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We have performed a detailed investigation of the new `breathing' pyrochlorecompound LiInCr$_4$O$_8$ through Rh substitution with measurements of magneticsusceptibility, specific heat, and x-ray powder diffraction. Theantiferromagnetic phase of LiInCr$_4$O$_8$ is found to be slowly suppressedwith increasing Rh, up to the critical concentration of $x$ = 0.1 where theantiferromagnetic phase is still observed with the peak in specific heat $T_p$= 12.5 K, slightly lower than $T_p$ = 14.3 K for the $x$ = 0 compound. From themeasurements of magnetization we also uncover evidence that substitutionincreases the amount of frustration. Comparisons are made with theLiGa$_y$In$_{1-y}$Cr$_4$O$_8$ system as well as other frustratedpyrochlore-related materials and find comparable amounts of frustration. Theresults of this work shows that engineered breathing pyrochlores presents animportant method to further understand the complex magnetism in frustratedsystems.

Investigation of the complex magnetism in the breathing pyrochlore LiIn(Cr$_{1-x}$Rh$_x$)$_4$O$_8$