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 Mn₁₂-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 ρ given by ρ ≡ 2ℏ/Δ²₀, where 2 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). Δ₀ is the minimum energy gap at the anti-crossing, Δ₀/ℏ being the tunneling rate thereat. Numerical integration leads to P(ρ) = 1 − exp [ − [(π)/(2ρ)]]. 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.