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The $A$MnO$_{2}$ delafossites ($A$=Na, Cu), are model frustratedantiferromagnets, with triangular layers of Mn$^{3+}$~spins. At lowtemperatures ($T_{N}$=65 K), a $C2/m \rightarrow P\overline{1}$ transition isfound in CuMnO$_2$, which breaks frustration and establishes magnetic order. Incontrast to this clean transition, $A$=Na only shows short-range distortions at$T_N$. Here we report a systematic crystallographic, spectroscopic, andtheoretical investigation of CuMnO$_2$. We show that, even in stoichiometricsamples, non-zero anisotropic Cu displacements co-exist with magnetic order.Using X-ray/neutron diffraction and Raman scattering, we show that highpressures acts to decouple these degrees of freedom. This manifests as anisostuctural phase transition at $\sim$10 GPa, with a reversible collapse ofthe $c$-axis. This is shown to be the high pressure analog of the $c$-axisnegative thermal expansion seen at ambient pressure. DFT simulations confirmthat dynamical instabilities of the Cu$^{+}$ cations and edge-shared MnO$_{6}$layers are intertwined at ambient pressure. However, high pressure selectivelyactivates the former, before an eventual predicted re-emergence of magnetism atthe highest pressures. Our results show that the lattice dynamics and localstructure of CuMnO$_2$ are quantitatively different to non-magnetic Cudelafossites, and raise questions about the role of intrinsic inhomogeniety infrustrated antiferromagnets.

Decoupling lattice and magnetic instabilities in frustrated CuMnO$_2$