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We study spin susceptibility and magnetic order at the edges/surfaces oftwo-dimensional and three-dimensional topological insulators when the Fermisurface is nested. We find that due to spin-momentum locking as well astime-reversal symmetry, spin susceptibility at the nesting wavevector has astrong {\em helical} feature. It follows then, a {\em helical} spin densitywave (SDW) state emerges at low temperature due to Fermi surface nesting. Thehelical feature of spin susceptibility also has profound impact on the magneticorder in magnetically doped surface of three dimensional topologicalinsulators. In such system, from the mean field Zener theory, we predict a {\emhelical} magnetic order.

Spin Susceptibility and Helical Magnetic Orders at the Edges/Surfaces of Topological Insulators Due to Fermi Surface Nesting