We have performed spin- and angle-resolved photoemission spectroscopy of Bi2Te3 and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface (FS) of Bi2Te3 reaches maximally 25% of the in-plane counterpart while such a sizable out-of-plane spin component does not exist in the more circular FS of TlBiSe2, indicating that the hexagonal deformation of the FS is responsible for the deviation from the ideal helical spin texture. The observed out-of-plane polarization is much smaller than that expected from existing theory, suggesting that an additional ingredient is necessary for correctly understanding the surface spin polarization in Bi2Te3.

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