Fig. 3: Atomic structure, spin texture and effective spin polarization at the Fermi surface of Mn₃GaN.

Atomic and magnetic structure of antiperovskite Mn₃GaN in the noncollinear \({\Gamma }_{5g}\) AFM configuration in 3D view (a) and projected to the (111) plane with \({\hat{{\rm{M}}}}_{\bar{1}10}\) and \({\hat{C}}_{\bar{1}10}\) symmetries indicated (b). Components of spin \({{\boldsymbol{s}}}_{{n{\boldsymbol{k}}}_{{\|}}}=({s}_{{n{\boldsymbol{k}}}_{{\|}}}^{x},{s}_{n{{\boldsymbol{k}}}_{{\|}}}^{y},{s}_{n{{\boldsymbol{k}}}_{{\|}}}^{z})\) (c) and spin magnitudes \({s}_{{n{\boldsymbol{k}}}_{{\|}}}\equiv {{{|}}{\boldsymbol{s}}}_{n{{\boldsymbol{k}}}_{{\|}}}{{|}}\) (d) for five bands (labeled by index n) contributing to the Fermi surface of Mn₃GaN and plotted in the 2DBZ of Mn₃GaN (001). Components of the effective spin polarization \({{\boldsymbol{p}}}_{{\boldsymbol{k}}_{{\|}}}=({p}_{{{\boldsymbol{k}}}_{{\|}}}^{x},{p}_{{{\boldsymbol{k}}}_{{\|}}}^{y},{p}_{{{\boldsymbol{k}}}_{{\|}}}^{z})\) (e) and polarization magnitude \({p}_{{{\boldsymbol{k}}}_{{\|}}}\equiv {{|}}{{\boldsymbol{p}}}_{{{\boldsymbol{k}}}_{{\|}}}{{|}}\) (f).