Geometric Spin Rotation in Triangular Antiferromagnets

Abstract

We describe a geometric phenomenon in which a traveling wave made of degenerate Goldstone modes leaves behind a transformed ground state. In a triangular Heisenberg antiferromagnet, a pulse of circularly polarized spin waves rotates the spins within their plane. An exact solution of the nonlinear equations of motion demonstrates that the accumulated rotation is a geometric phase related to parallel transport of the order parameter. We point out a curious analogy between the motion of the magnetic order parameter and that of a wobbling coin. This phenomenon opens a new route for controlling antiferromagnetic order by spin waves and may extend to other frustrated magnets as well as other physical systems with noncommuting broken-symmetry generators.

Figures (2)

• Figure 1: A wobbling coin: a full wobble results in a net rotation of the coin's surface. Analogously, under circularly polarized spin waves, the magnetization triad $\{\mathbf{m}_1, \mathbf{m}_2, \mathbf{m}_3\}$ (red, green, and blue arrows) exhibits the same motion, leaving the antiferromagnet's ground state rotated.
• Figure 2: Parallel transport of the magnetization triad on the unit sphere. After completing a loop, the triad is rotated relative to its initial orientation by the angle $\gamma$ equal to the solid angle $\Omega$ enclosed by the loop. Here $\gamma = \Omega = \pi/2$.