Ferromagnetism and glassiness on the surface of topological insulators

Abstract

We investigate the nature of the ordering among magnetic adatoms, randomly deposited on the surface of topological insulators. Restricting ourselves to dilute impurity and weak coupling (between itinerant fermion and magnetic impurities) limit, we show that for arbitrary amount of chemical doping away from the apex of the surface Dirac cone the magnetic impurities tend to arrange themselves in a spin-density-wave pattern, with the periodicity approximately $\pi/k_F$, where $k_F$ is the Fermi wave vector, when magnetic moment for impurity adatoms is isotropic. However, when magnetic moment possesses strong Ising or easy-axis anisotropy, pursuing both analytical and numerical approaches we show that the ground state is ferromagnetic for low to moderate chemical doping, despite the fragmentation of the system into multiple ferromagnetic islands. For high doping away from the Dirac point as well, the system appears to fragment into many ferromagnetic islands, but the magnetization in these islands is randomly distributed. Such magnetic ordering with net zero magnetization, is referred here as ferromagnetic spin glass, which is separated from the pure ferromagnet state by a first order phase transition. We generalize our analysis for cubic topological insulators (supporting three Dirac cones on a surface) and demonstrate that the nature of magnetic orderings and the transition between them remains qualitatively the same. We also discuss the possible relevance of our analysis to recent experiments.Comment: 14 pages, 10 figure

Interlayer RKKY coupling in bulk Rashba semiconductors under topological phase transition

“…In its topological phase, BiTeI becomes insulating in the bulk and conducting only through its surfaces. The exchange interaction between magnetic impurities mediated by topological insulator surface states was previously studied [57][58][59][60][61][62][63][64][65] . In our case, the exchange interaction couples not only two magnetic impurities but two one-dimensional chains of spins at the top and bottom edges of the sample, mediated by the helical electrons residing on the side surfaces.…”

Surface magnetism in topological crystalline insulators

“…Interesting effects may arise when the symmetry protecting a topological band structure is broken. In topological insulators protected by time-reversal symmetry (TRS), magnetic impurities on a surface break this symmetry and form collective states [9][10][11][12][13], which may be understood in terms of a gap opening in the surface spectrum [14].In contrast, TCI's are not protected by TRS, so the loss of this symmetry does not by itself energetically favor ordering of magnetic moments [15,16]. However, a uniform magnetization can undermine one or more relevant crystalline symmetries [17,18].…”

“…Interesting effects may arise when the symmetry protecting a topological band structure is broken. In topological insulators protected by time-reversal symmetry (TRS), magnetic impurities on a surface break this symmetry and form collective states [9][10][11][12][13], which may be understood in terms of a gap opening in the surface spectrum [14].…”

Spin stiffness and domain walls in Dirac-electron mediated magnets

“…As with graphene, impurity spins exchange-coupled to the surface electrons develop effective inter-impurity interactions with a long-range, monotonic character (1/R 3 ) when the Fermi surface is point-like. Unlike graphene, this effective spin coupling is anisotropic due to the strong spin-orbit interactions typically present in these systems [24][25][26][27][28]. Depending on precisely how the impurities couple to the surface electrons this is thought to lead to ferromagnetic ordering or spin-glass behavior.…”