Quantum and thermal ionic motion, oxygen isotope effect, and superexchange distribution in La${}_2$CuO${}_4$

Abstract

We study the zero-point and thermal ionic motion in La${}_2$CuO${}_4$ by means of high-resolution neutron diffraction experiments. Our results demonstrate anisotropic motion of O and to a lesser extent of Cu ions, both consistent with the structure of coupled CuO${}_6$ octahedra, and quantify the relative effects of zero-point and thermal contributions to ionic motion. By substitution of ${}^{18}$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 $⟨J⟩$, 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.

13 pages, 9 figures