First principle calculations of the magnetic structure of the RE-based i-MAX phases – a family of nanolaminated magnetic materials

The recently discovered in-plane ordered MAX phases (henceforth i-MAX) with the chemical formula (Mo_2/3RE_1/3)₂AlC (RE = lanthanide), have opened the possibility to manufacture magnetically ordered 2D derivatives. Neutron diffraction (ND) and muon spin rotation (mSR) studies revealed that the i-MAX phases order magnetically as spin density waves with ordering temperatures between 3.5 K and 29 K. However, many open questions remain regarding the nature of these magnetic structures. Particularly, mSR revealed that for RE heavier than Gd, the magnetic structure fluctuates on a time scale of ms, short-range order was observed for RE = Ho and Er in ND and field dependent magnetization measurements show a rich phase diagram under an applied magnetic field. To help explain the experimental observations, a first-principles approach is used to construct an effective spin Hamiltonian for the RE-i-MAX system. The exchange interactions are calculated from perturbation theory using the Liechtenstein formula. The existence of spin density waves is explained from competing antiferromagnetic interactions in the RE layer, and the experimentally observed trend in the magnetic transition temperatures is well reproduced by a mean field calculation based on the computed exchange interactions. In addition, the strongest exchange interaction for RE = Nd, Gd, Tb and Dy is found to be between RE atoms separated by the Al layer. This result has strong implications on the possibility to retain magnetism in the 2D derivative.