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Complex magnetoelastic properties in the frustrated kagome-staircase compounds (Co<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub></mml:math>Ni<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mrow /><mml:mi>x</mml:mi></mml:msub></mml:math>)<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><…
High-resolution heat-capacity and thermal-expansion measurements on single crystals of the kagome-staircase compounds (Co${}_{1\ensuremath{-}x}$Ni${}_{x}$)${}_{3}$V${}_{2}$O${}_{8}$ are presented. The parent compounds Co${}_{3}$V${}_{2}$O${}_{8}$ and Ni${}_{3}$V${}_{2}$O${}_{8}$ undergo a sequence of first- and second-order magnetic phase transitions. The low-temperature ($T\ensuremath{\leqslant}40$ K) magnetic entropy evolves monotonically with the doping content $x$ from the full value expected for …