Role of Orbital Polarization in Weak Ferromagnetism

A density functional theory to deal in a first-principles manner with the phenomenon of weak ferromagnetism (WF) is applied to the triangular antiferromagnet M${\mathrm{n}}_3$Sn. It explains successfully the two different types of WF due, respectively, to magnetic anisotropy and antisymmetric exchange. We take into account, for the first time, the orbital moment contribution to WF and show that, due to the noncollinearity of the spin and orbital moments of the Mn atoms, both spin and orbital moments give a comparable contribution to the ferromagnetic component. Our results are in good agreement with experimental data.