Spin tunneling in a swept magnetic field

We present a theory whose goal is to account for the recent exciting hysteresis experiments on the spin cluster crystal Mn-12-acetate that indicate the occurrence of spin tunneling. We have found the tunneling probability P For the tunneling of spin from one spin state into another at a spin level crossing in response to a swept applied magnetic field H. It is shown that P is a function of only one parameter, the dimensionless sweep rate rho given by rho = 2<(tau)over bar>(h) over bar/Delta(0)(2), where 2<(tau)over bar> is the rate at which the two energy levels approach each other as the field is swept (being proportional to the sweep rate dH/dt). Delta(0) is the minimum energy gap at the anti-crossing, Delta(0)/(h) over bar being the tunneling rate thereat. Numerical integration leads to P(rho) = 1 - exp[-tau/2 rho]. We find that, contrary to widespread belief, the experiments cannot be understood in terms of tunneling of individual spin clusters in the presence of a static applied transverse field. Rather, the required transverse field must have dynamic nuclear spins and other dynamic spin clusters as its source.