Magnetic properties of three-dimensional magnetic topological insulators: the effects of hexagonal warping

We have investigated the magnetic properties of three-dimensional topological insulators, doped with magnetic atoms. The spin-orbit locking of surface electrons results in interesting magnetic behaviors, absent in conventional insulators without spin-orbit coupling. In particular, the ferromagnetic-paramagnetic transition temperature has a strong dependence on different system parameters. Here, using the mean-field formalism we have studied the effects of hexagonal warping on the order parameter, critical temperature, and magnetic susceptibility of system.