Model of nuclear relaxation inYBa2Cu3O7−δ

Abstract

We examine nuclear spin-lattice relaxation rates (1/${\mathit{T}}_1$) at copper (Cu), oxygen (O), and yttrium (Y) sites in ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_{7\mathrm{-}\mathrm{\delta }}$. We use a two-hole band model consisting of strongly Heisenberg superexchange coupled spins (S=1/2) on Cu sites that are exchange coupled with strength ${\mathit{J}}_{\mathit{p}\mathit{d}}$ to itinerant oxygen holes introduced by doping. The Cu(1) (chain) spins are modeled by one-dimensional Heisenberg chains; the Cu(2) (planar) spins are modeled by two-dimensional Schwinger boson mean-field theory. We first consider the limit of ${\mathit{J}}_{\mathit{p}\mathit{d}}$=0 to explain the following: (i) qualitatively the superlinear behavior of 1/${\mathit{T}}_1$ versus temperature T on Cu(1) (chain sites) in terms of their quasi-one-dimensional character, (ii) the insufficiency of arguments producing a ${\mathit{T}}^{1/2}$ temperature dependence on Cu(2) (planar) sites due to the vastly stronger temperature dependence of the antiferromagnetic fluctuations, (iii) the development of an anomaly in 1/${\mathit{T}}_1$T similar to experimental data due to anisotropy and/or quantum disorder induced ‘‘spin gaps,’’ (iv) the need to produce some recalibration of estimates of transferred Cu(2) to Cu nuclear coupling with proper account of intersite fluctuations, and (v) the dramatic reduction of the transferred Cu spin fluctuation contribution to 1/${\mathit{T}}_1$ on Y and O(2,3) (planar) sites arising from form-factor effects (and hence the observation of metallic Korringa behavior at these nuclei). Next, we demonstrate formally that for finite values of ${\mathit{J}}_{\mathit{p}\mathit{d}}$ the low-temperature proportionality of O(2,3) and Cu(2) rates may be understood as arising from coupling of Cu- and O-hole spin susceptibilities in the presence of a Cu(2) anisotropy or spin gap.