Rare-earth-based-in-plane-ordered MAX phases ($R\text{−}i$-MAX) are a family of nano-laminated compounds with chemical formula (${\mathrm{Mo}}_{2/3}{R}_{1/3}{)}_2\text{AlC}$ that have attracted interest as potential precursors for magnetic two-dimensional (2D) derivatives. Experimental investigations of the magnetic properties of these materials have revealed complicated magnetic phase diagrams with multiple magnetic phase transitions as a function of temperature and external field, commensurate and incommensurate magnetic ordering, as well as fluctuations of the magnetic moments when rare-earths heavier than Gd are introduced. In this work, the magnetic exchange interactions of $R\text{−}i$-MAX phases, where $R$ = Nd, Sm, Gd, Tb, Dy, Ho, and Er are calculated using density functional theory and are measured experimentally using magnetic diffuse neutron scattering measurements on powder samples with $R$ =Tb and Er. Good quantitative agreement is found between the measured and calculated exchange interactions, as well as between the observed and calculated relative magnetic ordering temperatures. The strongest interaction is found to be for rare-earths separated by the Al layer, with much weaker interactions in the carbide layer. These results may have significant implications on the existence of magnetism in the two-dimensional derivatives of the MAX phases. This study is an initial step in developing a computational framework for the prediction and optimization of potential 2D magnets in the $R\text{−}i$-MAX family of compounds.

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• Density of states
• Electronic structure
• Exchange interaction
• Magnetic interactions
• Magnetism
• RKKY interaction
• Antiferromagnets
• Magnetic systems
• Rare-earth magnetic materials
• Density functional theory
• First-principles calculations
• Neutron diffraction
• Neutron scattering
• Neutron techniques