Long-range order in arrays of composite and monolithic magnetotoroidal moments

Abstract

Magnetotoroidal order, also called ferrotoroidicity, is the most recently established type of ferroic state. It is based on a spontaneous and uniform alignment of unit-cell-sized magnetic whirls, called magnetotoroidal moments, associated with a macroscopic toroidization. Because of its intrinsic linear magnetoelectric coupling, this new ferroic state could be useful in the development of spintronic devices. We exploit two-dimensional periodic arrays of magnetostatically coupled nanomagnets as model systems for the investigation of long-range magnetotoroidal order. We present two pathways promoting this order, namely, (i) structures comprising a ring of uniformly magnetized sub-micrometer-sized bar magnets and (ii) structures in which each magnetic building block itself hosts a magnetic vortex. For both cases, calculations of the magnetic-dipole interaction and micromagnetic simulations reveal the conditions for the formation of spontaneous magnetotoroidal order. We confirm this order and the formation of magnetotoroidal domains in our arrays with magnetic force microscopy. We identify the presence of two types of domain-wall states emerging from the competition of two intrinsic microscopic couplings. Our work not only identifies the microscopic conditions promoting spontaneous magnetotoroidal order but also highlights the possibility to tailor mesoscale magnetic arrays toward elusive types of ferroic order.