-1),we expect to lower its magnetostructural transformation temperature and enhance its magnetism in order to expand its scope of application.In this paper,the role of Ni-Mn hybridization on the martensitic transformation temperature and the magnetism of the martensitic state of Mn50Ni41Sn9Cux alloys was studied.XRD measurement shows that the lattice constants increase with increasing Cu content in Mn50Ni41-xSn9Cux (x=0,1,3,5) alloys,and thus Ni-Mn hybridizatiidion between normal Ni 3d e g and excess Mn 3d decreases due to the lattice expansion and the decrease in the Ni content. The weakened Ni-Mn hybridization leads to the decrease of both the martensitic transformation temperature and the austenitic Curie temperature from 278 K and 290 K to 129 K and 237 K,respectively.It should be pointed out that the phenomenological and conventional valence electron concentration rule has not been able to explain the change of the martensitic transformation temperature in Mn50Ni41-xSn9Cux alloys,and only the microscopic Ni-Mn hybridization theory can explain that.Ni-Mn hybridization not only affects the martensitic transformation but also influences the magnetism of the martensitic state.It is found that the martensite is changed from a canonical spin glass to a cluster spin glass and its saturation magnetization increases from 19.5 emu/g to 24.1 emu/g.Furthermore,both the ac magnetic susceptibility and the magnetic relaxation measurements show that the system has changed gradually from a spin glass state with coexistence of ferromagnetic and antiferromagnetic interaction to a single ferromagnetic state.Therefore, increasing the Cu content in Mn50Ni41-xSn9Cux alloys has been proven to be an effective way of enhancing the ferromagnetic interaction of the martensitic state.Tuning the exchange interaction of the system is very crucial to tailoring the exchange bias effect of the system.With different Cu contents,a continuous tailoring of the spontaneous exchange bias field from 0 Oe (1 Oe=79.5775 A/m) to 1182 Oe is realized.The method of changing the Ni-Mn hybridization strength mentioned above provides a new way to control the martensitic transformation temperature and the magnetic properties of the martensitic state.