Spin fluctuations in quantum dots

TL;DR

This paper investigates spin susceptibilities in quantum dots with anisotropic exchange, revealing that fluctuations do not prevent the divergence of susceptibility at the Stoner instability point.

Contribution

It extends the universal Hamiltonian to include uniaxial anisotropic exchange and analyzes how level fluctuations influence the Stoner instability in quantum dots.

Findings

Spin susceptibility diverges at the Stoner point regardless of level randomness.

Fluctuations of single-particle levels do not alter the critical point for instability.

The problem reduces to the statistics of extrema of a Gaussian process.

Abstract

We explore the static longitudinal and dynamic transverse spin susceptibilities in quantum dots and nanoparticles within the framework of the Hamiltonian that extends the universal Hamiltonian to the case of uniaxial anisotropic exchange. For the limiting cases of Ising and Heisenberg exchange interactions we ascertain how fluctuations of single-particle levels affect the Stoner instability in quantum dots. We reduce the problem to the statistics of extrema of a certain Gaussian process. We prove that, in spite possible strong randomness of the single-particle levels, the spin susceptibility and all its moments diverge simultaneously at the point which is determined by the standard criterion of the Stoner instability involving the mean level spacing only.