Theory of nuclear relaxation inLa2CuO4

Abstract

We calculate the nuclear spin-lattice relaxation rates (1/${\mathit{T}}_1$) in the quasi-two-dimensional antiferromagnet ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, both above and below the Néel temperature ${\mathit{T}}_{\mathit{N}}$, paying particular attention to the form factors associated with different nuclear sites. The smallness of the interplanar coupling J’ compared with the intraplanar coupling J and the absence of on-site Ising anisotropy result in some interesting behaviors of the relaxation rates. For J≫T>${\mathit{T}}_{\mathit{N}}$, and to leading order, (i) 1/${\mathit{T}}_1^{\mathrm{Cu}}$∼(aT/ħc${)}^{3/2}$ξ/a, where ξ is the two-dimensional correlation length which diverges exponentially at low T, c is the T=0 two-dimensional spin-wave velocity (proportional to J) and a is the lattice spacing; (ii) 1/${\mathit{T}}_1^{\mathrm{O}}$∼(aT/ħc${)}^3$; and (iii) 1/${\mathit{T}}_1^{\mathrm{La}}$∼A(aT/ħc${)}^3$+B(aT/ħc${)}^{3/2}$ξ/a, where we expect B≪A although a precise estimate is unavailable. If anisotropies of the couplings (in spin space) are neglected, the only other relevant temperature scale is set by Δ=2 √JJ’ , which defines the crossover between two- and three-dimensional behavior; in ${\mathrm{La}}_2$ ${\mathrm{CuO}}_4$, Δ≊20 K.