  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.
