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Inhomogeneity in the ground state is an intriguing, emergent phenomenon inmagnetism. Recently, it has been observed in the magnetostructural channel ofthe geometrically frustrated $\alpha$-NaMnO$_2$, for the first time in theabsence of active charge degrees of freedom. Here we report an in-depthnumerical and local-probe experimental study of the isostructural sistercompound CuMnO$_2$ that emphasizes and provides an explanation for the crucialdifferences between the two systems. The experimentally verified, much morehomogeneous, ground state of the stoichiometric CuMnO$_2$ is attributed to thereduced magnetoelastic competition between the counteracting magnetic-exchangeand elastic-energy contributions. The comparison of the two systemsadditionally highlights the role of disorder and allows an understanding of thepuzzling phenomenon of phase separation in uniform antiferromagnets.

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