Magnetic droplets in a metal close to a ferromagnetic quantum critical point

TL;DR

This paper investigates how a magnetic impurity near a ferromagnetic quantum critical point forms a large magnetic droplet, affecting susceptibility behavior at various temperatures, with implications for quantum criticality and Kondo physics.

Contribution

It provides a detailed analysis of impurity susceptibility near a ferromagnetic quantum critical point using analytical and Monte Carlo methods, revealing new temperature-dependent behaviors.

Findings

Susceptibility follows a logarithmic law at intermediate temperatures.

At very low temperatures, susceptibility saturates to a finite value.

Strong damping by conduction electrons suppresses quantum fluctuations.

Abstract

Using analytical and path integral Monte Carlo methods, we study the susceptibility $\chi_{dc}(T)$ of a spin-S impurity with XY rotational symmetry embedded in a metal. Close to a ferromagnetic quantum critical point, the impurity polarizes conduction electrons in its vicinity and forms a large magnetic droplet with moment M>>S. At not too low temperatures, the strongly damping paramagnon modes of the conduction electrons suppress large quantum fluctuations (or spin flips) of this droplet. We show that the susceptibility follows the law $\chi_{dc}(T)=(M^{2}/T)[1-(\pi g)^{-1}\ln(gE_{0}/T)]$, where the parameter g>>1 describes the strong damping by conduction electrons, and E_0 is the bandwidth of paramagnon modes. At exponentially low temperatures T << T_{*} ~ E_{0}\exp(-\pi g/2) we show that spin flips cannot be ignored. In this regime we find that $\chi_{dc}(T) \approx \chi_{dc}(0) [1-(2/3)(T/T_{*})^2]$, where $\chi_{dc}(0)\sim M^{2}/T_{*}$ is finite and exponentially large in g. We also discuss these effects in the context of the multi-channel Kondo impurity model.