Altermagnetic Instabilities from Quantum Geometry

TL;DR

This paper explores the role of quantum geometry in altermagnetic instabilities, establishing a theoretical link and providing an example with MnTe to understand how quantum metrics influence magnetic fluctuations.

Contribution

It introduces a theoretical framework connecting quantum metric to altermagnetic instabilities and demonstrates this with an effective MnTe model.

Findings

Quantum metric favors altermagnetism.

Derived a criterion for altermagnetic instabilities.

Explicitly computed quantum metric and susceptibility for MnTe.

Abstract

Altermagnets are a newly identified type of collinear anti-ferromagnetism with vanishing net magnetic moment, characterized by lifted Kramers' degeneracy in parts of the Brillouin zone. Their time-reversal symmetry broken band structure has been observed experimentally and is theoretically well-understood. On the contrary, altermagnetic fluctuations and the formation of the corresponding instabilities remains largely unexplored. We establish a correspondence between the quantum metric of normal and the altermagnetic spin-splitting of ordered phases. We analytically derive a criterion for the formation of instabilities and show that the quantum metric favors altermagnetism. We recover the expression for conventional q=0 instabilities where the spin-splitting terms of the normal state model are locally absent. As an example, we construct an effective model of MnTe and illustrate the relationship between quantum geometry and altermagnetic fluctuations by explicitly computing the quantum metric and the generalized magnetic susceptibility.