  Using x-ray emission spectroscopy, we find appreciable local magnetic moments
until 30-40 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 "spin-smectic" 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 near-degeneracy with other smectic
phases. This possible lack of long-range correlation agrees with the null
results from neutron powder diffraction. An orientationally-disordered,
spin-smectic state resolves previously perceived contradictions in high
pressure iron and could be integral to explaining its puzzling
superconductivity.
