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We find that dipolar interactions favor ferromagnetic ordering of elongatedcrystals of Mn12 Acetate below 0.8 K. Ordered crystals must possess domainwalls. Motion of the wall corresponds to a moving front of Landau-Zenertransitions between quantum spin levels. Structure and mobility of the wall arecomputed. The effect is robust with respect to inhomogeneous broadening anddecoherence.

Dipolar Ordering and Quantum Dynamics of Domain Walls in Mn-12 Acetate