Competing Jahn-Teller and spin Jahn-Teller ordering in $A$Cr$_2$O$_4$ spinels*

Magnetic ordering is strongly linked to structural distortions in the frustrated antiferromagnets ZnCr$_2$O$_4$ and MgCr$_2$O$_4$. These systems undergo spin Jahn-Teller distortions at the onset of magnetic order. The addition of magnetic $A$ site cations in $A$Cr$_2$O$_4$ spinels can relieve frustration. High-resolution variable-temperature synchrotron powder X-ray diffraction, detailed magnetic studies, and heat capacity measurements show that dilute amounts of Jahn-Teller active Cu$^{2+}$ or Co$^{2+}$ on the $A$ sites of these spinels have different effects on structure but similar effects on magnetism. Partial replacement of $A$ by Cu$^{2+}$ generates Jahn-Teller distortions at temperatures above the endmember Neel temperatures, yet spin interactions remain frustrated to $\sim$ 12 K. This contrasts with Co$^{2+}$ substitution which also maintains frustration, but results in a suppression of spin Jahn-Teller ordering in ZnCr$_2$O$_4$. We report decoupled Jahn-Teller and spin Jahn-Teller ordering in the canonical frustrated systems ZnCr$_2$O$_4$ and MgCr$_2$O$_4$ that is tunable by varying the identity of the magnetic $A$ site substituent.