Dynamics of thes=12linear Heisenberg antiferromagnet in a magnetic field: Experiment and theory

Proton spin-lattice relaxation times have been measured in the quasi-one-dimensional $s=\frac{1}{2}$ Heisenberg antiferromagnetic compounds CuSe${\mathrm{O}}_4$·5${\mathrm{H}}_2$O and CuS${\mathrm{O}}_4$·5${\mathrm{H}}_2$O, in order to study the magnetic field dependence of the 1D quantum spin dynamics at various temperatures. Information is obtained on the low-frequency behavior of the spin autocorrelation functions for the linear chains. The transverse component shows at high $T$ a marked decrease with magnetic field above the saturation field $B_c$. Towards lower temperatures a pronounced maximum just below $B_c$ develops and the decrease above $B_c$ becomes more abrupt. The longitudinal component behaves more smoothly near and above $B_c$. The field dependence of the relaxation rates is well explained at all nonzero temperatures by finite-chain calculations. For $T=0\mathrm{}$ we present analytical calculations of autocorrelation functions based on the predominance of a two-parameter spin-wave continuum for the quantum spin dynamics yielding a nondivergent behavior at $\omega =0\mathrm{}$ and $B=0\mathrm{}$. Exact results are obtained for fields above $B_c$. Further, an effective $\mathrm{XY}$ approach is used for low but finite $T$. Here, good agreement is found with the proton relaxation data for very low temperatures.