Frustration and Jahn-Teller ordering in magnetic spinel oxides

Geometrically frustrated magnetic systems have become extremely important for the study of novel phenomena often present in highly degenerate magnetic ground states. Extensive study of the canonically frustrated ZnCr$_2$O$_4$ and MgCr$_2$O$_4$ has increased the understanding of frustration in three-dimensional systems, however little is known about the structural effect of dilute magnetism on the $A$ site. We present the effects on magneto-structural coupling of dilute magnetic cations on the diamagnetic $A$ site of ZnCr$_2$O$_4$ and MgCr$_2$O$_4$. In ZnCr$_2$O$_4$ and MgCr$_2$O$_4$, a spin-driven structural distortion concomitant with the onset of long-range magnetic order resolves the large ground state degeneracy at temperatures far below the theoretical Curie-Weiss temperature. Employing variable temperature high-resolution synchrotron powder diffraction studies and magnetic susceptibility measurements, we show the changes in spin-lattice coupling in the solid solutions Zn$_{1-x}$Co$_x$Cr$_2$O$_4$, Zn$_{1-x}$Cu$_x$Cr$_2$O$_4$ and Mg$_{1-x}$Cu$_x$Cr$_2$O$_4$ for $x \leq 0.2$. These results highlight the effect of dilute $A$ site magnetism on magnetic frustration as well as the role of dilute Jahn-Teller active Cu$^{2+}$ on spin-lattice coupling in these frustrated systems.