Non-relativistic ferromagnetotriakontadipolar order and spin splitting in hematite

TL;DR

This paper reveals that hematite exhibits a ferroic ordering of rank-5 magnetic triakontadipoles below the Morin transition, leading to non-relativistic spin splitting, with implications for manipulating magnetic properties.

Contribution

It demonstrates the presence of magnetic triakontadipoles in hematite and explains their role in spin splitting, offering new insights into magnetic multipole orderings.

Findings

Magnetic triakontadipoles are ordered below the Morin transition.

Spin splitting arises from non-relativistic magnetic multipoles.

Order persists above the Morin transition in the weak ferromagnetic phase.

Abstract

We show that hematite, $\alpha$-Fe$_2$O$_3$, below its Morin transition, has a ferroic ordering of rank-5 magnetic triakontadipoles on the Fe ions. In the absence of spin-orbit coupling, these are the lowest-order ferroically aligned magnetic multipoles, and they give rise to the $g$-wave non-relativistic spin splitting in hematite. We find that the ferroically ordered magnetic triakontadipoles result from the simultaneous antiferroic ordering of the charge hexadecapoles and the magnetic dipoles, providing a route to manipulating the magnitude and the sign of the magnetic triakontadipoles as well as the spin splitting. Furthermore, we find that both the ferroic ordering of the magnetic triakontadipoles and many of the spin-split features persist in the weak ferromagnetic phase above the Morin transition temperature.