Geometric frustration in the cubic spinelsMAl2O4(M=Co

X-ray diffraction, magnetic susceptibility, electron-spin resonance, and heat-capacity investigations were performed on $M{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ compounds with $M=\mathrm{Co}$, Fe, Mn, and Zn. All compounds crystallize in cubic spinel structure $A{B}_{2}{\mathrm{O}}_{4}$ with minor inversion between $A$ and $B$ sites. $\mathrm{Co}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ and $\mathrm{Fe}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ reveal spin-glass-like ground states with freezing temperatures well below the Curie-Weiss temperatures indicating strong geometric frustration. Below the freezing temperatures, the heat capacities show a ${T}^{2}$ temperature dependence for $T\ensuremath{\rightarrow}0\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ as has recently been observed in some related geometrically frustrated magnets, in contrast to the linear dependence expected for common spin glasses. The heat capacity of $\mathrm{Fe}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ exhibits an additional orbital contribution. With the absence of a cooperative Jahn-Teller distortion, this points toward an orbital freezing. $\mathrm{Mn}{\mathrm{Al}}_{2}{\mathrm{O}}_{4}$ orders antiferromagnetically below ${T}_{N}=40\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ with a reduced value of the ordered moment and a large paramagnetic component.