Geometric frustration in the cubic spinelsMAl2O4(M=Co, Fe, and Mn)

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 $T\to 0\mathrm{K}$ 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 $T_N=40\mathrm{K}$ with a reduced value of the ordered moment and a large paramagnetic component.