We have measured the magnon Raman cross-sections for bismuth ferrite as a function of temperature near the newly discovered magnetic phase transitions near T₂ = 140.3 ± 0.2 K and T₁ = 201.0 ± 0.8 K (Singh et al 2008 J. Phys.: Condens. Matter 20 252203) and evaluate the critical exponents (α = 0.05 and α′ = 0.09) characterizing that at 140.3 K and (α = 0.06 and α′ = 0.13) that at 201.0 K. These are , and hence the data fit a logarithmic divergence about as well. The occurrence of divergences in the electric susceptibility proportional to the specific heat anomaly in non-ferroelectric transitions due to piezoelectric coupling was first reported by Kizhaev et al (1986 JETP Lett. 43 445); in the present paper we apply an analogous theory to magnetoelastic coupling at magnetic transitions. This is an application of the basic Pippard relationship between susceptibilities and specific heat (Pippard 1956 Phil. Mag. 1 473) to a magnetoelastic system. The observations are related to the mechanical loss anomalies observed at the same temperatures (Redfern et al 2008 Preprint cond-mat). Our results support the distorted spin cycloid model of Zalesskii et al (2003 Phys. Solid State 45 141) and not the earlier model of Sosnowska et al (1982 J. Phys. C: Solid State Phys. 15 4835).