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

High-resolution heat-capacity and thermal-expansion measurements on single crystals of the 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 sequence of first- and second-order magnetic phase transitions. The low-temperature ($T⩽40$ K) magnetic entropy evolves monotonically with the doping content $x$ from the full value expected for Ni${}^{2+}$ $S=1$ magnetic moments in Ni${}_3$V${}_2$O${}_8$ to only half the value expected for Co${}^{2+}$ $S=3/2$ moments in Co${}_3$V${}_2$O${}_8$. The thermal-expansion coefficients ${\alpha }_i$ ($i=a$, $b$, and $c$) show a strong anisotropy for all (Co${}_{1-x}$Ni${}_x$)${}_3$V${}_2$O${}_8$ compounds. The low-temperature expansivities indicate that Co doping (Ni doping) yields changes similar to uniaxial pressures along $a$ or $b$ ($c$). Linear Grüneisen parameters ${\Gamma }_i$ are extracted for the three main axes $i$ and are found to exhibit a complex temperature and doping dependence. For each axis, ${\Gamma }_i$ and ${\alpha }_i$ exhibit a sign change at low temperature at the critical concentration $x_c\simeq 0.25$ where the incommensurate magnetic propagation vector changes. Our study motivates further investigations to understand how the multiple and complex parameters such as magnetic frustration, magnetic anisotropy, and mixture of $S=1$ and $3/2$ ions affect the rich magnetoelastic properties of (Co${}_{1-x}$Ni${}_x$)${}_3$V${}_2$O${}_8$.

Figure 1

Specific heat $C_p$ of Co${}_3$V${}_2$O${}_8$, (Co${}_{0.5}$Ni${}_{0.5}$)${}_3$V${}_2$O${}_8$, and Ni${}_3$V${}_2$O${}_8$ as a function of temperature $T$ on a log-log scale. Dotted lines indicate the low-temperature $T^3$ and $T^4$ power-law regimes.

Figure 2

Specific heat $C_p$ versus temperature $T$ of Co${}_3$V${}_2$O${}_8$, (Co${}_{0.5}$Ni${}_{0.5}$)${}_3$V${}_2$O${}_8$, and Ni${}_3$V${}_2$O${}_8$. Dotted lines indicate a fit to the data above 60 K to obtain the phonon contribution to $C_p$ (see text for details).

Figure 3

(a) Magnetic specific heat divided by temperature $C_p^{\text{mag}}/T$ versus $T$. (b) Magnetic entropy $S$ versus temperature $T$ of (Co${}_{1-x}$Ni${}_x$)${}_3$V${}_2$O${}_8$ single crystals.

Figure 4

Magnetic entropy $S_{\text{mag}}$ of (Co${}_{1-x}$Ni${}_x$)${}_3$V${}_2$O${}_8$, at $T=40$ K, as a function of the Ni concentration $x$.

Figure 5

Thermal expansion coefficients ${\alpha }_a$, ${\alpha }_b$, and ${\alpha }_c$ versus temperature $T$ of (a) Co${}_3$V${}_2$O${}_8$ and (b) Ni${}_3$V${}_2$O${}_8$.

Figure 6

Temperature dependence of the relative length $\left[L\right(T)-L(30\mathrm{K}\left)\right]/\mathrm{L}\left(30\mathrm{K}\right)$ measured along the $a$, $b$, and $c$ axes [(a), (b), and (c), respectively], of the thermal-expansion coefficient $\alpha$ extracted for the $a$, $b$, and $c$ axes [(d), (e), and (f), respectively], and of the Grüneisen parameter $\Gamma$ extracted for the $a$, $b$, and $c$ axes [(g), (h), and (i), respectively] for (Co${}_{1-x}$Ni${}_x$)${}_3$V${}_2$O${}_8$ samples of concentration $x=0$, 0.12, 0.20, 0.28, 0.35, 0.5 and 1.

Figure 7

Temperature dependence of the Grüneisen parameters ${\Gamma }_i$ on an expanded vertical scale of (a) (Co${}_{0.8}$Ni${}_{0.2}$)${}_3$V${}_2$O${}_8$ and (b) (Co${}_{0.65}$Ni${}_{0.35}$)${}_3$V${}_2$O${}_8$ for the $a$, $b$, and $c$ axes.

Figure 8

Magnetic ($T,x$) phase diagram of (Co${}_{1-x}$Ni${}_x$)${}_3$V${}_2$O${}_8$ extracted from the specific heat (squares) and thermal expansion (diamonds: $a$ axis; circles: $b$ axis; and triangles: $c$ axis). Full stars correspond to transition temperatures extracted from neutron experiments by Qureshi et al. (Refs. 7 and 8) and open stars to transitions obtained from specific heat by Kumarasiri and Lawes (Ref. 24).

Figure 9

Anomalies in the magnetic entropy $S_{\text{mag}}$ and length changes $\Delta L_i/L_i$ at the first-order transitions.

Figure 10

Anomalies of the magnetic specific heat divided by temperature $C_p^{\text{mag}}/T$ and thermal-expansion coefficients ${\alpha }_i$ at the second-order transitions.