Spin-glass phase of cuprates

TL;DR

This paper models the spin glass phase of cuprates using a non-linear sigma model with disorder, predicting spiral spin correlations and identifying a critical disorder threshold relevant to experimental observations.

Contribution

It introduces a phenomenological model linking hole localization to spiral spin correlations and analyzes the stability of these states under disorder using renormalization group methods.

Findings

Disorder destroys the collinear fixed point of the model.

A critical disorder strength exists beyond which topological defects proliferate.

Experimental data suggest the disorder exceeds this critical threshold in the spin glass regime.

Abstract

We investigate a phenomenological model for the spin glass phase of La_{2-x}Sr_xCuO_4, in which it is assumed that holes doped into the CuO_2 planes localize near their Sr dopant, where they cause a dipolar frustration of the antiferromagnetic environment. In absence of long-range antiferromagnetic order, the spin system can reduce frustration, and also its free energy, by forming a state with an ordered orientation of the dipole moments, which leads to the appearance of spiral spin correlations. To investigate this model, a non-linear sigma model is used in which disorder is introduced via a randomly fluctuating gauge field. A renormalization group study shows that the collinear fixed point of the model is destroyed through the disorder and that the disorder coupling leads to an additive renormalization of the order parameter stiffness. Further, the stability of the spiral state against the formation of topological defects is investigated with the use of the replica trick. A critical disorder strength is found beyond which topological defects proliferate. Comparing our results with experimental data, it is found that for a hole density x > 0.02, i.e. in the entire spin glass regime, the disorder strength exceeds the critical threshold. In addition, some experiments are proposed in order to distinguish if the incommensurabilities observed in neutron scattering experiments correspond to a diagonal stripe or a spiral phase.