Sound-wave soft-mode interaction near displacive phase transitions: Spin reorientation in ErFeO3

We present experimental and theoretical results of the sound-wavespin-wave interaction in the spin reorientation region for the orthoferrite ErFeO3. Near the transition temperatures Tl=87°K and Tu=96. 6°K, a longitudinal sound wave propagating along the c axis exhibits a sound-waveorder-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 Tl and Tu is 0.8%. This gives a magnetoelastic coupling constant of |B33-B3118×106 erg/cm3. Attenuation peaks at Tl and Tu arise from the same resonant interaction. Shear waves, with polarization vector along the a axis, exhibit velocity dips at Tl and Tu indicating an interaction linear in the strain and the order parameter. A theoretical fit to the velocity curve yields the magnetoelastic coupling constant |B55|=2. 2×106 erg/cm3. Again, spin-wave damping leads to attenuation peaks at Tl and Tu. 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.