Sound-Wave—Soft-Mode Interaction near Displacive Phase Transitions: Spin Reorientation in ErFeO3

We present experimental and theoretical results of the sound-wave—spin-wave interaction in the spin reorientation region for the orthoferrite ErFe${\mathrm{O}}_3$. Near the transition temperatures $T_l=87\mathrm{}$ °K and $T_u=96.\mathrm{}6$ °K, a longitudinal sound wave propagating along the c axis exhibits a sound-wave—order-parameter interaction which is linear in the strain and quadratic in the order parameter. This leads to steplike discontinuities in the sound velocity. The experimentally observed velocity change at $T_l$ and $T_u$ is 0.8%. This gives a magnetoelastic coupling constant of $|B_{33}-B_{31}|\sim 18\times {10}^6$ erg/${\mathrm{cm}}^3$. Attenuation peaks at $T_l$ and $T_u$ arise from the same resonant interaction. Shear waves, with polarization vector along the $a$ axis, exhibit velocity dips at $T_l$ and $T_u$ indicating an interaction linear in the strain and the order parameter. A theoretical fit to the velocity curve yields the magnetoelastic coupling constant $\left|B_{55}\right|=2.\mathrm{}2\times {10}^6$ erg/${\mathrm{cm}}^3$. Again, spin-wave damping leads to attenuation peaks at $T_l$ and $T_u$. Finally, shear waves, with polarization vector along the $b$ axis, do not give any coupling to the order parameter, but only a coupling to the optical branch of the spin-wave spectrum. This leads to a small noticeable sound-wave velocity change in the spin reorientation region. All these effects can be quantitatively described by a linearized set of coupled spin-wave and sound-wave equations of motion.