Growth of compositionally uniform ${\mathrm{I}\mathrm{n}}_x{\mathrm{G}\mathrm{a}}_{1-x}\mathrm{N}$ layers with low relaxation degree on GaN by molecular beam epitaxy

500-nm-thick ${\mathrm{I}\mathrm{n}}_x{\mathrm{G}\mathrm{a}}_{1-x}\mathrm{N}$ layers with $x=$ 0.05-0.14 are grown using plasma-assisted molecular beam epitaxy, and their properties are assessed by a comprehensive analysis involving x-ray diffraction, secondary ion mass spectrometry, and cathodoluminescence as well as photoluminescence spectroscopy. We demonstrate low degrees of strain relaxation (10% for $x=0.12$), low threading dislocation densities ($1\times {10}^9\mathrm{c}{\mathrm{m}}^{-2}$ for $x=0.12$), uniform composition both in the growth and lateral direction, and a narrow emission band. The unique sum of excellent materials properties make these layers an attractive basis for the top-down fabrication of ternary nanowires.