Distribution of Tunnel Splittings in Mn₁₂ Acetate

In magnetic fields applied parallel to the anisotropy axis, the relaxation of the magnetization of Mn₁₂-acetate measured for different sweep rates collapses onto a single scaled curve. The form of the scaling implies that the dominant symmetry-breaking process responsible for tunneling is a locally varying second-order transverse anisotropy, forbidden by tetragonal symmetry in the perfect crystal, which gives rise to a broad distribution of tunnel splittings in a real crystal of Mn₁₂ acetate. Different forms applied to even- and odd-numbered steps provide a clear distinction between even resonances (associated with crystal anisotropy) and odd resonances (which require a transverse magnetic field).