Structural ground states of $\left(A,A^{\prime }\right){\mathrm{Cr}}_2{\mathrm{O}}_4(A=\mathrm{Mg},\mathrm{Zn}; A^{\prime }=\mathrm{Co},\mathrm{Cu})$ spinel solid solutions: Spin-Jahn-Teller and Jahn-Teller effects

We examine the effect of small amounts of magnetic substituents in the $A$ sites of the frustrated spinels ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ and ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$. Specifically, we look for the effects of spin and lattice disorder on structural changes accompanying magnetic ordering in these compounds. Substitution of Co${}^{2+}$ on the nonmagnetic Zn${}^{2+}$ site in ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ where 0 $<$ $x$ $\le$ 0.2 completely suppresses the spin-Jahn-Teller distortion of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ although these systems remain frustrated, and magnetic ordering occurs at very low temperatures of $T$ $<$ 20 K. On the other hand, the substitution of Jahn-Teller active Cu${}^{2+}$ for Mg${}^{2+}$ and Zn${}^{2+}$ in ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ where 0 $<$ $x$ $\le$ 0.2 induce Jahn-Teller ordering at temperatures well above the Néel temperatures of these solid solutions, and yet spin interactions remain frustrated with long-range magnetic ordering occurring below 20 K without any further lattice distortion. The Jahn-Teller distorted solid solutions ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ adopt the orthorhombic $Fddd$ structure of ferrimagnetic ${\mathrm{CuCr}}_2{\mathrm{O}}_4$. Total neutron scattering studies of ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ suggest that there are local $A{\mathrm{O}}_4$ distortions in these Cu${}^{2+}$-containing solid solutions at room temperature and that these distortions become cooperative when average structure distortions occur. Magnetism evolves from compensated antiferromagnetism in ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ and ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ to uncompensated antiferromagnetism with substitution of magnetic cations on the nonmagnetic cation sites of these frustrated compounds. The sharp heat capacity anomalies associated with the first-order spin-Jahn-Teller transitions of ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ and ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ become broad in ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$, ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$, and ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ when $x$ $>$ 0. We present a temperature-composition phase diagram summarizing the structural ground states and magnetic properties of the studied spinel solid solutions.

Figure 1

Room-temperature synchrotron x-ray diffraction of the compounds (a) ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$, (b) ${\mathrm{Zn}}_{0.9}{\mathrm{Co}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$, and (c) ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$. All samples are well described in the cubic space group $Fd\overline{3}m$ and no impurity peaks are observed. (d) A unit-cell expansion occurs with substitution of Co${}^{2+}$ for Zn${}^{2+}$ in ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$. The dashed line is a linear fit to the lattice parameters of ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$.

Figure 2

The inverse scaled temperature-dependent susceptibility of the spinels ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ are shown along with the Curie-Weiss model. Magnetism evolves from compensated antiferromagnetism in ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ to uncompensated antiferromagnetism in ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$. The Curie-Weiss fit was modeled to the susceptibility in the temperature range 200 K $<$ $T$ $<$ 390 K.

Figure 3

Suppression of the spin-Jahn-Teller distortion in ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ with increase in $x$. (a) Inverse scaled magnetic susceptibility as a function of temperature for (a) ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$, (b) ${\mathrm{Zn}}_{0.9}{\mathrm{Co}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$, and (c) ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ measured in a 1000-Oe field. The dashed black line is the paramagnetic model which describes the data in the paramagnetic regime where spins are disordered. Compensated antiferromagnetic interactions of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ shown by the positive deviation of the inverse susceptibility from the Curie-Weiss model become uncompensated with the introduction of Co${}^{2+}$ in place of Zn${}^{2+}$ as illustrated by negative deviation of the susceptibility of ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ from the paramagnetic model. The middle panel shows variable-temperature high-resolution x-ray powder diffraction of the cubic (800) reflection. Geometric frustration in ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ drives the lattice distortion shown by the splitting of the (800) reflection at the Néel temperature (12.3 K) of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$. The spin-Jahn-Teller distortion of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ is suppressed even when only 10$\%$ Co${}^{2+}$ cations are substituted for Zn${}^{2+}$. (d) The sharp heat capacity anomaly observed at the spin-Jahn-Teller distortion temperature of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ is suppressed in ${\mathrm{Zn}}_{0.9}{\mathrm{Co}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (e) and strongly suppressed in ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (f).

Figure 4

Low-temperature synchrotron x-ray diffraction of (a) ${\mathrm{Zn}}_{0.9}{\mathrm{Co}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and (d) ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ modeled to the cubic space group $Fd\overline{3}m$. The (800) reflections of ${\mathrm{Zn}}_{0.9}{\mathrm{Co}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ at room temperature are shown here in (b) and (e), respectively, and near 5 K in (c) and (f), respectively. A broadening of the (800) reflection is observed at low temperature in ${\mathrm{Zn}}_{0.9}{\mathrm{Co}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{0.8}{\mathrm{Co}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$.

