Quantum tunneling and classical barrier reduction for a mesoscopic spin

Abstract

I show that for a large spin with uniaxial anisotropy it is, in principle, impossible to distinguish classical energy-barrier reduction due to a transverse magnetic field from an increase in the tunneling rate of excited levels. Given a suitable definition of the quantum energy barrier, I derive an expression for the field dependence of the barrier height that agrees with the classical result up to a constant of order unity. Numerical results show that for a mesoscopic spin (Sϳ10) the barrier decreases in a series of steps, which recent experiments may have revealed. ͓S0163-1829͑98͒08317-9͔

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“…From these and similar data we deduce the Þeld dependence of T B , as summarized in Fig. 2 26 The solid line in Fig. 2 is a Þt of the measured T B to the predicted quadratic dependence on Þeld.…”

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“…2b contains a horizontal dotted line -an empirically determined "tunnel threshold". When the tunnel splitting for a particular pair of levels approaches this threshold, tunneling for that pair begins to become the dominant relaxation mechanism [33,34,36,37]. For example, at H T ∼ 4.2 kOe (marked by the red vertical dotted line), the tunnel splitting for m = ±3 reaches the threshold and tunneling between these levels begins to dominate over relaxation through higher levels.…”