  We show nonrelativistic (NR) giant magnon dispersion relations by probing the
torsional Newton Cartan (TNC) geometry with (semi)classical nonrelativistic
rigidly rotating strings. We construct NR sigma models over $ R \times S^2 $
and consider two specific limiting cases those are of particular interest. Both
of these limiting conditions give rise to what we identify as the \emph{small}
momentum limit of the giant magnon dispersion relation in the dual SMT at
\emph{strong} coupling. We further generalize our results in the presence of
background NS-NS fluxes. Our analysis reveals that unlike its relativistic
counterpart, the NR string theory lacks of single spike solutions.
