Antiferromagnets with random vacancies and substitutional spins on the triangular lattice

TL;DR

This paper provides a theoretical analysis of how random vacancies and substitutional spins affect the static and dynamic properties of antiferromagnets on a triangular lattice, revealing significant modifications to magnon spectra and magnetic order stability.

Contribution

It introduces an analytical description of defect-induced magnetic distortions and their impact on magnon spectra and long-range order in triangular lattice antiferromagnets.

Findings

Defects cause magnetic distortions described by electrostatic equations.

Magnon spectrum is weakly renormalized at high momenta but strongly at low momenta.

Long-wavelength magnons become overdamped and localized due to impurities.

Abstract

We discuss theoretically static and dynamical properties of $XY$ and Heisenberg antiferromagnets on triangular lattice with random vacancies and substitutional spins. It is shown that the distortion of $120^\circ$ magnetic order produced by a single defect is described by electrostatic equations for a field of an electrically neutral complex of six charges located around the impurity. The first finite term in the multipole expansion of this field is the octupole moment which decays as $1/r^3$ with the distance $r$. The linearity of equations allows to describe analytically the distortion of the long-range magnetic order at a small concentration $c$ of defects. We obtain analytically renormalization of the elastic neutron scattering cross section and the magnon spectrum $\epsilon_{\bf k}$ in the leading order in $c$. We find that the scattering on impurities renormalizes weakly the bare spectrum $\epsilon_{\bf k}\propto k$ at $k\gg\sqrt c$. However the renormalization is substantial of the long-wavelength magnon spectrum at $k\ll\sqrt c$: $\epsilon_{\bf k}\propto \sqrt{c /\ln(1/k)}$ at $k\to0$ and there is a parametrically large region in which magnons with not too small momenta are overdamped and localized. This strong modification of the long-wavelength spectrum leads to the stabilization of the slightly distorted magnetic long-range order at $T<T_N\sim S^2J/\ln(1/c)$ and to the considerable change in the density of states and in the specific heat. The overdamped modes arise also in quasi-2D spin systems on a stacked triangular lattice.