Spin dynamics of a truncatedXYchain: Magnetic resonance of Sm impurities in PrEtSO4

The magnetic relaxation of dilute Sm spins substituting for Pr spins in PrEtS${\mathrm{O}}_4$ has been measured by electron-spin echoes. The Pr spins form linear chains and are coupled by a nearest-neighbor $\mathrm{XY}$ interaction. Their spin dynamics therefore differs markedly from that of previously studied Heisenberg systems. Since the Sm-Pr interaction is small relative to the Pr-Pr coupling, the Sm spins effectively terminate the $\mathrm{XY}$ chains and act as magnetic probes of the dynamics of Pr spins near the ends of the chains. For comparison with experiment the longitudinal spin-correlation functions for a truncated $\mathrm{XY}$ chain have been calculated exactly. The boundary is found to have important physical consequences, particularly with regard to the asymptotic time dependence of the correlation functions. Use of these functions in the analysis of the experiment leads to satisfactory agreement for the magnitude, but not for the angular dependence, of the Sm spin-relaxation rates. It is inferred that an additional contribution to the relaxation is present.