Quantum Step Heights in Hysteresis Loops of Molecular Magnets

We present an analytical theory on the heights of the quantum steps observed in the hysteresis loops of molecular magnets. By considering the dipolar interaction between molecular spins, our theory successfully yields the step heights measured in experiments, and reveals a scaling law for the dependence of the heights on the sweeping rates hidden in the experiment data on Fe$_8$ and Mn$_4$. With this theory, we show how to accurately determine the tunnel splitting of a single molecular spin from the step heights.