We construct traveling wave solutions with vortex helix structures for the Schrodinger map equation partial derivative m/partial derivative t = m x (Delta m - m3 (e) over right arrow3) on R-3 x R of the form m(s(1), s(2), s(3) - delta vertical bar log epsilon vertical bar epsilon t) with traveling velocity delta vertical bar log epsilon vertical bar epsilon along the direction of the s3 axis. We use a perturbation approach which gives a complete c...