  We theoretically investigate tunneling magnetoresistance (TMR) devices, which
are probing the spin-momentum coupled nature of surface states of the
three-dimensional topological insulator Bi$_{2}$Se$_{3}$. Theoretical
calculations are performed based on a realistic tight-binding model for
Bi$_{2}$Se$_{3}$. We study both three dimensional devices, which exploit the
surface states of Bi$_{2}$Se$_{3}$, as well as two-dimensional devices, which
exploit the edge states of thin Bi$_{2}$Se$_{3}$ strips. We demonstrate that
the material properties of Bi$_{2}$Se$_{3}$ allow a TMR ratio at room
temperature of the order of 1000%. Analytical formulas are derived that allow a
quick estimate of the achievable TMR ratio in these devices. The devices can be
used to measure the spin polarization of the topological surface states as an
alternative to spin-ARPES. Unlike TMR devices based on magnetic tunnel
junctions the present devices avoid the use of a second ferromagnetic electrode
whose magnetization needs to be pinned.
