Coupling of spins to lattice and/or orbital degrees of freedom generates a plethora of collective phenomena in crystals including magnetoelasticity. Magnetoelasticity is manifested in the change of the crystal lattice (crystal symmetry, lattice constants) induced by external magnetic fields or by the onset of magnetic orders.
We study the dynamical coupling between spins and lattice vibrations (phonons) in insulating magnets with complex spin orders including ACr2O4 (A=Mn, Fe, Co, Ni and Cu) spinels by infrared spectroscopy. Their crystal structure is shown in Figure 1. We also investigate coupled f−d spin systems such as Tb3Fe(BO3)4 and Nd3Fe(BO3)4.
For spinel compounds with orbital degeneracy at the A-site in the cubic phase (i.e. for A=Fe, Ni and Cu), clear splitting of infrared-active phonon modes (see Figure 2) and/or activation of silent vibrational modes have been observed upon the Jahn-Teller transition and at the onset of the subsequent long-range magnetic order [1,2]. The temperature dependence of the phonon modes is summarized in Figure 3.
In spite of their multiferroic and magnetoelectric character, MnCr2O4 and CoCr2O4 without orbital degeneracy exhibit no considerable magnetoelasticity as they closely preserve the high-temperature cubic spinel structure even in their magnetic ground state.
Our experimental observations clearly indicate that, in these spinel compounds the criterion for strong magnetoelasticity is the orbital degeneracy of the A-site magnetic ions [1,2].
 S. Bordács et al., Phys. Rev. Lett. 103, 077205 (2009).