High-pressure synthesis and structural, transport, and magnetic properties of rutile-type $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ and $\mathrm{CrRe}{\mathrm{O}}_4$

We have synthesized the cation ordered rutile-type $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ and $\mathrm{CrRe}{\mathrm{O}}_4$ under high-pressure and high-temperature conditions and performed detailed characterizations on their structural, transport, and magnetic properties via x-ray and neutron powder diffraction, resistivity, magnetic susceptibility, and specific heat measurements. $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ crystallizes in the inverse trirutile structure with lattice parameters $a=b=4.55221\left(5\right)\AA$ and $c=8.8934\left(1\right)\AA$ in the space group $P{4}_2/mnm$. It undergoes a second-order antiferromagnetic transition at $T_{\mathrm{N}}\approx 67\mathrm{K}$ with the magnetic structure described by the propagation vector $\mathbf{k}=\left[0.5,0,0.5\right]$. For $\mathrm{CrRe}{\mathrm{O}}_4$, it adopts a monoclinically distorted rutile-like structure with unit-cell parameters $a=9.3393\left(2\right)\AA$, $b=5.6869\left(1\right)\AA$, $c=4.6243\left(1\right)\AA$, and $\beta =92.043{\left(8\right)}^{\circ }$ in the space group $C2/m$. It also exhibits an antiferromagnetic order at $T_{\mathrm{N}}=98\mathrm{K}$ with the magnetic structure described by the propagation vector $\mathbf{k}=\left[1,0,0.5\right]$. Interestingly, a large paramagnetic Weiss temperature of ${\theta }_{\mathrm{CW}}=-478\mathrm{K}$ is evidenced from the Curie-Weiss fitting to the inverse magnetic susceptibility. The temperature dependence of resistivity ρ($T$) for both compounds can be described with Mott's variable range hopping mechanism in the one-dimensional model for $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ and the three-dimensional model for $\mathrm{CrRe}{\mathrm{O}}_4$, respectively. For both compounds, a weak resistivity anomaly can be discerned around $T_{\mathrm{N}}$ from the temperature derivative curves, signaling the interplay of charge and spin degrees of freedom for these $3d$(Cr)-$5d$(Re) coupled electron systems.

Figure 1

Schematic drawing of the crystal structures for (a) the simple rutile $A{\mathrm{O}}_2$, (b) the monoclinically distorted “birutile”$AB{\mathrm{O}}_4$, and (c) the inverse trirutile $A_{2}B{\mathrm{O}}_6$. The crystal structures of these rutile-type derivatives are featured by edge-shared $A/B{\mathrm{O}}_6$ octahedral chains along the $c$ axis for the simple rutile (a) and the inverse trirutile (c), or along the $b$ axis for the “birutile” (b).

Figure 2

Observed (cross), calculated (line), and their difference (bottom line) profiles for (a) XRD and (b) NPD of $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ after Rietveld refinements. The first and second row of tick marks in (a) represent the Bragg positions of the trirutile $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ and the impurity $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$, respectively. The tick marks in (b) represent the Bragg positions of the trirutile $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$, $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$, and the monoclinic $\mathrm{CrRe}{\mathrm{O}}_4$, respectively.

Figure 3

(a) Temperature dependence of the magnetic susceptibility χ($T$) and the specific heat divided by temperature $C$/$T$ for $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$. (b) Temperature dependence of the inverse susceptibility ${\chi }^{-1}\left(T\right)$ and the Curie-Weiss fitting curve shown by the solid line. (c) Field dependence of the isothermal magnetization $M$($H$) at 2 K.

Figure 4

(a) Observed (cross), calculated (line), and difference (bottom line) NPD profiles for $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ at 2 K. The first and second reflection marks correspond to the $\mathrm{C}{\mathrm{r}}_2{\mathrm{O}}_3$ and $\mathrm{CrRe}{\mathrm{O}}_4$ minor impurities, and the third row belongs to the crystal and magnetic structure of $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$. The magnetic reflections are indicated by the arrows. (b) The magnetic structure of $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$ with the Cr moments (red) lying on the $bc$ plane, and the small value of the Re moments (green) approximately lying on the $ac$ plane.

Figure 5

(a) Temperature dependence of the resistivity ρ($T$) for $\mathrm{C}{\mathrm{r}}_2\mathrm{Re}{\mathrm{O}}_6$. (b) A plot of lnρ vs $T^{-1/2}$ showing an inflection point around $T_{\mathrm{N}}$, which can be seen from the maximum of the $d\ln \rho /d\left(T^{-1/2}\right)$ curve. The linear fitting curves shown by the dotted lines are used to extract the activation energies below and above $T_{\mathrm{N}}$.

Figure 6

Observed (cross), calculated (line), and their difference (bottom line) profiles of (a) XRD pattern at 295 K and (b) NPD pattern at 120 K for $\mathrm{CrRe}{\mathrm{O}}_4$ after Rietveld refinements. The tick marks represent the Bragg positions of the birutile structure.

Figure 7

Temperature dependence of (a) the magnetic susceptibility χ($T$) and (b) its inverse ${\chi }^{-1}\left(T\right)$ for $\mathrm{CrRe}{\mathrm{O}}_4$ measured in the zero-field-cooled (ZFC) and field-cooled (FC) modes. The Curie-Weiss fitting curve is shown by the solid line. (c) Field dependence of the isothermal magnetization $M$($H$) at 2 K.

Figure 8

(a) Observed (cross), calculated (line), and difference (bottom line) NPD profiles for $\mathrm{CrRe}{\mathrm{O}}_4$ at 2 K. The series of vertical marks define the Bragg positions for both crystal and magnetic structures. The magnetic reflections are indicated by the arrows. (b) The magnetic structure of $\mathrm{CrRe}{\mathrm{O}}_4$, showing the antiferromagnetic arrangement of the Cr moments (red) lying on the $ac$ plane, and the tiny magnitude of the ordered Re moments (green) with a single component along the $b$ axis.

Figure 9

(a) Temperature dependence of the resistivity ρ($T$) for $\mathrm{CrRe}{\mathrm{O}}_4$. (b) A plot of lnρ vs $T^{-1/4}$ showing a slope change around $T_{\mathrm{N}}$, which can be seen from the plateau of the $d\ln \rho /d\left(T^{-1/4}\right)$ curve. The linear fitting curves shown by the dotted lines are used to extract the activation energies below and above $T_{\mathrm{N}}$.

Figure 10

(a) Temperature dependence of the specific heat $C$($T$) for $\mathrm{CrRe}{\mathrm{O}}_4$. (b) The $C$($T$) data below 12 K in the form of $C$/$T$ vs $T^2$. The solid line is a linear fitting curve. (c) The magnetic contribution $C_m\left(T\right)$ and the associated entropy $S$($T$) around $T_{\mathrm{N}}$.