Abstract
We present a systematic construction of effective Lagrangians for the low energy and momentum region of ferromagnetic and antiferromagnetic spin waves in crystalline solids. We fully exploit the spontaneous symmetry breaking pattern SU(2)→U(1), the fact that spin waves are its associated Goldstone modes, the crystallographic space group and time reversal symmetries. We show how to include explicit SU(2) breaking terms due to spin-orbit and magnetic dipole interactions. The coupling to electromagnetic fields is also discussed in detail. For definiteness we work with the space group [Formula: see text] and present our results to next to leading order.
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