Effects of inter-vanadium distance and $A$-site magnetism in $A\mathrm{V}{}_2{\mathrm{O}}_4$ ($A\hspace{0.17em}=\hspace{0.17em}\mathrm{Cd}, \mathrm{Mg}, \mathrm{Zn}$) spinels near the itinerant electron limit

We present temperature dependent powder x-ray diffraction measurements of the spinel $A{\mathrm{V}}_2{\mathrm{O}}_4$ ($A=\mathrm{Cd}, \mathrm{Mg}, \mathrm{Zn}$, and ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$). The result shows that even though the V-V distance is an important governing parameter, the $A$-site magnetism also has a significant effect on the physical properties of $A{\mathrm{V}}_2{\mathrm{O}}_4$. This is demonstrated by comparing the structural and transport properties of nonmagnetic $A$-site ions $A{\mathrm{V}}_2{\mathrm{O}}_4$ ($A$ $=\mathrm{Cd}, \mathrm{Mg}, \mathrm{Zn}$) with the magnetic $A$-site ion substitutional sequence ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$.

Figure 1

Nonmagnetic $A$-site $A{\mathrm{V}}_2{\mathrm{O}}_4$. Results of the Rietveld refinements showing the temperature dependencies of the lattice parameters and the fit (solid lines) to the lattice parameters of the cubic phase (top), and the percentage of the changes in the lattice parameters $a$ (center) and $c$ (bottom) for (a) ${\mathrm{CdV}}_2{\mathrm{O}}_4$, (b) ${\mathrm{MgV}}_2{\mathrm{O}}_4$, and (c) ${\mathrm{ZnV}}_2{\mathrm{O}}_4$.

Figure 2

Magnetic $A$-site ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$. Results of the Rietveld refinements showing the temperature dependencies of the lattice parameters and the fit (solid lines) to the lattice parameters of the cubic phase (top), and the percentage of the changes in the lattice parameters $a$ (center) and $c$ (bottom) for (a) $x=$ 0.2, (b) $x=$ 0.4, and (c) $x=$ 0.6.

Figure 3

The XRD pattern of a selected peak of (a) ${\mathrm{CdV}}_2{\mathrm{O}}_4$ (440), (b) ${\mathrm{ZnV}}_2{\mathrm{O}}_4$ (400), and (c) ${\mathrm{Mn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{V}}_2{\mathrm{O}}_4$ (400) in the proximity of $T_S$ showing the evolution of the peak with temperature. The solid blue curves are the Lorentzian fit to the peaks.

Figure 4

The percentage of the tetragonal phase as a function of normalized temperature $T/T_S$.

Figure 5

The $R_{\text{V-V}}$ dependencies (plotted as $R_{\text{V-V}}^{-1}$) of (a) the relative changes of $a$ of $A{\mathrm{V}}_2{\mathrm{O}}_4$, (b) the relative changes of $c$, and (c) the $c/a$ ratio. The plots show the two schematic paths of how the magnitude of the tetragonal lattice distortion varies with $R_{\text{V-V}}$. The $A{\mathrm{V}}_2{\mathrm{O}}_4$ path (path 1) and the ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ (path 2) are indicated by solid and broken lines, respectively.

Figure 6

The $R_{\text{V-V}}$ dependencies (plotted as $R_{\text{V-V}}^{-1}$) of (a) the structural transition temperature and (b) the activation energy. The $A{\mathrm{V}}_2{\mathrm{O}}_4$ path (path 1) and the ${\mathrm{Mn}}_{1-x}{\mathrm{Co}}_x{\mathrm{V}}_2{\mathrm{O}}_4$ (path 2) are indicated by solid and broken lines, respectively.