We have carried out an experimental study of Ni-rich NiMn alloys in a series of compositions across the multicritical point and determined the phase diagram within that range. We have observed ferromagnetic long-range order with reentrant spin-glass/ferro-spin-glass phase for x≤25, an antiferromagnetic long-range order around x∼37, and a gradual change from a canonical spin-glass state to a long-range antiferromagnetic phase in the intermediate composition region. In order to explain the experimental observations, we have examined the physical properties from a density functional based first-principals theoretical analysis and used it to understand the experimental results. Using atomic spin dynamics simulations based on the Landau-Lifshitz-Gilbert equation, we have found the aging behavior and anomalously slow relaxation of magnetization in the composition range where experiment observes spin-glassy behavior.