Emergent magnetic monopole dynamics in macroscopically degenerate artificial spin ice

Thermally activated two-dimensional artificial square ice with height offsets between nanomagnets.

(A) Tilted-sample scanning electron microscopy (SEM) image of an artificial square ice with an introduced height offset h, which can be varied from sample to sample, until the competing interactions J1 and J2 are equalized and an extensive spin ice degeneracy is achieved. Scale bar, 400 nm. (B) XMCD image of the same artificial square ice array. Nanomagnets with moments pointing toward the incoming x-rays (indicated by a yellow arrow) appear dark, while those opposing the x-ray direction appear with bright contrast. (C) The 16 possible moment configurations on a four-nanomagnet vertex are traditionally listed into four topological types. Without a height offset (h = 0 nm), the ice rule–obeying (two-in-two-out) type I and II configurations have a significantly different energy. Once a critical height offset is introduced, their energies are equalized and spin ice degeneracy is realized. Highlighted with magenta, cyan blue, and yellow frames in (B) and (C) are type I, type II, and type III vertices, respectively.


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 charge. In solid-state physics, a classical analog to these elusive particles has emerged as topological excitations within pyrochlore spin ice systems. We present the first real-time imaging of emergent magnetic monopole motion in a macroscopically degenerate artificial spin ice system consisting of thermally activated Ising-type nanomagnets lithographically arranged onto a pre-etched silicon substrate. A real-space characterization of emergent magnetic monopoles within the framework of Debye-Hückel theory is performed, providing visual evidence that these topological defects act like a plasma of Coulomb-type magnetic charges. In contrast to vertex defects in a purely two-dimensional artificial square ice, magnetic monopoles are free to evolve within a divergence-free vacuum, a magnetic Coulomb phase, for which features in the form of pinch-point singularities in magnetic structure factors are observed.