The coexistence of superconductivity and ferromagnetism in nano-scale metallic grains

TL;DR

This paper investigates the coexistence of superconductivity and ferromagnetism in nano-scale metallic grains described by the universal Hamiltonian, especially in regimes where traditional BCS theory fails due to strong fluctuations.

Contribution

It demonstrates that superconductivity and ferromagnetism can coexist in small grains and identifies experimental signatures of their competition in various physical properties.

Findings

Superconductivity and ferromagnetism coexist in fluctuation-dominated regimes.

Ground-state spin and conductance fluctuations reveal competition effects.

Thermodynamic properties like heat capacity and spin susceptibility show signatures of coexistence.

Abstract

A nano-scale metallic grain in which the single-particle dynamics are chaotic is described by the so-called universal Hamiltonian. This Hamiltonian includes a superconducting pairing term and a ferromagnetic exchange term that compete with each other: pairing correlations favor minimal ground-state spin, while the exchange interaction favors maximal spin polarization. Of particular interest is the fluctuation-dominated regime where the bulk pairing gap is comparable to or smaller than the single-particle mean level spacing and the Bardeen-Cooper-Schrieffer theory of superconductivity breaks down. Superconductivity and ferromagnetism can coexist in this regime. We identify signatures of the competition between superconductivity and ferromagnetism in a number of quantities: ground-state spin, conductance fluctuations when the grain is weakly coupled to external leads and the thermodynamic properties of the grain, such as heat capacity and spin susceptibility.