Temperature-dependent spin momentum densities in Ni₂Mn_1.4Sn_0.6 shape memory alloy have been measured using 182 keV circularly polarized synchrotron radiations. Near the martensitic phase transition (T_M = 200 K), experimental magnetic Compton profiles (MCPs) unravel a dominating spin moment contribution from Mn sites. First-principles calculations are found to produce higher magnetic moment for orthorhombic structure than that for the L2₁ (cubic) structure, which is in tune with the present MCP data. It is also concluded that the spin moments of excess Mn atoms lying at Sn sites are antiferromagnetically coupled with Mn local spin moment in both the phases.