Spin dynamics inLa2−xSrxCuO4(0.02≤x≤0.08) fromLa139NQR relaxation: Fluctuations in a finite-length-scale system

${}_{}{}^{139}{}_{}{}^{}\mathrm{La}$ NQR spin-lattice relaxation rates (NSLR) versus temperature are presented for ${\mathrm{La}}_{2\mathrm{-}\mathit{x}}$ ${\mathrm{Sr}}_{\mathit{x}}$ ${\mathrm{CuO}}_4$ with x=0.02–0.08. The NSLR below ∼2${\mathit{T}}_{\mathit{N}}$(x) shows a power-law critical behavior while above ∼2${\mathit{T}}_{\mathit{N}}$(x) it follows an exponential law with a small x-dependent spin-stiffness constant, where ${\mathit{T}}_{\mathit{N}}$(x) is the magnetic ordering temperature. It is argued that the NSLR arises from fluctuations of the staggered magnetization in locally ordered mesoscopic domains. We infer that the magnetically ordered state is not a conventional spin glass, as is often assumed.