Quantum tunneling and dissipation in nanometer-scale magnets

Abstract

We summarize recent low-temperature noise and AC magnetic susceptibility measurements on the nanometer-scale magnetic protein horse-spleen ferritin. The experiments show a narrow resonance peak at about 10 6 Hz, which is discussed in the framework of recently-developed theories of macroscopic quantum coherence and tunneling in antiferromagnets; theory and experiment are argued to agree qualitatively, though quantitative discrepancies remain. We also review the recent analysis of a rather general spin-parity effect for tunneling in magnetic systems: systems with appropriate symmetry may exhibit quantum tunneling for integer spin, but not for half-odd-integer spin, where destructive interference between different tunneling paths suppresses the tunneling. Finally, we study the effect on this spin-parity phenomenon caused by dissipation, i.e. coupling to an environment consisting of a bath of harmonic oscillators. Using the real-time, Feynman-Vernon path integral formalism, we find models where an arbitrarily small amount of ohmic dissipation completely destroys the spin-parity effect (i.e., produces as such tunneling for half-odd-integer spins as for integer spins), and others where the effect appears to disappear gradually with increasing dissipation. Suprisingly, however, there is a sense in which the spin-parity effect is preserved in both types of models: a Calderia-Leggett type of analysis shows that neither experiences any tunnel splitting of its ground state. We present simple arguments for how this intriguing paradox might be resolved.