Although charge density wave (CDW) correlations exist in several families of cuprate superconductors, they exhibit substantial variation in CDW wave vector and correlation length, indicating a key role for CDW-lattice interactions. We investigated this interaction in ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$ using single-crystal x-ray diffraction to collect a large number of CDW peak intensities and determined the Cu and La/Ba atomic distortions induced by the formation of CDW order. Within the ${\mathrm{CuO}}_2$ planes, the distortions involve a periodic modulation of the Cu-Cu spacing along the direction of the ordering wave vector. The charge ordering within the copper-oxygen layer induces an out-of-plane breathing modulation of the surrounding lanthanum layers, which leads to a related distortion on the adjacent copper-oxygen layer. Our result implies that the CDW-related structural distortions do not remain confined to a single layer but rather propagate an appreciable distance through the crystal. This leads to overlapping structural modulations, in which ${\mathrm{CuO}}_2$ planes exhibit distortions arising from the orthogonal CDWs in adjacent layers as well as distortions from the CDW within the layer itself. We attribute this striking effect to the weak $c$-axis charge screening in cuprates and suggest this effect could help couple the CDWs between adjacent planes in the crystal.

• Received 20 December 2022
• Accepted 15 February 2023

DOI:https://doi.org/10.1103/PhysRevB.107.115125