  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.
