Authors
Abstract
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.
Keywords
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2. M Z Hasan and C L Kane, Rev. Mod. Phys. 82 (2010) 3045.
3. X-L Qi and S-C Zhang, Rev. Mod. Phys. 83 (2011) 1057.
4. Y Xia, et al., Nat. Phys. 5 (2009) 398.
5. Y-L Chen, et al., Science 329 (2010) 659.
6. M A Ruderman and C Kittel, Phys. Rev. 96 (1954) 99.
7. T Kasuya, Prog. Theor. Phys. 16 (1956) 45. K Yosida, Phys. Rev.106 (1957) 893.
8. J-J Zhu, D-X Yao, S-C Zhang, and K Chang, Phys. Rev. Lett. 106 (2011) 097201.
9. D A Abanin and D A Pesin, Phys. Rev. Lett. 106 (2011) 136802.
10. G Rosenberg and M Franz, Phys. Rev. B 85 (2012) 195119.
11. L Fu, Phys. Rev. Lett. 103 (2009) 266801.
12. D Hsieh et al., Nature 460 (2009) 1101.
13. R M White, “Quantum Theory of Magnetism: Magnetic Properties of Materials 3rd edition”, Springer (2007).
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