Tunneling in Mesoscopic Magnetic Molecules

Abstract

We present a theoretical study of magnetic relaxation of big molecules, M${\mathrm{n}}_{12}$${\mathrm{O}}_{12}$, at low temperature, when the relaxation time $\ensuremath{\tau}$ is temperature independent. If the magnetic field ${h}_{z}$ is not too low, tunneling can only take place if energy is exchanged with phonons. Then, $1/\ensuremath{\tau}\ensuremath{\sim}{h}_{z}^{3}$ for weak ${h}_{z}$. A steeper increase is expected for higher ${h}_{z}$. The effect of a transverse field ${h}_{x}$ is small. The maximum of $\ensuremath{\tau}({h}_{z})$ observed experimentally at ${h}_{z}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.2$ T might be due to tunneling without phonons in low field, with a relaxation rate reduced by hyperfine interactions.