The origin and the functions of more than a billion single-domain magnetic nanoparticles [reported in Proc. Natl. Acad. Sci. USA 89, 7683 (1992)] adjacent to billions of neurons in the brain neocortex are not known yet. There is empirical evidence implicating the sensitivity of many living organisms to constant or extremely low-frequency magnetic fields. Navigation and routing of migratory birds by the Earth's magnetic field and certain behaviors of magnetic bacteria are well-known examples. However, it seems that human beings are not able to sense the Earth's magnetic field. In this article, we first investigate the criticality of interacting magnetic superclusters in a mean-field approximation and then discuss the rotational Brownian motion of a single-domain magnetic dipole. Then, we consider the rotational Brownian motion in the presence of magnetic interactions. Ignoring the complexity of the dynamics, the anisotropy, and the long-range interaction of nanoparticles, we investigate numerically their behavior using a finite-size two-dimensional Ising-like model. It is shown that if the dipole coupling coefficient is fine-tuned to keep the model close to the critical state, then system sensitivity to an external magnetic field is maximized with an scaling behavior in terms of the number of magnetic superclusters.

• Received 21 February 2018
• Revised 2 August 2018

DOI:https://doi.org/10.1103/PhysRevE.98.032133