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Using X-ray emission spectroscopy, we find appreciable local magnetic moments until 30 GPa to 40 GPa in the high-pressure phase of iron; however, no magnetic order is detected with neutron powder diffraction down to 1.8 K, contrary to previous predictions. Our first-principles calculations reveal a "spinsmectic" state lower in energy than previous results. This state forms antiferromagnetic bilayers separated by null spin bilayers, which allows a complete relaxation of the inherent frustration of antiferromagnetism on a hexagonal close-packed lattice. The magnetic bilayers are likely orientationally disordered, owing to the soft interlayer excitations and the neardegeneracy with other smectic phases. This possible lack of long-range correlation agrees with the null results from neutron powder diffraction. An orientationally disordered, spinsmectic state resolves previously perceived contradictions in highpressure iron and could be integral to explaining its puzzling superconductivity. [ABSTRACT FROM AUTHOR]