Theory of Exchange Resonance in Antiferromagnetic Cu<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Cl</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>·2<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">H</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math>O

The low crystal symmetry of antiferromagnetic Cu${\mathrm{Cl}}_{2}$\ifmmode\cdot\else\textperiodcentered\fi{}2${\mathrm{H}}_{2}$O allows an antisymmetric, anisotropic, superexchange interaction (Moriya interaction) of the form ${\mathrm{D}}_{12}$\ifmmode\cdot\else\textperiodcentered\fi{}[${\mathrm{S}}_{1}$\ifmmode\times\else\texttimes\fi{}${\mathrm{S}}_{2}$] between corner and base-center copper ions. The classical magnetic-resonance frequencies and spin-wave frequencies have been derived for a four-sublattice model from a spin Hamiltonian consisting of nearest- and next-nearest-neighbor isotropic superexchange interactions, the Moriya interaction, and orthorhombic anisotropy energy. A set of highfrequency exchange modes was obtained in addition to the usual antiferromagnetic resonance modes. The former are characterized by the beating in opposition of ferromagnetic sublattices which would be degenerate in the absence of the Moriya interaction. The exchange frequencies are proportional to the geometric average of the ferromagnetic and antiferromagnetic exchange fields and are an order of magnitude larger than the antiferromagnetic frequencies. A resonance absorption experiment is proposed to detect the exchange modes; zero field magnetic resonance is expected at about 0.7 mm.

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