THEORY OF NUCLEAR-RELAXATION IN LA2CUO4

We calculate the nuclear spin-lattice relaxation rates (1/T1) in the quasi-two-dimensional antiferromagnet La2CuO4, both above and below the Neel temperature T(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 > T(N), and to leading order, (i) 1/T1Cu approximately (alpha-T/hc)3/2xi/alpha, where xi is the two-dimensional correlation length which diverges exponentially at low T, c is the T = O two-dimensional spin-wave velocity (proportional to J) and alpha is the lattice spacing; (ii) 1/T1O approximately (alpha-T/hc)3; and (iii) 1/T1La approximately A(alpha-T/hc)3 + B(alpha-T/hc)3/2 xi/alpha, 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 DELTA = 2 square-root-of JJ', which defines the crossover between two- and three-dimensional behavior; in La2CuO4, DELTA almost-equal-to 20 K. In the two-dimensional regime T(N) >> T >> DELTA, (i) 1/T1Cu approximately (alpha-T/hc)T/DELTA, (ii) 1/T1O approximately (alpha-T/hc)4ln(T/DELTA); and (iii) 1/T1La approximately A'(alpha-T/hc)4ln(T/DELTA) + B'(alpha-T/hc)2T/DELTA, with B'/A' approximately B/A. In the three-dimensional regime T < DELTA, one has (i) 1/T1Cu approximately (alpha-T/hc)(T/DELTA)2; (ii) 1/T1O approximately (alpha-T/hc)4(T/DELTA)3; and (iii) 1/T1La approximately A"(alpha-T/hc)4(T/DELTA)3 + B"(alpha-T/hc)2(T/DELTA)3, with B"/A" approximately B/A. These results for T < T(N) are sensitive to the hyperfine interactions assumed; we take the coupling to the Cu nuclei to be highly anisotropic and the couplings to La and O to be isotropic. However, gaps in the spin-wave spectrum, of, say, magnitude E, give rise to rates which vanish as e(-E/T) at temperatures T < E. In La2CuO4, Dzyaloshinskii-Moriya interaction gives rise to an E not too different from DELTA, and so a clean two- to three-dimensional crossover should not be present even though the quasi-two-dimensional behavior should hold over a wide range of temperature between T(N) and DELTA, and the relaxation rate for Cu in that temperature regime should be considerably larger than what one might expect based on the rates in cubic cuprate materials.