Giant anomalous Hall effect in epitaxial Mn\(_{3.2}\)Ge films with a cubic kagome structure

We report on the first example of epitaxial Mn\(_{3 + \delta}\)Ge thin films with a cubic \(L1_2\) structure. The films are found to exhibit frustrated ferromagnetism with an average magnetization corresponding to 0.98\(~\pm~\)0.06\(~\mu_B\)/Mn, far larger than the parasitic ferromagnetism in hexagonal Mn\(_3\)Ge and the partially compensated ferrimagnetism in tetragonal Mn\(_3\)Ge. The Hall conductivity is the largest reported for the kagome magnets with a low temperature value of \(\sigma_{xy} = 1587~\)S/cm. Density functional calculations predict that a chiral antiferromagnetic structure is lower in energy than a ferromagnetic configuration in an ordered stoichiometric crystal. However, chemical disorder driven by the excess Mn in our films explains why a frustrated 120\(^\circ\) spin structure is not observed. Comparisons between the magnetization and the Hall resistivity indicate that a non-coplanar spin structure contributes the Hall signal. Anisotropic magnetoresistance and planar Hall effect with hysteresis up to 14 T provides further insights into this material.