We study the zero-point and thermal ionic motion in ${\text{La}}_2$${\text{CuO}}_4$ by means of high-resolution neutron-diffraction experiments. Our results demonstrate anisotropic motion of O and, to a lesser extent, Cu ions, both consistent with the structure of coupled ${\text{CuO}}_6$ octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of ${}^{18}\mathrm{O}$, we find that the oxygen isotope effect on the lattice dimensions is small and negative ($-0.01\%$), while the isotope effect on the ionic displacement parameters is significant ($-6$ to 50%). We use our results as input for theoretical estimates of the distribution of magnetic interaction parameters, $J$, in an effective one-band model for the cuprate plane. We find that ionic motion causes only small ($1\%$) effects on the average value $\langle J\rangle$, which vary with temperature and O isotope, but results in dramatic (10–20$\%$) fluctuations in $J$ values that are subject to significant (8–12%) isotope effects. We demonstrate that this motional broadening of $J$ can have substantial effects on certain electronic and magnetic properties in cuprates.

• Received 2 December 2013
• Revised 22 January 2014

DOI:https://doi.org/10.1103/PhysRevB.89.085113