Linear and Nonlinear Optical Response of Rare-Earth i-MAX Carbides

The layered carbides in the MAX and i-MAX families combine metallic conductivity, chemical versatility, and structural durability, making them promising for nonlinear and plasmonic photonic applications. We present a comprehensive ab initio study of their linear and nonlinear optical properties. Using DFT + U with spin–orbit coupling, we computed absorption spectra and second- and third-order susceptibilities for Mo₂AlC and (Mo_2/3RE_1/3)₂AlC (i-MAX; RE = Nd, Sm, Gd, Tb, Er, Lu). Linear and nonlinear optical responses, χ⁽²⁾ and χ⁽³⁾, show strong enhancement due to the Mo–d orbitals at the Fermi level. While centrosymmetric MAX phases suppress χ⁽²⁾, i-MAX phases exhibit a magnetization-odd (c-type) contribution allowed by the C2/c magnetic symmetry. Experimental Fourier transform infrared (FTIR) measurements on Gd–i-MAX particles reveal mid-infrared peaks, which we attribute to finite-size plasmon excitations. The pronounced low-energy resonances in high-aspect-ratio Gd–i-MAX flakes arise from collective Drude–plasmon modes whose energies are set by the density of states and Fermi velocity calculated here. These results establish rare-earth i-MAX carbides as a versatile platform for mid-infrared plasmonics and nonlinear optical technologies.