Spin-Lattice Relaxation by Quasi-Spin-Waves in Order-Disorder-Type Ferroelectrics: Polarization Fluctuations in ${\mathrm{Ca}}_2$Sr${\left({\mathrm{C}}_2{\mathrm{H}}_5\mathrm{C}{\mathrm{O}}_2\right)}_6$

A theory of nuclear spin-lattice relaxation by unstable, overdamped quasi-spin-waves-or critical polarization fluctuations - in order-disorder ferroelectrics is developed. If relaxation due to competing processes is not too fast, such an unstable mode will dominate the magnetic dipolar or electric quadrupolar relaxation rate not only right at the Curie point, but also in its neighborhood. In such a case, the temperature dependence of $T_1$ is given by $T_1\propto {|T-T_C|}^n$, where $0.5\le n\le 2$, depending on the details of the interaction between the ferroelectric dipoles and the Brillouin-zone size. The theory is applied to the case of ferroelectric dicalcium strontium propionate. This crystal exhibits an anomalous dip in $T_1$ on approaching $T_C$ which we believe is due to magnetic dipolar coupling to an overdamped, unstable quasi-spin-wave mode.