Elastic properties and anisotropic pinning of the flux-line lattice in single-crystalline ${\mathrm{La}}_{1.85}$${\mathrm{Sr}}_{0.15}$${\mathrm{CuO}}_4$

The temperature dependence of the sound velocity and the sound-attenuation coefficient in single-crystalline ${\mathrm{La}}_{1.85}$ ${\mathrm{Sr}}_{0.15}$ ${\mathrm{CuO}}_4$ have been measured in the mixed state with an ultrasonic technique. An increase in the sound velocity and an attenuation peak, due to the elasticity of the flux-line lattice and the flux-pinning effect, are observed at a temperature lower than the superconducting transition temperature ${\mathit{T}}_{\mathit{c}}$. The compression and tilt moduli of the flux-line lattice are found to be softened in the case of H⊥c. The anisotropic activation energies that are necessary to depin the flux-line lattice are separately evaluated by measurements under various settings of the directions of the wave vector k, the polarization vector u, and the magnetic field H using an analysis based on the thermally assisted flux-flow model. The estimated activation energies are 1140 K (at 0 K, 6 T) for H⊥c, u∥c, 201 K (at 0 K, 14 T) for H⊥c, u∥(c×H), and 93 K (at 0 K, 6 T) for H∥c, u⊥c. These results are consistent with the intrinsic pinning mechanism. The activation energies determined by ultrasonic measurements are found to be smaller than those determined by resistivity measurements.