Neutron scattering, magnetometry, and quantum Monte Carlo study of the randomly diluted spin-1/2 square-lattice Heisenberg antiferromagnet

Abstract

We have successfully grown sizable single crystals of La 2Cu 1− z (Zn,Mg) z O 4 with up to nearly half of the magnetic Cu sites replaced by non-magnetic Zn and Mg. Neutron scattering, SQUID magnetometry, and complementary quantum Monte Carlo (QMC) simulations demonstrate that this material is an excellent model system for the study of site percolation of the square-lattice Heisenberg antiferromagnet (SLHAF) in the quantum-spin limit S=1/2. Carefully oxygen-reduced samples exhibit Néel order up to the percolation threshold for site dilution, z p≈40.7%. For z>10%, the material exhibits a low-temperature tetragonal (LTT) structural phase, with a transition temperature that increases linearly with doping. Above z≈25%, Néel order occurs in the LTT phase. Up to at least z=35%, the Néel temperature T N( z) of the experimental system corresponds to the temperature at which QMC indicates that the spin correlations for the nearest-neighbor S=1/2 SLHAF have grown to approximately 100 lattice constants. Neutron scattering measurements of the static structure factor in the paramagnetic regime allow the determination of the two-dimensional spin correlations, which are found to be in excellent quantitative agreement with QMC over a wide common temperature and doping range. Neutron scattering and QMC results for the temperature dependence of the static structure factor amplitude S(π,π) are in good agreement as well. As the concentration of non-magnetic sites is increased, the magnetic correlation length ξ( T, z) crosses over from an exponential dependence on ρ s/ T to power-law behavior in the temperature regime studied. Fits to a heuristic cross-over form for ξ( T, z) allow an estimate of the spin stiffness, ρ s= ρ s( z), which approaches zero at z= z p. The combined experimental and numerical data presented here provide valuable quantitative information for tests of theories of the randomly diluted S=1/2 SLHAF.