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In both spinel compounds GeCo$_2$O$_4$ and GeNi$_2$O$_4$ which orderantiferromagnetically (at $T_N = 23.5 K$ and $T_{N_1} = 12.13 K$, $T_{N_2} =11.46 K$) with different Curie Weiss temperatures ($T_{CW}$=80.5 K and -15 K),the usual magnetic frustration criterion $f=|T_{CW}|/T_N>>1$ is not fulfilled.Using neutron powder diffraction and magnetization measurements up to 55 T,both compounds are found with a close magnetic ground state at low temperatureand a similar magnetic behavior (but with a different energy scale), eventhough spin anisotropy and first neighbor exchange interactions are quitedifferent. This magnetic behavior can be understood when considering the mainfour magnetic exchange interactions. Frustration mechanisms are thenenlightened.Comment: submitted to Phys.Rev.B (2006

physical review. b, condensed matter and materials physics

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Magnetic frustration in the spinel compoundsGeCo2O4andGe