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The low-temperature magnetic properties of \tcr{polycrystalline}Na$_2$IrO$_3$, a candidate material for the realization of a quantumspin-liquid state, were investigated by means of muon-spin relaxation andnuclear magnetic resonance methods under chemical and hydrostatic pressure. TheLi-for-Na chemical substitution promotes an inhomogeneous magnetic order,whereas hydrostatic pressure (up to 3.9\,GPa) results in an enhancement of theordering temperature $T_\mathrm{N}$. In the first case, the inhomogeneousmagnetic order suggests either short- or long-range correlations of broadlydistributed $j=\,$\textonehalf\ Ir$^{4+}$ magnetic moments, reflecting localdisorder. The increase of $T_\mathrm{N}$ under applied pressure points at anincreased strength of three dimensional interactions arising from interlayercompression.

Chemical- and hydrostatic-pressure effects on the Kitaev honeycomb material Na$_2$IrO$_3$