Long-range order in arrays of composite and monolithic magneto-toroidal moments

TL;DR

This paper investigates long-range magneto-toroidal order in nanomagnet arrays, demonstrating how specific structures promote this order and confirming domain formation through microscopy, advancing understanding of ferroic states for spintronics.

Contribution

It introduces two pathways to achieve spontaneous magneto-toroidal order in nanomagnet arrays and identifies conditions promoting this elusive ferroic state.

Findings

Magneto-toroidal order confirmed in nanomagnet arrays.

Two types of domain-wall states identified.

Conditions for spontaneous order established.

Abstract

Magneto-toroidal 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 magneto-toroidal moments, associated with a macroscopic toroidization. Because of its intrinsic 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 magneto-toroidal 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 magneto-toroidal order. We confirm this order and the formation of magneto-toroidal domains in our arrays by 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 magneto-toroidal order but also highlights the possibility tailor mesoscale magnetic arrays towards elusive types of ferroic order.