Orbital Magnetic Moment of Magnons

In experiments and applications usually the spin magnetic moment of magnons is considered. In this Paper we identify an additional degree of freedom of magnons: an \emph{orbital} magnetic moment brought about by spin-orbit coupling.Our microscopic theory uncovers that spin magnetization $\vec{M}^\mathrm{S}$ and orbital magnetization $\vec{M}^\mathrm{O}$ are independent quantities. They are not necessarily collinear; thus, even when the total spin moment is compensated due to antiferromagnetism ($\vec{M}^\mathrm{S} = \vec{0}$), $\vec{M}^\mathrm{O}$ may be nonzero. This scenario of orbital weak ferromagnetism is realized in paradigmatic kagome antiferromagnets with Dzyaloshinskii-Moriya interaction. We demonstrate that magnets exhibiting a magnonic orbital moment are omnipresent and propose transport experiments for probing it.