Effective interaction in a non-Fermi liquid conductor and spin correlations in under-doped cuprates

TL;DR

This paper investigates the effective spin interactions in a 1D t-J model for under-doped cuprates, revealing a doping-dependent spin stiffness that suggests reentrant spin coupling and potential experimental tests.

Contribution

It introduces a novel analysis of the generalized spin stiffness in the t-J model, showing a maximum at finite doping indicating reentrant spin correlations in under-doped cuprates.

Findings

High spin stiffness near zero doping

Sharp decrease of stiffness with doping

Maximum at finite doping indicating reentrant coupling

Abstract

The effective interaction between the itinerant spin degrees of freedom in the paramagnetic phases of hole doped quantum Heisenberg antiferromagnets is investigated theoretically, based on the single-band t-J model on 1D lattice, at zero temperature. The effective spin-spin interaction for this model in the strong correlation limit, is studied in terms of the generalized spin stiffness constant as a function of doping concentration. The plot of this generalized spin stiffness constant against doping shows a very high value of stiffness in the vicinity of zero doping and a very sharp fall with increase in doping concentration, signifying the rapid decay of original coupling of semi-localized spins in the system. Quite interestingly, this plot also shows a maximum occurring at a finite value of doping, which strongly suggests the tendency of the itinerant spins to couple again in the unconventional paramagnetic phase. As the doping is further increased, this new coupling is also suppressed and the spin response becomes analogous to almost Pauli-like. The last two predictions of ours are quite novel and may be directly tested by independent experiments and computational techniques in future. Our results in general receive good support from other theoretical works and experimental results extracted from the chains of YBa$_2$Cu$_3$O$_{6+x}$.

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