Dipolar Cairo lattice: Geometrical frustration and short-range correlations

Abstract

We have studied low-energy configurations in two-dimensional arrays consisting of Ising-type dipolar coupled nanomagnets lithographically defined onto a two-dimensional Cairo lattice, thus dubbed the dipolar Cairo lattice. Employing synchrotron-based photoemission electron microscopy (PEEM), we perform real-space imaging of moment configurations achieved after thermal annealing. These states are then characterized in terms of vertex populations, spin-and emergent magnetic charge correlations, and a topology-enforced emergent ice rule. The results reveal a strong dominance of short-range correlations and the absence of long-range order, reflecting the high degree of geometrical spin frustration present in this example of an artificial frustrated spin system.

Elevated effective dimension in tree-like nanomagnetic Cayley structures

“…The extensive degeneracy and nature of the ground state in spin glasses have been an area of extensive research over multiple decades, resulting in theoretical spin glass models that became, among other examples, the basis of error-correcting codes 7 , problems of optimization 8 , and brain science paradigms 9,10 . Inspired by recent research on artificial frustrated systems [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28] , a first step towards the realization of artificial Ising spin glasses was made recently 29 . There, Ising-type single-domain nanomagnets are lithographically arranged onto Gaussian random sites and orientations with a controlled degree of disorder, the feature commonly believed to be the main ingredient in spin glasses.…”

Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices

“…The results in Ref. [63] present an experimental study of twodimensional artificial spin ice, where Ising-like nanoislands are placed on the centers of the edges of the so-called Cairo lattice (see Fig. 1).…”

“…Figures 1(a) and 1(b) show the lattice parameters a, b, and c. With this notation the calculations were performed for a = 472 nm, b = 344 nm, and various values of c, as in Ref. [63], with the only difference that we calculated the properties of the ground states for c > 600 nm. Since the 042129-2 sizes of the nanoislands are below the critical threshold for a single-domain state, and the shape anisotropy highlights the direction for the magnetic moment, we investigated the model of Ising-like point dipoles.…”

“…For clarity and presentation of our model, we calculated the centers of the nanoislands and placed the lattice of point dipoles on the lattice shown in the image obtained in Ref. [63] by scanning electron microscopy (SEM) [Fig. 1(b)].…”

“…Based on SEM data [see Fig. 1(b) [63]], the nanoislands are seemingly identical, while around 5% disorder in the form of a Gaussian is often used in past kinetic Monte Carlo simulations to match experimental observations [64]. As a result, for each configuration of dipolar moments in the Ising model we can match the spin excess M and in the case of "all-to-all" dipolar interaction the total energy,…”