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Domain wall of a ferromagnet on a three-dimensional topological insulator.

Wakatsuki R, Ezawa M, Nagaosa N - Sci Rep (2015)

Bottom Line: Most of them come from the peculiar surface or edge states.Especially, the quantized anomalous Hall effect (QAHE) without an external magnetic field is realized in the two-dimensional ferromagnet on a three-dimensional TI which supports the dissipationless edge current.The chirality and relative stability of the Neel wall and Bloch wall depend on the position of the Fermi energy as well as the form of the coupling between the magnetic moments and orbital of the host TI.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Physics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

ABSTRACT
Topological insulators (TIs) show rich phenomena and functions which can never be realized in ordinary insulators. Most of them come from the peculiar surface or edge states. Especially, the quantized anomalous Hall effect (QAHE) without an external magnetic field is realized in the two-dimensional ferromagnet on a three-dimensional TI which supports the dissipationless edge current. Here we demonstrate theoretically that the domain wall of this ferromagnet, which carries edge current, is charged and can be controlled by the external electric field. The chirality and relative stability of the Neel wall and Bloch wall depend on the position of the Fermi energy as well as the form of the coupling between the magnetic moments and orbital of the host TI. These findings will pave a path to utilize the magnets on TI for the spintronics applications.

No MeSH data available.


The energy dispersions of the bulk states and edge modes for (a), (a’) J3 = 0 and (b), (b’) J3 = J0.The edge mode appears inside the bulk band gap. The dispersion is almost independent of ϕ, i.e., the type of domain wall, for J3 = 0 (a), (a’), while it is sensitive when J3 = J0 (b), (b’). Probability distribution of the zero-energy wave function for ky = 0 for (c) J3 = 0, (d) J3 = J0. The dotted curve in (c) is given by Jackiw—Rebbi solution Eq. (12) in the text.
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f2: The energy dispersions of the bulk states and edge modes for (a), (a’) J3 = 0 and (b), (b’) J3 = J0.The edge mode appears inside the bulk band gap. The dispersion is almost independent of ϕ, i.e., the type of domain wall, for J3 = 0 (a), (a’), while it is sensitive when J3 = J0 (b), (b’). Probability distribution of the zero-energy wave function for ky = 0 for (c) J3 = 0, (d) J3 = J0. The dotted curve in (c) is given by Jackiw—Rebbi solution Eq. (12) in the text.

Mentions: A magnetic domain wall separates the two domains with up and down spins, i.e., the regions of . Therefore, the difference of σxy is and hence one chiral edge channel is expected to appear along the domain wall. We show the energy dispersion and the probability distribution of the edge channel wave function along the x direction obtained numerically for J3 = 0 in Fig. 2(a,a’), and J3 = J0 in Fig. 2(b,b’), respectively.


Domain wall of a ferromagnet on a three-dimensional topological insulator.

Wakatsuki R, Ezawa M, Nagaosa N - Sci Rep (2015)

The energy dispersions of the bulk states and edge modes for (a), (a’) J3 = 0 and (b), (b’) J3 = J0.The edge mode appears inside the bulk band gap. The dispersion is almost independent of ϕ, i.e., the type of domain wall, for J3 = 0 (a), (a’), while it is sensitive when J3 = J0 (b), (b’). Probability distribution of the zero-energy wave function for ky = 0 for (c) J3 = 0, (d) J3 = J0. The dotted curve in (c) is given by Jackiw—Rebbi solution Eq. (12) in the text.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4555097&req=5

f2: The energy dispersions of the bulk states and edge modes for (a), (a’) J3 = 0 and (b), (b’) J3 = J0.The edge mode appears inside the bulk band gap. The dispersion is almost independent of ϕ, i.e., the type of domain wall, for J3 = 0 (a), (a’), while it is sensitive when J3 = J0 (b), (b’). Probability distribution of the zero-energy wave function for ky = 0 for (c) J3 = 0, (d) J3 = J0. The dotted curve in (c) is given by Jackiw—Rebbi solution Eq. (12) in the text.
Mentions: A magnetic domain wall separates the two domains with up and down spins, i.e., the regions of . Therefore, the difference of σxy is and hence one chiral edge channel is expected to appear along the domain wall. We show the energy dispersion and the probability distribution of the edge channel wave function along the x direction obtained numerically for J3 = 0 in Fig. 2(a,a’), and J3 = J0 in Fig. 2(b,b’), respectively.

Bottom Line: Most of them come from the peculiar surface or edge states.Especially, the quantized anomalous Hall effect (QAHE) without an external magnetic field is realized in the two-dimensional ferromagnet on a three-dimensional TI which supports the dissipationless edge current.The chirality and relative stability of the Neel wall and Bloch wall depend on the position of the Fermi energy as well as the form of the coupling between the magnetic moments and orbital of the host TI.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Physics, University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.

ABSTRACT
Topological insulators (TIs) show rich phenomena and functions which can never be realized in ordinary insulators. Most of them come from the peculiar surface or edge states. Especially, the quantized anomalous Hall effect (QAHE) without an external magnetic field is realized in the two-dimensional ferromagnet on a three-dimensional TI which supports the dissipationless edge current. Here we demonstrate theoretically that the domain wall of this ferromagnet, which carries edge current, is charged and can be controlled by the external electric field. The chirality and relative stability of the Neel wall and Bloch wall depend on the position of the Fermi energy as well as the form of the coupling between the magnetic moments and orbital of the host TI. These findings will pave a path to utilize the magnets on TI for the spintronics applications.

No MeSH data available.