Magneto-Elastic Coupling in the Layered Manganite La$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$

We have studied the magneto-elastic coupling in the double layered Mn perovskite La$_{1.2}$Sr$_{1.8}$Mn$_2$O$_7$ with an ultrasonic velocity technique. The temperature profile of both the in-plane and out-of-plane longitudinal velocities showed a large stiffening anomaly below the insulating paramagnetic to metallic ferromagnetic transition. Magnetic fluctuations effects consistent with the layered structure are evidenced as a frequency dependent velocity softening above the transition. The magneto-elastic coupling has been studied in magnetic field values up to 8 Tesla: the observations are consistent with a substantial magnetic anisotropy and a ferromagnetic order parameter with moments lying in the layers.