Spin Response of Electrons on the Surface of a Topological Insulator

The surface of a topological insulator hosts a very special form of a quasi-two dimensional metallic system when it is embedded in a topologically trivial medium like the vacuum. The electronic properties of this unusual 2D metal are distinct in many aspects from both the conventional two-dimensional electron gas systems in quantum well heterostructures as well as those of a single layer graphene. In this paper, we study one of these distinct features i.e., the response of the electronic spins to an applied magnetic field perpendicular to the surface. We find an unusual behaviour of the spin magnetization and susceptibility as a function of both the magnetic field and the chemical potential for a generic topological surface. We propose that this behavior could be studied by the recently developed experimental technique called \beta NMR which is highly sensitive to the surface electron spins. We explain how this technique could be used to probe for spontaneous magnetic ordering caused by magnetic dopants or interactions discussed in the recent literature.