Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co$_{1-x}$Ni$_x$)$_3$V$_2$O$_8$

High resolution heat capacity and thermal expansion experiments performed on single crystalline kagome-staircase compounds (Co $_{1 - x}$ 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 complex sequence of first- and second-order magnetic phase transitions. The low-temperature ( $T < 40$ K) magnetic entropy evolves monotonously with the doping content $x$ , from the full S=1 Ni $^{2 +}$ magnetic entropy in Ni $_{3}$ V $_{2}$ O $_{8}$ to half of the S=3/2 Co $^{2 +}$ magnetic entropy in Co $_{3}$ V $_{2}$ O $_{8}$ . Thermal expansion coefficients $α_{i}$ ( $i = a$ , $b$ and $c$ ) show a strong anisotropy for all (Co $_{1 - x}$ Ni $_{x}$ ) $_{3}$ V $_{2}$ O $_{8}$ compounds. The low-temperature magnetic distortion indicates that Co-doping (Ni-doping) has similar effects to applying a uniaxial pressures along $a$ or $b$ ( $c$ ). Linear Gr"{u}neisen parameters $Γ_{i}$ are extracted for the three main axes $i$ and exhibit a complex behavior with both temperature and doping. For each axis, $Γ_{i}$ and $α_{i}$ exhibit a sign change (at low temperature) at the critical concentration $x_{c} ≃ 0.25$ , at which the incommensurate magnetic propagation vector changes. Beyond our study, an understanding of the multiple and complex parameters (magnetic frustration, magnetic anisotropy, mixture of S=1 and S=3/2 ions, etc.) is now necessarily to bring light to the rich magneto-elastic properties of (Co $_{1 - x}$ Ni $_{x}$ ) $_{3}$ V $_{2}$ O $_{8}$ .

Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co $_{1 - x}$ Ni $_{x}$ ) $_{3}$ V $_{2}$ O $_{8}$

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Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co $_{1 - x}$ Ni $_{x}$ ) $_{3}$ V $_{2}$ O $_{8}$

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Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co1−x1−x​Nixx​)33​V22​O88​

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Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co1−x1−x​Nixx​)33​V22​O88​

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Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co $_{1 - x}$ Ni $_{x}$ ) $_{3}$ V $_{2}$ O $_{8}$

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Complex magneto-elastic properties in the frustrated kagome-staircase compounds (Co $_{1 - x}$ Ni $_{x}$ ) $_{3}$ V $_{2}$ O $_{8}$

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