Ultrasound velocity measurements of cubic spinel ${\text{GeCo}}_2{\text{O}}_4$ in single crystal were performed for the investigation of shear and compression moduli. The shear moduli in the paramagnetic state reveal the absence of Jahn-Teller activity despite the presence of orbital degeneracy in the ${\text{Co}}^{2+}$ ions. Such a Jahn-Teller inactivity indicates that the intersite orbital-orbital interaction is much stronger than the Jahn-Teller coupling. The compression moduli in the paramagnetic state near the Néel temperature $T_N$ reveal that the most relevant exchange path for the antiferromagnetic transition lies in the [111] direction. This exchange-path anisotropy is consistent with the antiferromagnetic structure with the wave vector $q\parallel \left[111\right]$, suggesting the presence of bond frustration due to competition among a direct ferromagnetic interaction and several distant-neighbor antiferromagnetic interactions. In the Jahn-Teller-inactive condition, the bond frustration can be induced by geometrical orbital frustration of $t_{2g}\text{−}{t}_{2g}$ interaction between the ${\text{Co}}^{2+}$ ions, which can be realized in the pyrochlore lattice of the high-spin ${\text{Co}}^{2+}$ with $t_{2g}$-orbital degeneracy. In ${\text{GeCo}}_2{\text{O}}_4$, the tetragonal elongation below $T_N$ releases the orbital frustration by quenching the orbital degeneracy.

• Received 27 May 2008

DOI:https://doi.org/10.1103/PhysRevB.78.094420