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Origin of the long-wavelength magnetic modulation in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mtext>Ca</mml:mtext></mml:mrow><mml:mn>3</mml:mn></mml:msub><mml:msub><mml:mrow><mml:mtext>Co</mml:mtext></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mtext>O</mml:mtext><mml:mn>6</mml:mn></mml:msub></mml:mrow></mml:math>
The origin of the long-wavelength incommensurate magnetic structure of ${\text{Ca}}_{3}{\text{Co}}_{2}{\text{O}}_{6}$ is discussed considering possible interchains super-superexchange paths. The experimental value of the propagation vector $k=(0,0,\ensuremath{\Delta})$ with $\ensuremath{\Delta}>1$ can be reproduced only if one considers the next-nearest super-superexchange interaction. A spin-dimer analysis using the extended Huckel tight-binding method confirms that, despite …