Quantum critical response function in quasi-two dimensional itinerant antiferromagnets

TL;DR

This paper re-examines neutron scattering data on quantum-critical magnetic fluctuations in itinerant antiferromagnets, comparing experimental results with a theory predicting unique separable response functions and infinite dynamical critical exponent.

Contribution

It provides a detailed comparison of experimental neutron scattering results with a novel quantum-critical theory involving topological defect correlations and predicts specific unusual behaviors.

Findings

Experimental results are consistent with the theory's predictions of separable response functions.

The energy dependence follows a hyperbolic tangent form below a cutoff energy.

The theory implies an infinite dynamical critical exponent, z.

Abstract

We re-examine the experimental results for the magnetic response function $\chi''({\bf q}, E, T)$, for ${\bf q}$ around the anti-ferromagnetic vectors ${\bf Q}$, in the quantum-critical region, obtained by inelastic neutron scattering, on an Fe-based superconductor, and on a heavy Fermion compound. The motivation is to compare the results with a recent theory, which shows that the fluctuations in a generic anti-ferromagnetic model for itinerant fermions map to those in the universality class of the dissipative quantum-XY model. The quantum-critical fluctuations in this model, in a range of parameters, are given by the correlations of spatial and of temporal topological defects. The theory predicts a $\chi''({\bf q}, E, T)$ (i) which is a separable function of $({\bf q -Q})$ and of ($E$,$T$), (ii) at crticality, the energy dependent part is $\propto \tanh (E/2T)$ below a cut-off energy, (iii) the correlation time departs from its infinite value at criticality on the disordered side by an essential singularity, and (iv) the correlation length depends logarithmically on the correlation time, so that the dynamical critical exponent $z$ is $\infty$ . The limited existing experimental results are found to be consistent with the first two unusual predictions from which the linear dependence of the resistivity on T and the $T \ln T$ dependence of the entropy also follow. More experiments are suggested, especially to test the theory of variations on the correlation time and length on the departure from criticality.