Influence of incommensurate structure on the elastic constants of crystalline Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ by Brillouin light scattering spectroscopy

TL;DR

This study uses Brillouin light scattering spectroscopy to determine the elastic constants of the high-temperature superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+eta}$, revealing a new relationship for incommensurate systems.

Contribution

The paper derives and validates a new expression relating elastic constants of incommensurate sublattices, applicable to any composite incommensurate crystal.

Findings

Elastic constants of Bi$_2$Sr$_2$CaCu$_2$O$_{8+eta}$ were determined.

A new relationship for elastic constants in incommensurate systems was validated.

Results support previous sublattice assignments in the material.

Abstract

Brillouin light scattering spectroscopy was used to probe the room-temperature elasticity of crystalline high-$T_c$ superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. A complete set of best-estimate elastic constants was obtained using established relationships between acoustic phonon velocities and elastic constants along with a simple expression relating crystal elastic constant $C_{22}$ to the corresponding constants of the constituent incommensurate sublattices. This latter relationship, which was derived and validated in the present work, has important implications for those studying incommensurate systems as it appears that it may be applied in its general form to any composite incommensurate crystal. The results obtained in this work are also consistent with sublattice assignments of Bi$_2$Sr$_2$O$_4$ and CaCu$_2$O$_4$ reported in a previous Brillouin scattering study.