Magnetic phase transitions in RCo 2 Laves phases with R as a rare earth element are accompanied by changes in crystallographic space group. For purely structural transitions they would be described as improper ferroelastic and therefore fulfil the condition for multiferroic phase transitions in combining two out of three properties, ferro/antiferromagnetism, ferroelectricity and ferroelasticity. Here lattice parameter data from the literature and new measurements of elastic and anelastic

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... ies, by resonant ultrasound spectroscopy, for NdCo 2 and ErCo 2 have been analysed from this perspective. The temperature dependence of symmetry-breaking shear strains is consistent with the cubic ↔ tetragonal transition in NdCo 2 being close to tricritical in character and the cubic ↔ rhombohedral transition in ErCo 2 being first order. Elastic softening and acoustic loss within the stability ranges of the ferroelastic phases can be understood in terms of a combination of intrinsic softening due to strain/order parameter coupling and ferroelastic twin-wall motion. Softening ahead of the transitions does not fit with standard macroscopic descriptions of dynamic effects from other systems but, rather, in the case of NdCo 2 , might be attributed to the involvement of a second zone centre order parameter related to a separate instability driven by cooperative Jahn-Teller distortions. In ErCo 2 , acoustic loss in the temperature interval above the transition point is discussed in terms of a possible tweed microstructure associated with strain coupling to local magnetic ordering. The overall multiferroic behaviour can be understood in terms of a single magnetic order parameter (irrep m + 4 of magnetic space group Fd3m1 ) which couples with a structural order parameter (irrep + 3 or + 5 ). The coupling is linear/quadratic which, in the case of two separate instabilities, causes them to combine in a single multiferroic phase transition.