Magnetic inhomogeneity on a triangular lattice: the magnetic-exchange versus the elastic energy and the role of disorder

Inhomogeneity in the ground state is an intriguing, emergent phenomenon in magnetism. Recently, it has been observed in the magnetostructural channel of the geometrically frustrated $\alpha$-NaMnO$_2$, for the first time in the absence of active charge degrees of freedom. Here we report an in-depth numerical and local-probe experimental study of the isostructural sister compound CuMnO$_2$ that emphasizes and provides an explanation for the crucial differences between the two systems. The experimentally verified, much more homogeneous, ground state of the stoichiometric CuMnO$_2$ is attributed to the reduced magnetoelastic competition between the counteracting magnetic-exchange and elastic-energy contributions. The comparison of the two systems additionally highlights the role of disorder and allows an understanding of the puzzling phenomenon of phase separation in uniform antiferromagnets.