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In superfluid $^3$He-B confined in a slab geometry, domain walls betweenregions of different order parameter orientation are predicted to beenergetically stable. Formation of the spatially-modulated superfluid stripephase has been proposed. We confined $^3$He in a 1.1 $\mu$m high microfluidiccavity and cooled it into the B phase at low pressure, where the stripe phaseis predicted. We measured the surface-induced order parameter distortion withNMR, sensitive to the formation of domains. The results rule out the stripephase, but are consistent with 2D modulated superfluid order.

Evidence for a Spatially-Modulated Superfluid Phase of $^3$He under Confinement