Quantum geometric ferromagnetism by singular saddle point

TL;DR

This paper introduces a novel mechanism for ferromagnetism driven by quantum geometry at singular saddle points with band touching, supported by a specific orbital model.

Contribution

It demonstrates quantum geometric ferromagnetism arising from divergent quantum metric and density of states at saddle points, linking to flat-band ferromagnetism.

Findings

Quantum metric divergence induces ferromagnetic correlations.

Logarithmic density of states divergence supports ferromagnetism.

The mechanism is exemplified in a two-dimensional orbital model.

Abstract

We propose ferromagnetism that occurs in electrons at a saddle point with band touching, which we call the singular saddle point. At the singular saddle point, the divergent quantum metric induces ferromagnetic correlation, and the logarithmic divergence of the density of states ensures ferromagnetism within Stoner theory. This is a prototypical example of quantum geometric ferromagnetism. The two-dimensional $t_{2g}$-orbital model accommodates the ferromagnetism by this mechanism, which is continuously connected to the exactly proven flat-band ferromagnetism.