The crystal and magnetic structures of antiperovskite compounds Mn3SnC, Mn3Sn0.95C0.9, and Mn3Sn0.93Si0.07C0.94 were studied as a function of temperature and magnetic field by neutron powder diffraction. For Mn3SnC, the magnetic field induces a dramatic variation of antiferromagnetic moment and lattice parameter. Because of this spin-lattice coupling, the "square" antiferromagnetic (AFM) structure plays a key role in inducing a negative thermal expansion in the material. Moreover, the thermal expansion parameter is closely related to the rate of change of the AFM moment, which can be controlled by introducing vacancies or by doping. The variations of the AFM moment and lattice parameter in Mn3SnC with magnetic field make it possible to use the tunable properties for technical applications.