Origin of the gossamer ferromagnetism in MnTe

Absence of net magnetization in altermagnets is both a blessing (no stray fields) and a curse (no obvious way to manipulate altermagnetic domains by external fields). Yet, MnTe was demonstrated experimentally to have no measurable stray fields and yet controllable by external magnetic field---a win-win situation. In this paper, we discuss possible mechanisms driving this ultrasmall canting of Mn moments and, most importantly, the microscopic mechanism of coupling the canting with the altermagnetic order. It appears to be a higher (third) order effect in (already small) spin-orbit coupling, which explains the unusually weak, barely measurable ferromagnetism in MnTe. Microscopic understanding of the beneficial properties of MnTe opens a road to controllable design of similar altermagnets for spintronics applications.