Low-energy theory of a two-dimensional itinerant chiral magnet

Armin Rahmani; Rodrigo A. Muniz; Ivar Martin

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arXiv · 1310.6792

Low-energy theory of a two-dimensional itinerant chiral magnet

Armin Rahmani·Rodrigo A. Muniz·Ivar Martin

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Abstract

Effective actions, such as nonlinear sigma models, are important tools in studying low-energy fluctuations of magnetically ordered states. Here we derive an effective action for the smooth order-parameter distortions of noncoplanar magnetic textures [with an SO(3) order parameter, as opposed to the SO(3)/SO(2)=S^2 of collinear magnets] coupled to itinerant electrons. Noncoplanar magnetic textures commonly arise in the presence of electron-mediated long-range spin exchange interactions, giving rise to the emergence of rich electronic phenomena such as anomalous quantum Hall effect. We parameterize the smooth order-parameter distortions of such a magnetic texture by certain non-Abelian fields, and derive the action in terms of these fields by integrating out the itinerant electrons. As a concrete example, we perform explicit calculations for a triangular-lattice model with tetrahedral magnetic ordering. The action encodes the charge and spin quantum-Hall responses as well as the energetics of twisting the magnetic texture.

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Armin Rahmani, Rodrigo A. Muniz, Ivar Martin. 2013-10-25. Low-energy theory of a two-dimensional itinerant chiral magnet. https://arxiv.org/abs/1310.6792

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