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Ultrasound velocity measurements of magnesium chromite spinel MgCr$_2$O$_4$ reveal elastic anomalies in the paramagnetic phase that are characterized as due to geometrical frustration. The temperature dependence of the tetragonal shear modulus $(C_{11}-C_{12})/2$ exhibits huge Curie-type softening, which should be the precursor to spin Jahn-Teller distortion in the antiferromagnetic phase. The trigonal shear modulus $C_{44}$ exhibits nonmonotonic temperature dependence with a characteristic minimum at $sim$50 K, indicating a coupling of the lattice to dynamical molecular spin state. These results strongly suggest the coexistence of dynamical spin Jahn-Teller effect and dynamical molecular spin state in the paramagnetic phase, which is compatible with the coexistence of magnetostructural order and dynamical molecular spin state in the antiferromagnetic phase.
Ultrasound velocity measurements were performed on a single crystal of spin-frustrated ferrite spinel ZnFe$_2$O$_4$ from 300 K down to 2 K. In this cubic crystal, all the symmetrically-independent elastic moduli exhibit softening with a characteristi
Ultrasound velocity measurements of cubic spinel GeCo$_2$O$_4$ in single crystal were performed for the investigation of shear and compression moduli. The shear moduli in the paramagnetic state reveal an absence of Jahn-Teller activity despite the pr
Ultrasound velocity measurements of the orbitally-frustrated GeCo$_2$O$_4$ reveal unusual elastic instabilities due to the phonon-spin coupling within the antiferromagnetic phase. Shear moduli exhibit anomalies arising from the coupling to short-rang
The low-dimensional s=1/2 compound (NO)[Cu(NO3)3] has recently been suggested to follow the Nersesyan-Tsvelik model of coupled spin chains. Such a system shows unbound spinon excitations and a resonating valence bond ground state due spin frustration
We consider the superexchange in `frustrated Jahn-Teller systems, such as the transition metal oxides NaNiO_2, LiNiO_2, and ZnMn_2O_4, in which transition metal ions with doubly degenerate orbitals form a triangular or pyrochlore lattice and are conn