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Magnetic excitations from the two-dimensional interpenetrating Cu framework in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msub><mml:mi>Ba</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>Cu</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mi mathvariant="normal">O</mml:mi><mml:mn>4</mml:mn></mml:msub><mml:msub><mml:mi>Cl</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:math>
We report detailed neutron scattering studies on ${\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{4}{\mathrm{Cl}}_{2}$. The compound consists of two interpenetrating sublattices of Cu, labeled as ${\mathrm{Cu}}_{\mathrm{A}}$ and ${\mathrm{Cu}}_{\mathrm{B}}$, each of which forms a square-lattice Heisenberg antiferromagnet. The two sublattices order at different temperatures and effective exchange couplings within the sublattices differ by an order of magnitude. …