Breathing Pyrochlore Lattice Realized in $A$-Site Ordered Spinel Oxides ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$

A unique type of frustrated lattice is found in two $A$-site ordered spinel oxides, ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$. Because of the large size mismatch between ${\mathrm{Li}}^{+}$ and ${\mathrm{Ga}}^{3+}/{\mathrm{In}}^{3+}$ ions at the $A$ site, the pyrochlore lattice, made up of ${\mathrm{Cr}}^{3+}$ ions carrying spin $3/2$, becomes an alternating array of small and large tetrahedra, i.e., a “breathing” pyrochlore lattice. We introduce a parameter, the breathing factor $B_f$, which quantifies the degree of frustration in the pyrochlore lattice: $B_f$ is defined as $J^{\prime }/J$, where $J^{\prime }$ and $J$ are nearest-neighbor magnetic interactions in the large and small tetrahedra, respectively. ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ with $B_f\sim 0.6$ shows magnetic susceptibility similar to that of conventional Cr spinel oxides such as ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$. In contrast, ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ with a small $B_f\sim 0.1$ exhibits a spin-gap behavior in its magnetic susceptibility, suggesting a proximity to an exotic singlet ground state. Magnetic long-range order occurs at 13.8 and 15.9 K for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$, respectively, in both cases likely owing to the coupling to structural distortions.

Figure 1

(a) Crystal structure of ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$. Coordination polyhedra made of oxide ions are depicted. (b) Breathing pyrochlore lattice made of ${\mathrm{Cr}}^{3+}$ ions embedded in the two compounds. Cr-Cr bonds on the small (filled sticks) and large tetrahedra (open sticks) have bond lengths $d$ and $d^{\prime }$ and antiferromagnetic interactions $J$ and $J^{\prime }$, respectively.

Figure 2

Powder neutron diffraction patterns for (a) ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and (b) ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ measured on bank 6 ($2\theta =154°$) of the General Materials Diffractometer at room temperature. Filled circles are experimental data, and vertical bars indicate the positions of Bragg reflections. The curve on the data shows a calculated pattern, and the bottom curve shows a difference plot between the experimental and calculated intensities.

Figure 3

(a) Temperature dependence of magnetic susceptibility $\chi$ measured in a magnetic field of 1 T for polycrystalline samples of ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$. The data for a polycrystalline sample of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ are also shown for comparison [6]. Solid lines are calculated curves produced by classical Monte Carlo simulations with $J^{\prime }=0.5J$ ($J=53.3\mathrm{K}$) for the Ga data and by the exact result for an isolated tetrahedron ($J=56.8\mathrm{K}$) for the In data. The inset shows inverse susceptibilities with Curie-Weiss fits. (b) Temperature dependences of field-cooled and zero-field-cooled $\chi$’s measured at various magnetic fields for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ (upper panel) and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ (lower panel). (c) $M\mathrm{\text{−}}H$ curves for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ measured at 5 K. The broken line shows an initial straight line.

Figure 4

Temperature dependence of heat capacity divided by temperature $C_p/T$ for polycrystalline samples of ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ and ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$. Filled and open symbols represent data measured at magnetic fields of 0 and 9 T for each sample, respectively.

Figure 5

Nearest-neighbor magnetic interaction versus the Cr-Cr distance for various Cr spinel oxides. The $J$ value of ${\mathrm{ZnCr}}_2{\mathrm{O}}_4$ is estimated by fitting $\chi$, $C_p$, and EPR intensity [19, 20, 21]. The $J$’s of ${\mathrm{CdCr}}_2{\mathrm{O}}_4$ and ${\mathrm{HgCr}}_2{\mathrm{O}}_4$ are estimated by Curie-Weiss fits to $\chi$ [6, 7, 22]. The dotted line is a guide for the eyes. Plotted for ${\mathrm{LiGaCr}}_4{\mathrm{O}}_8$ or ${\mathrm{LiInCr}}_4{\mathrm{O}}_8$ is a pair of points corresponding to the two Cr-Cr distances in the small and large tetrahedra.