Dislocation-induced spin tunneling in ${\mathrm{Mn}}_{12}$ acetate

A comprehensive theory of quantum spin relaxation in ${\mathrm{Mn}}_{12}$ acetate crystals is developed that takes into account imperfections of the crystal structure and is based upon the generalization of the Landau-Zener effect for incoherent tunneling from excited energy levels. It is shown that linear dislocations at plausible concentrations provide the transverse anisotropy which is the main source of tunneling in ${\mathrm{Mn}}_{12}.$ Local rotations of the easy axis due to dislocations result in a transverse magnetic field generated by the field applied along the c axis of the crystal, which explains the presence of odd tunneling resonances. Long-range deformations due to dislocations produce a broad distribution of tunnel splittings. The theory predicts that at sub-Kelvin temperatures the relaxation curves for different tunneling resonances can be scaled onto a single master curve. The magnetic relaxation in the thermally activated regime follows the stretched-exponential law with the exponent depending on the field, temperature, and concentration of defects.