Non-relativistic ferromagnetotriakontadipolar order and spin splitting in hematite

We show that hematite, 𝛼-Fe₂O₃, 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.

本研究揭示了赤铁矿（𝛼-Fe₂O₃）在其莫林相变以下，具有铁磁性序，即在铁离子上排列着五阶磁三角多极子。在不存在自旋-轨道耦合的情况下，这些是最低阶的铁磁性对齐磁多极子，并导致赤铁矿中的g波非相对论性自旋分裂。研究发现，铁磁性序的磁三角多极子源于电荷十六极子和磁偶极子的同时反铁磁性序，从而为操控磁三角多极子的幅度和符号以及自旋分裂提供了一个途径。此外，我们发现在莫林相变温度以上的弱铁磁性相中，磁三角多极子的铁磁性序以及许多自旋分裂特征得以持续存在。