Effective Field Theory Approach to Ferromagnets and Antiferromagnets in Crystaline Solids
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 R 3 c and present our results to next to leading order.
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