CrN electronic structure and vibrational modes: An optical analysis

The optical properties of paramagnetic CrN over the wavelength range 250 nm--30 μm were determined from transmission and reflection spectra of 44--11 000-nm-thick epitaxial CrN(001) layers that were grown on MgO(001) by ultrahigh vacuum magnetron sputtering at 700 ^∘C and were found to be pure cubic single crystals by x-ray diffraction ω-2θ, ω, and φ scan analyses. The imaginary part of the dielectric function exhibits a steep onset at ω=0.64 eV as well as peaks at ω=1.5 and 2.9 eV due to direct interband transitions and indicates a depletion in the density of states at the Fermi level with an upper limit for free carriers of 3×10¹⁹ cm^-3. This is attributed to local magnetic moments that cause splitting of the t2g bands and the formation of an indirect band gap of 0.19±0.46 eV, as estimated by comparing the optical transition energies with reported direct gap energies from calculations with different magnetic ordering and Coulomb interaction terms. The dielectric function shows a strong resonance at ω₀=48.7±0.2 meV, and values of εdc=53±5 and ε_∞=22±2 below and above the resonance, respectively, providing values for transverse and longitudinal optical phonon frequencies at the zone center of 11.7 THz and 18.2 THz (corresponding to ω=48.7±0.2 and 75.6±6.8 meV), respectively, and a Born effective charge of 4.4±0.9. The vibrational frequencies are confirmed by Raman spectroscopy peaks at 800, 1170, and 1330 cm^-1 which are attributed to 2TO(X), 2LO(X), and 2LO(L) modes and correspond to single-phonon energies of 49.6 meV, 72.5 meV, and 82.5 meV, respectively. They are quantitatively comparable to those reported for ScN, a semiconductor with the same crystal structure as cubic CrN. In conclusion, both electronic interband transitions and optical phonon frequencies suggest that CrN is a Mott-Hubbard-type insulator with a small to negligible indirect band gap.