Magnon-induced long-range correlations and their neutron-scattering signature in quantum magnets

TL;DR

This paper investigates how magnons influence long-range correlations and their signatures in neutron scattering in quantum magnets, revealing differences between ferromagnets and antiferromagnets at zero temperature.

Contribution

It provides a detailed analysis of the nonanalytic behavior of longitudinal susceptibility in quantum ferromagnets and antiferromagnets, highlighting the absence of certain singularities in ferromagnets due to ground state properties.

Findings

Long-range correlations induce singular wave-number dependence in classical magnets.

Quantum antiferromagnets show a $k^{d-3}$ scaling of susceptibility for 1<d<3.

Quantum ferromagnets lack this nonanalyticity due to zero magnon number fluctuations.

Abstract

We consider the coupling of the magnons in both quantum ferromagnets and antiferromagnets to the longitudinal order-parameter fluctuations, and the resulting nonanalytic behavior of the longitudinal susceptibility. In classical magnets it is well known that long-range correlations induced by the magnons lead to a singular wave-number dependence of the form $1/k^{4-d}$ in all dimensions 2<d<4, for both ferromagnets and antiferromagnets. At zero temperature we find a profound difference between the two cases. Consistent with naive power counting, the longitudinal susceptibility in a quantum antiferromagnet scales as $k^{d-3}$ for 1<d<3, whereas in a quantum ferromagnet the analogous result, $k^{d-2}$, is absent due to a zero scaling function. This absence of a nonanalyticity in the longitudinal susceptibility is due to the lack of magnon number fluctuations in the ground state of a quantum ferromagnet; correlation functions that are sensitive to other fluctuations do exhibit the behavior predicted by simple power counting. Also of interest is the dynamical behavior as expressed in the longitudinal part of the dynamical structure factor, which is directly measurable via neutron scattering. For both ferromagnets and antiferromagnets there is a logarithmic singularity at the magnon frequency with a prefactor that vanishes as $T\to 0$. In the antiferromagnetic case there also is a nonzero contribution at T=0 that is missing for ferromagnets. Magnon damping due to quenched disorder restores the expected scaling behavior of the longitudinal susceptibility in the ferromagnetic case; it scales as $k^{d-2}$ if the order parameter is not conserved, or as $k^d$ if it is. Detailed predictions are made for both two- and three-dimensional systems at both T=0 and in the limit of low temperatures, and the physics behind the various nonanalytic behaviors is discussed.