Tunnel Magnetoresistance scan of a pristine three-dimensional topological insulator

Though the Fermi surface of surface states of a 3D topological insulator (TI) has zero magnetization, an arbitrary segment of the full Fermi surface has a unique magnetic moment consistent with the type of spin-momentum locking in hand. We propose a three-terminal set up, which directly couples to the magnetization of a chosen segment of a Fermi surface hence leading to a finite tunnel magnetoresistance (TMR) response of the nonmagnetic TI surface states, when coupled to spin polarized STM probe. This multiterminal TMR not only provides a unique signature of spin-momentum locking for a pristine TI but also provides a direct measure of momentum resolved out of plane polarization of hexagonally warped Fermi surfaces relevant for $Bi_2Te_3$, which could be as comprehensive as spin-resolved ARPES. Implication of this unconventional TMR is also discussed in the broader context of 2D spin-orbit (SO) materials.