Frustration-Induced Magnetostructural Inhomogeneity in the Triangular Antiferromagnet $\alpha$-NaMnO$_2$

Phase inhomogeneity of otherwise chemically homogenous electronic systems is an essential ingredient leading to fascinating functional properties, such as high-$T_c$ superconductivity in cuprates, colossal magnetoresistance in manganites, and giant electrostriction in relaxors. In these materials distinct phases compete and can coexist due to intertwined ordered parameters. Charge degrees of freedom play a fundamental role, although phase-separated ground states have been envisioned theoretically also for pure spin systems with geometrical frustration that serves as a source of phase competition. Here we report a paradigmatic magnetostructurally inhomogenous ground state of the geometrically frustrated $\alpha$-NaMnO$_2$ that stems from the system's aspiration to remove magnetic degeneracy and is possible only due to the existence of near-degenerate crystal structures. Synchrotron X-ray diffraction, nuclear magnetic resonance and muon spin relaxation show that the spin configuration of a monoclinic phase is disrupted by magnetically short-range ordered nanoscale triclinic regions, thus revealing a novel complex state of matter.