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BaCuSiO, a quantum antiferromagnet with a double-layer structure of Cu ions in a distorted planar-rectangular coordination and with a dimerized spin singlet ground state, is studied by means of the electron paramagnetic resonance technique. It is argued that multiple absorptions observed at low temperatures are intimately related to a thermally-activated spin-triplet exciton superstructure. Analysis of the angular dependence of exciton modes in BaCuSiO allows us to accurately estimate anisotropy parameters. In addition, the temperature dependence of EPR intensity and linewidth is discussed.

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