In superfluid ^{3}He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially modulated superfluid stripe phase has been proposed. We confined ^{3}He in a 1.1 μm high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the formation of domains. The results rule out the stripe phase, but are consistent with 2D modulated superfluid order.
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