Muon spin relaxation studies of incommensurate magnetism and superconductivity in stage-4 La₂CuO_4.11 and La_1.88Sr_0.12CuO₄

We report muon spin relaxation (μSR) measurements using single crystals of oxygen-intercalated stage-4 La₂CuO_4.11 (LCO:4.11) and La_1.88Sr_0.12CuO₄ (LSCO:0.12), in which neutron scattering studies have found incommensurate magnetic Bragg reflections. In both systems, zero-field μSR measurements show muon spin precession below the Néel temperature T_N with frequency 3.6 MHz at T→0, having a Bessel function line shape, characteristic of spin-density-wave systems. The amplitude of the oscillating and relaxing signals of these systems is less than half the value expected for systems with static magnetic order in 100% of the volume. Our results are consistent with a simulation of local fields for a heuristic model with (a) incommensurate spin amplitude modulation with the maximum ordered Cu moment size of ∼0.36μ_B, (b) static Cu moments on the CuO₂ planes forming "islands" having typical radius 15-30 Å, comparable to the in-plane superconducting coherence length, and (c) the measured volume fraction of magnetic muon sites V_μ increasing progressively with decreasing temperature below T_N towards V_μ ∼40% for LCO:4.11 and 18% for LSCO:0.12 at T→0. These results may be compared with correlation lengths in excess of 600 Å and along range ordered moment of 0.15±0.05μB measured with neutron scattering techniques, In this paper we discuss a model that reconciles these apparently contradictory results. In transverse magnetic field μSR measurements, sensitive to the in-plane magnetic field penetration depth λ_ab, the results for LCO:4.11 and LSCO:0.12 follow correlations found for underdoped, overdoped and Zn-doped high-T_c cuprate systems in a plot of T_c versus the superconducting relaxation rate σ(T→O). This indicates that the volume-integrated value of n_s/m* (superconducting carrier density/effective mass) is a determining factor for T_c, not only in high-T_c cuprate systems without static magnetism, but also in the present systems where superconductivity coexists with static spin-density-wave spin order.