Artificial spin ices consist of nanomagnets arranged on the sites of various periodic and
aperiodic lattices. They have enabled the experimental investigation of a variety of …

Geometric frustration and the ice rule are two concepts that are intimately connected and
widespread across condensed matter. The first refers to the inability of a system to satisfy …

This review is a study of how the idea of spin ice has evolved over the years, with a focus on
the scientific questions that have come to define the subject. Since our initial discovery of …

Magnetic monopoles, proposed as elementary particles that act as isolated magnetic south
and north poles, have long attracted research interest as magnetic analogs to electric …

Ferrotoroidicity—the fourth form of primary ferroic order—breaks both space and time-
inversion symmetry. So far, direct observation of ferrotoroidicity in natural materials remains …

Artificial spin ice systems are lithographically prepared arrays of interacting nanoscale
magnetic moments with collective behavior resulting from the chosen array geometry. These …

Two-dimensional arrays of interacting magnetic nanostructures offer a remarkable
playground for simulating, experimentally, lattice spin models. Initially designed to capture …

Spin glasses, generally defined as disordered systems with randomized competing
interactions,, are a widely investigated complex system. Theoretical models describing spin …

The photonic spin Hall effect, a deep subdiffraction-limited shift between the opposite spin
components of light, emerges when light undergoes an evolution of polarization or trajectory …

In frustrated spin systems, magnetic phase transitions underpin the formation of exotic,
frustration-driven magnetic phases. Of great importance is the ability to manipulate these …