# Special Condensed Matter seminar

"Topological magnon transport in ferromagnets"

Magnons (spin waves) are low-energy excitations in magnets. We
theoretically study effects caused by Berry curvature due to
magnon band structure in ferromagnetic insulators, in analogy with
anomalous Hall and spin Hall effect for electrons. From the
semiclassical theory, the Berry curvature causes thermal Hall
effect for magnons, and we calculate its thermal Hall
conductivity. The same result is reproduced by linear response
theory. We demonstrate this for the (classical) magnetostatic
waves due to dipolar interaction in ferromagnets such as YIG.
Furthermore, we also discuss the "gapped" variant of this effect
in magnonic crystals. In the magnonic crystals, spatial
periodicity opens a magnonic gap in the band structure. By
formulating the gauge field and Chern number, we demonstrate that
in some magnonic crystals which are periodic structures of two
different ferromagnetic materials, the Chern numbers become
nonzero, causing topological chiral edge modes similar to the
quantum Hall effect.

[1] R. Matsumoto, S. Murakami, Phys. Rev. Lett. 106, 197202
(2011).

[2] R. Matsumoto, S. Murakami, Phys. Rev. B 84, 184406 (2011).

[3] R. Shindou, R. Matsumoto, S. Murakami, arXiv:1204.3349.