Magnetic moment and magnetic anisotropy of Ge₃Mn₅ thinfilms on Ge(111) substrate: A density functional study

Magnetism and magnetic anisotropy energy (MAE) of the Ge₃Mn₅ bulk, free-standing surface, and Ge₃Mn₅(001)|Ge(111) thinfilms and superlattice have been systemically investigated by using the relativistic first-principles electronic structure calculations. For Ge₃Mn₅ adlayers on Ge(111) substrates within Mn1 termination, the direction of magnetization undergoes a transition from in-plane at 1 monolayer (ML) thickness (MAE = -0.50 meV/ML) to out-of-plane beginning at 3 ML thickness (nearly invariant MAE = 0.16 meV/ML). The surficial/interfacial MAE is extracted to be 1.23/-0.54 meV for Mn1-termination; the corresponding value is 0.19/1.03 meV for Mn2/Ge-termination; the interior MAE is averaged to be 0.09 meV per ML. For various Ge₃Mn₅ systems, the in-plane lattice expansion and/or interlayer distance contraction would enhance the out-of-plane MAE. Our theoretical magnetic moments and MAEs fit well with the experimental measurements. Finally, the origination of MAE is elucidated under the framework of second-order perturbation with the electronic structure analyses.