  Quantum tunneling of the magnetization is a phenomenon that impedes the use
of small anisotropic spin systems for storage purposes even at the lowest
temperatures. Phonons, usually considered for temperature dependent relaxation
of magnetization over the anisotropy barrier, also contribute to magnetization
tunneling for integer spin quantum numbers. Here we demonstrate that certain
spin-phonon Hamiltonians are unexpectedly robust against the opening of a
tunneling gap, even for strong spin-phonon coupling. The key to understanding
this phenomenon is provided by an underlying supersymmetry that involves both
spin and phonon degrees of freedom.