Figure 5

Rietveld refinement of room-temperature high-resolution synchrotron x-ray powder diffraction of (a) ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ (b) ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$, and (c) ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ to the cubic space group $Fd\overline{3}m$. All samples show a very small ${\mathrm{Cr}}_2{\mathrm{O}}_3$ impurity with concentrations $<$1$\%$ in all samples. (d) The cubic lattice constant in ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ decreases linearly with increase in Cu${}^{2+}$ concentration. Error bars are smaller than data symbols.

Figure 6

The inverse scaled temperature-dependent susceptibility of the spinels ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ are shown along with the Curie-Weiss fits that were modeled in the temperature range 200 K $<$ $T$ $<$ 390 K. Compensated antiferromagnetism in ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ evolves to uncompensated antiferromagnetism in ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$.

Figure 7

Spin-Jahn-Teller and Jahn-Teller ordering in ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$. The top panel shows the scaled inverse susceptibility of ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ (a), ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (b), and ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (c) measured in a 1000-Oe field. Compensated antiferromagnetic interactions in ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ (a) and ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (b) evolve to uncompensated antiferromagnetic interactions in ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (c). Geometric frustration of spins in ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ drives a structural distortion at $T_N$ = 12.9 K that is indicated by the splitting of the high-symmetry (800) reflection. Cooperative Jahn-Teller ordering spurs average structure distortions in ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ at $T$ $\sim$ 35 K and ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ at $T$ $\sim$ 110 K. The structural distortions in ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ are decoupled from the magnetism and no further structural distortions occur near the Néel temperature of these compounds although they exhibit spin frustration. (d) There is a sharp heat capacity anomaly at the Néel temperature of ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ with a shoulder feature plausibly indicating a slight separation in temperature of the magnetic and structural transitions. (e) ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ shows a broad heat capacity anomaly with a kink at $T_N$. (f) Similarly, ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ shows a broad heat capacity peak in the temperature range 6 K $\le$ $T$ $\le$ 80 K.

Figure 8

Low-temperature structures of (a) ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and (d) ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ indexed to the orthorhombic $Fddd$ structure. Data are shown in black, the structural model in orange, and the difference between the structural model and the data is in blue. Below the respective Jahn-Teller ordering temperatures of ${\mathrm{Mg}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Mg}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$, the coincident (731) and (553) reflections shown in (b) and (c) split into several reflections as shown in (c) and (f).

Figure 9

High-resolution synchrotron x-ray powder diffraction of the systems (a) ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$, (b) ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$, and (c) ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ measured at room temperature. All compounds are well indexed by the cubic space group $Fd\overline{3}m$. (d) A linear decrease of the cubic lattice constant occurs with Cu${}^{2+}$ substitution for Zn${}^{2+}$. Error bars are smaller than data symbols.

Figure 10

The inverse scaled temperature-dependent susceptibility of the spinels ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ are shown along with the Curie-Weiss model. Compensated antiferromagnetism in ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ evolves to uncompensated antiferromagnetism in ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$. The Curie-Weiss fit was modeled to the temperature range 200 K $<$ $T$ $<$ 390 K.

Figure 11

Spin-Jahn Teller and Jahn-Teller distortions in ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$. The top panel shows inverse scaled susceptibility measurements of ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ measured under a 1000-Oe field. Compensated antiferromagnetism is observed in ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ (a) and ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (b) below the Néel temperature while ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (c) shows uncompensated antiferromagnetism. A lattice distortion accompanies magnetic ordering in ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ as shown by the splitting of the high-symmetry (800) reflection at the Néel temperature. Jahn-Teller active Cu${}^{2+}$ on the $A$ sites of ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ drives lattice distortions at approximately 45 and 110 K, respectively, where the coincident (511) and (333) reflections split into several low-temperature reflections. There is a large heat capacity anomaly at the spin-Jahn-Teller distortion temperature of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ (d). Broad heat capacity anomalies are observed in ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (e) and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (f) over the temperature range where structural and magnetic changes occur. The line features in the variable temperature data of sample ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ are due to slight temperature fluctuations during the measurement.

Figure 12

Synchrotron powder diffraction patterns of ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (a) and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (d) collected near 6 K and indexed to the orthorhombic space group $Fddd$. Data are shown in black, the model is in orange, while the difference is in blue. The high-temperature coincident cubic $Fd\overline{3}m$ reflections (511) and (333) shown in (b) for ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and in (e) for ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ are split at lower temperatures following the cubic to orthorhombic lattice distortion. These low-temperature reflections as indexed to the orthorhombic $Fddd$ structure are shown in (c) and (f) for ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$, respectively.

