Abstract
By considering an extended double-exchange model with spin-orbit coupling (SOC), we derive a general form of the Berry phase γ that electrons pick up when moving around a closed loop. This form generalizes the well-known result valid for SU(2) invariant systems, γ=ω/2, where ω is the solid angle subtended by the local magnetic moments enclosed by the loop. The general form of γ demonstrates that collinear and coplanar magnetic textures can also induce a Berry phase different from 0 or π, smoothly connecting the result for SU(2) invariant systems with the well-known result of Karplus and Luttinger for collinear ferromagnets with finite SOC. By taking the continuum limit of the theory, we also derive the corresponding generalized form of the real-space Berry curvature. The new expression is a generalization of the scalar spin chirality, which is presented in an explicitly covariant form. We finally show how these simple concepts can be used to understand the origin of the spontaneous topological Hall effect that has been recently reported in collinear and coplanar antiferromagnetic phases of correlated materials.
| Original language | English |
|---|---|
| Article number | 024420 |
| Journal | Physical Review B |
| Volume | 101 |
| Issue number | 2 |
| DOIs | |
| State | Published - Jan 22 2020 |
Funding
We thank S. Nakatsuji, N. Nagaosa, and D. A. Tennant for useful discussions. Work by H.Z. was supported by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division. S.-S.Z. and C.D.B. are supported by funding from the Lincoln Chair of Excellence in Physics and from the Los Alamos National Laboratory Directed Research and Development program. The work of G.B.H. at ORNL was supported by Laboratory Director's Research and Development funds. The work by H.I. was supported by JSPS KAKENHI Grants No. JP19K14649, No. JP18H04222, and No.18H03676.