Apparent ferromagnetism in the pinwheel artificial spin ice

Abstract

Magnetic artificial spin ice provides examples of how competing interactions between magnetic nanoelements can lead to a range of fascinating and unusual phenomena. We examine theoretically a class of spin ice tilings, called pinwheel, for which near degeneracy of spin configuration energies can be achieved. The pinwheel tiling is a simple but crucial variant on the square ice geometry, in which each nanoelement of square ice is rotated some angle about its midpoint. Surprisingly, this rotation leads to an intriguing phase transition; and even though the spins are not parallel to one another, a ferromagnetic phase is found for rotation angles near 45• . Here, magnetic domains and domain walls are found when viewed in terms of net magnetisation. Moreover, the ferromagnetic behaviour of the system depends on its anisotropy which we can control by array shape and size.

Superferromagnetism and Domain-Wall Topologies in Artificial “Pinwheel” Spin Ice

“…In particular, Morrison et al 21 pointed out the importance of vertex of interactions and their dependence on geometry. A simply modified square ASI system provides a recent example of emergent dynamics: the 'pinwheel' ice 22,23 . The pinwheel geometry is obtained by rotating each island in square ASI around its centre 23 .…”

Intermediate phase and pseudo phase transition in an artificial spin ice model

“…The effects of open boundaries on nanomagnetic arrays have also been discussed by Macêdo et al 38 for the pinwheel artificial spin ice, where it was shown that for OBC the ground state is composed by domains that are not present in the system with PBC. In addition, they found that different domain structures appear depending on the lattice shape and edge types.…”

Heisenberg pseudo-exchange and emergent anisotropies in field-driven pinwheel artificial spin ice

“…8 The square ASI geometry has an antiferromagnetic (AFM) ground state (GS) ordering, where each set of four islands is formed by two orthogonal pairs of collinear Ising spins lying in a plane, with one pair aligned head-to-head and the other pair tail-to-tail. 1 In square ASI, the GS is well defined, 9 with the higher energy states separated significantly in energy, 1,10 and field-driven reversal occurs through sequential chain flipping 11,12 also referred to as Dirac strings. The recently reported 'pinwheel' geometry 10,[13][14][15] is created by rotating each island in a square lattice about its centre by 45 o (c.f.…”

“…As the island rotation angle is increased from 0 to 45 o , the dominant nearest-neighbour (NN) coupling in square ASI decreases in favour of an increased coupling to more distant islands. 10 In a small range of rotation angles around 45 o , the energy level spacings are significantly reduced, creating a near-degenerate system with two-dimensional (2-D) superferromagnetic 16 GS ordering. 10 The transition between square and pinwheel ice has been mapped as a function of rotation angle, yielding insight into defect formation and the demonstration of a true ice manifold in a 2-D system.…”

“…ally for zero-field conditions and little difference is found. 10,17 However, end-states have been shown to be important in defining a chirality for monopoles in kagome ASI, giving rise to anisotropic reversal; 18 in determining microwave frequency dynamics of square 19 and Kagome 20 ASI; in the systematic creation of vortex flux closure states in coupled islands; 21 and in altering the reversal fields in coupled 1-D island chains. 22 In pinwheel ASI, the reduction in the interaction strengths means that this system aught to be particularly sensitive to modifications to the dipolar coupling due to the presence of end-states.…”