Ca-doping of BiFeO₃: The role of strain in determining coupling between ferroelectric displacements, magnetic moments, octahedral tilting, and oxygen-vacancy ordering

Elastic and anelastic properties of a member of the BiFeO ₃-CaFeO_2.5 perovskite solid solution (BCFO), which is known to have multiple instabilities, have been investigated by resonant ultrasound spectroscopy. This phase, with 64% Bi and 36% Ca on the A site, is antiferromagnetic (T_N ∼650 K) and has an ordered arrangement of oxygen vacancies with tetragonal lattice geometry. The inverse mechanical quality factor, Q^-1, has a maximum near 100 K, correlating closely with a peak in dielectric loss, reported previously, consistent with a loss mechanism that involves the movement of oxygen vacancies accompanied by local lattice distortion. At higher temperature, there is a further acoustic loss peak that is correlated with complex impedance anomalies. There is no clear relationship to the magnetic transition, and the observations are interpreted as relating to ionic conductivity. A small stiffening, scaling with the square of the magnetic order parameter below T_N, indicates that the main coupling with strain is biquadratic, confirming that conventional coupling of magnetic order with symmetry-breaking shear strains is weak in BCFO. Data from the literature for BCFO indicates that local strain fields are likely to be responsible for suppressing the spin cycloid present in BiFeO₃.