  We study solutions for rigidly rotating strings on a two sphere. Among them
we find two limiting cases that have a particular interest, one is the already
known giant magnon and the other we call the single spike solution. The
limiting behavior of this last solution is a string infinitely wrapped around
the equator. It differs from that solution by the existence of a single spike
of height theta that points toward the north pole.
  We study its properties and compute its energy E and angular momentum J as a
function of theta. We further generalize the solution by adding one angular
momentum to obtain a solution on S3. We find a spin chain interpretations of
these results in terms of free fermions and the Hubbard model but the exact
relation with the same models derived from the field theory is not clear.