Figure 13

(a) The evolution of lattice parameters of ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ as a function of temperature revealing a structural distortion at 110 K where three orthorhombic $Fddd$ lattice constants emerge from the cubic $Fd\overline{3}m$ lattice constant. (b) There is a slight change in slope in the temperature-dependent cell volume of ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ at the structural distortion temperature. Error bars obtained from Rietveld refinement are smaller than data symbols and do not incorporate uncertainties in the temperature.

Figure 14

The spinel structure of ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ in the cubic $Fd\overline{3}m$ phase near 300 K and in the orthorhombic $Fddd$ phase near 6 K are shown in (a) and (b), respectively. Edge-sharing ${\mathrm{CrO}}_6$ (blue) octahedra are corner connected to (Zn/Cu)${\mathrm{O}}_4$ (gray) tetrahedra. The shared (Zn/Cu) atomic site is shown in gray (Zn atomic fraction) and dark red (Cu atomic fraction). The ideal tetrahedral angle of 109.54${}^{\circ }$ observed in the cubic phase (a) of ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ is distorted to two angles of 111.898${}^{\circ }$ and 105.99${}^{\circ }$ in the orthorhombic phase (b); the (Zn/Cu)${\mathrm{O}}_4$ (gray) tetrahedra appear more flattened in the orthorhombic phase (b) filling the tetrahedral voids between the ${\mathrm{CrO}}_6$ octahedra, while small gaps can be seen between the(Zn/Cu)${\mathrm{O}}_4$ (gray) tetrahedra and the ${\mathrm{CrO}}_6$ (blue) octahedra in the cubic phase (a) of ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$.

Figure 15

Pair distribution functions for ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (a) and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ (b) measured at 300 and 15 K show that the local structure varies slightly from room temperature to low temperature. The low-$r$ region is shown in (a) and (b) to point out the slight increase in intensity of the pair distribution function at low temperature. The difference between the 15- and the 300-K pair distribution functions is shown at the bottom. Least-squares refinement of the pair distribution functions of these compounds at 15 K is well modeled by the $Fddd$ structure as shown in (c) and (d).

Figure 16

Least-squares refinement of the pair distribution function of ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ collected at 300 K are indexed to the cubic $Fd\overline{3}m$ structure [(a) and (b)] and to the orthorhombic $Fddd$ structure [(c) and (d)]. A smaller difference curve and slightly better ${\chi }^2$ parameters are obtained when the orthorhombic model is applied to the room-temperature data suggesting that dynamic Jahn-Teller distortion may be present at ambient temperature that becomes static at the Jahn-Teller distortion temperatures of these compounds.

Figure 17

Least-squares refinement of the 300-K pair distribution function of ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$ to a two-phase model of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ and ${\mathrm{CuCr}}_2{\mathrm{O}}_4$ shows that the environment around Zn${}^{2+}$ varies from that around Cu${}^{2+}$ at low $r$ as shown by the different Zn-O and Cu-O bond lengths of the ${\mathrm{ZnO}}_4$ and ${\mathrm{CuO}}_4$ tetrahedra. The phase fractions of the ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ model are 90$\%$ for ${\mathrm{Zn}}_{0.9}{\mathrm{Cu}}_{0.1}{\mathrm{Cr}}_2{\mathrm{O}}_4$ and 80$\%$ for ${\mathrm{Zn}}_{0.8}{\mathrm{Cu}}_{0.2}{\mathrm{Cr}}_2{\mathrm{O}}_4$. The differences in Zn-O and Cu-O bond lengths of the $A{\mathrm{O}}_4$ tetrahedra are smaller at high $r$.

Figure 18

Temperature-composition phase diagrams of the spinel solid solutions ${\mathrm{Zn}}_{1-x}{\mathrm{Co}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ (a), ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ (b), and ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ (c). At high temperatures, all systems are paramagnetic (PM) and cubic in the space group $Fd\overline{3}m$. Magnetism evolves from frustrated compensated antiferromagnetism (${\mathrm{AFM}}_C$) in ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ and ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ to glassy uncompensated antiferromagnetism (${\mathrm{gAFM}}_U$) when $x=0.2$. A transition from cubic $Fd\overline{3}m$ to orthorhombic $Fddd$ symmetry occurs in ${\mathrm{Mg}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ and ${\mathrm{Zn}}_{1-x}{\mathrm{Cu}}_x{\mathrm{Cr}}_2{\mathrm{O}}_4$ when $x\ge 0.1$ due to Jahn-Teller distortions of tetrahedral ${\mathrm{CuO}}_4$. We have recently reported that tetragonal $I{4}_1/amd$ and orthorhombic $Fddd$ structures coexist in the spin-Jahn-Teller phases of ${\mathrm{MgCr}}_2{\mathrm{O}}_4$ and ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ [6].