CoF2:a model system for magnetoelastic coupling and elastic softening mechanisms associated with paramagnetic ⇆ antiferromagnetic phase transitions

Resonant ultrasound spectroscopy has been used to monitor variations in the elastic and anelastic behaviour of polycrystalline CoF2 through the temperature interval 10-290 K and in the frequency range similar to 0.4-2 MHz. Marked softening, particularly of the shear modulus, and a peak in attenuation occur as the Neel point (TN = 39 K) is approached from both high and low temperatures. Although the effective thermodynamic behaviour can be represented semiquantitatively with a Bragg-Williams model for a system with spin 1 = 2, the magnetoelastic coupling follows a pattern which is closely analogous to that of a Landau tricritical transition which is co-elastic in character. Analysis of lattice parameter data from the literature confirms that linear spontaneous strains scale with the square of the magnetic order parameter and combine to give effective shear and volume strains on the order of 1 h. Softening of the shear modulus at T > T-N is attributed to coupling of acoustic modes with dynamical local ordering of spins and can be represented by a Vogel-Fulcher expression. At T < T-N the coupling of strains with the antiferromagnetic order parameter leads to softening of the shear modulus by up to similar to 2%, but this is accompanied by a small and frequency-dependent acoustic loss. The loss mechanism is attributed to spin-lattice relaxations under the influence of externally applied dynamic shear stress. CoF2 provides a reference or end-member behaviour against which the likely antiferromagnetic component of magnetoelastic behaviour in more complex multiferroic materials, with additional displacive instabilities, Jahn-Teller effects and ferroelastic microstructures, can be compared.