Variable-range hopping conduction in epitaxial CrN(001)

Epitaxial CrN(001) layers, grown by dc magnetron sputtering on MgO(001) substrates at growth temperatures Tₛ $=$ 550--850 ^∘{}C, exhibit electronic transport that is dominated by variable-range hopping (VRH) at temperatures 120 K. A transition from Efros-Shklovskii to Mott VRH at 30 ±{} 10 K is well described by a universal scaling relation. The localization length decreases from 1.3 nm at Tₛ $=$ 550 ^∘{}C to 0.9 nm for Tₛ $=$ 600--750 ^∘{}C, but increases again to 1.9 nm for Tₛ $=$ 800--850 ^∘{}C, which is attributed to changes in the density of localized states associated with N vacancies that form due to kinetic barriers for incorporation and enhanced desorption at low and high Tₛ, respectively. The low-temperature transport data provide lower limits for the CrN effective electron mass of 4.9mₑ, the donor ionization energy of 24 meV, and the critical vacancy concentration for the metal-insulator transition of 8.4 × 10¹⁹ cm^-3. The room temperature conductivity is dominated by Hubbard band states near the mobility edge and decreases monotonically from 137 {Ω}^-1cm^-1 for Tₛ $=$ 550 ^∘{}C to 14 {Ω}^-1cm^-1 for Tₛ $=$ 850 ^∘{}C due to a decreasing structural disorder, consistent with the measured x-ray coherence length that increases from 7 to 36 nm for Tₛ $=$ 550 to 850 ^∘{}C, respectively, and a carrier density that decreases from 4 × 10²⁰ to 0.9 × 10²⁰ cm^-3, as estimated from optical reflection and Hall effect measurements. The absence of an expected discontinuity in the conductivity at {~}280 K suggests that epitaxial constraints suppress the phase transition to a low-temperature orthorhombic antiferromagnetic phase, such that CrN remains a cubic paramagnetic insulator over the entire measured temperature range of 10--295 K. These results contradict previous experimental studies that report metallic low-temperature conduction for CrN, but support recent computational results suggesting a band gap due to strong electron correlation and a stress-induced phase transition.