Transition to superparamagnetism in chains of magnetosome crystals

Magnetotactic bacteria use chains of magnetic crystals to orient them in the Earth's field. Magnetic measurements show that these chains are in a single-domain state with all the moments pointing along the chain axis. Yet many of the crystals in the chains fall in either the multidomain (MD) or the superparamagnetic (SP) size range for isolated crystals. Magnetostatic coupling between crystals keeps the magnetization uniform and prevents thermally assisted transitions between states. The SP critical size for a chain of magnetite crystals is calculated using a new algorithm. The network of stable states and transition states connecting them is determined using a homotopy continuation method. This determines the energy barriers between stable states, and the critical size can then be calculated using a master equation. As the number of crystals in the chain increases, the SP critical volume approaches a limit that is nearly independent of the shape of the crystals. The cube root of this volume is about 10 nm. Most magnetosome crystal sizes are well above this limit. About half of the magnetosome crystals found in sediments would be MD in isolation. However, there is also a population of cubo-octahedral crystals, a large fraction of which would be SP in isolation. Such crystals are also formed in fresh water by bacteria in the genus Magnetospirillum. The difference in size and shape between the populations of isometric and nonisometric crystals may be related to redox conditions and the choice of magnetoaerotaxis mechanism.