# Magnetic quantum tunneling and the topological phase

## Abstract

Recent observations are reviewed of the magnetic susceptibility of single-domain, 7.5 nm antiferromagnetic iron-oxide particles, which are a constituent of naturally occurring horse-spleen ferritin proteins. Measurements conducted with an ultra-sensitive integrated DC SQUID microsusceptometer reveal a well-defined resonance near a frequency of about 1 MHz which develops below about 200 mK. As our theoretical analysis indicates, the observed extreme sensitivity of this resonance to particle concentration, and to external magnetic field, supports the idea that collective quantum tunneling of the orientation of the Néel vector is occurring in the particle. The theoretical analysis contains an interesting surprise: it predicts that particles with an odd number of electronic spins cannot tunnel; tunneling is only permitted for particles with an even number of spins. This is an interference effect arising from a recently discovered 'topological term' in the spin Lagrangian. This result has broader implications: it leads to the correct path-integral interpretation of the Kramers theorem of atomic physics, and shows how this theorem manifests itself in collective magnetic quantum tunneling. I will discuss how this 'spin-parity' effect might be seen in magnetic-particle experiments. © 1994.