Magnetic scaling in cuprate superconductors

V. Barzykin; D. Pines

doi:10.1103/PhysRevB.52.13585

paper

Magnetic scaling in cuprate superconductors

arXiv:cond-mat/9505090 · doi:10.1103/PhysRevB.52.13585

Abstract

We determine the magnetic phase diagram for the YBa $_{2}$ Cu $_{3}$ O $_{6 + x}$ and La $_{2 - x}$ Sr $_{x}$ CuO $_{4}$ systems from various NMR experiments. We discuss the possible interpretation of NMR and neutron scattering experiments in these systems in terms of both the non-linear $σ$ -model of nearly localized spins and a nearly antiferromagnetic Fermi liquid description of magnetically coupled quasiparticles. We show for both the 2:1:4 and 1:2:3 systems that bulk properties, such as the spin susceptibiltiy, and probes at the antiferromagnetic wavevector $(π, π)$ , such as $^{63} T_{1}$ , the $^{63} C u$ spin relaxation time, both display a crossover at a temperature $T_{cr}$ , which increases linearly with decreasing hole concentration, from a non-universal regime to a $z = 1$ scaling regime characterized by spin pseudogap behavior. We pursue the consequences of the ansatz that $T_{cr}$ corresponds to a fixed value of the antiferromagnetic correlation length, $ξ$ , and show how this enables one to extract the magnitude and temperature dependence of $ξ$ from measurements of $T_{1}$ alone. We show that like $T_{cr}$ , the temperature $T_{*}$ which marks a crossover at low temperatures from the $z = 1$ scaling regime to a quantum disordered regime, exhibits the same dependence on doping for the 2:1:4 and 1:2:3 systems, and so arrive at a unified description of magnetic behavior in the cuprates, in which the determining factor is the planar hole concentration. We apply our quantitative results for YBa $_{2}$ Cu $_{3}$ O $_{7}$ to the recent neutron scattering experiments of Fong {\em et al}, and show that the spin excitation near $40 m e V$ measured by them corresponds to a spin gap excitation, which is overdamped in the normal state, but becomes visible in the superconducting state.

18 pages, RevTex, 18 figures are available upon request; submitted to Phys. Rev. B

Magnetic scaling in cuprate superconductors

Abstract

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