Artificial out-of-plane Ising antiferromagnet on the kagome lattice with very small farther-neighbor couplings

Abstract

Despite their simple formulation, short-range classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular, due to their macroscopic ground-state degeneracy. Recent experiments on artificial spin systems comprising arrays of chirally coupled nanomagnets provide a significant strengthening of the nearest-neighbor couplings compared to systems with dipolar-coupled nanomagnets. This opens the way to design artificial spin systems emulating Ising models with nearest-neighbor couplings. In this paper, we compare the results of an extensive investigation with tensor network and Monte Carlo simulations of the nearest-and farther-neighbor (J 1 − J 2 − J 3|| ) kagome Ising antiferromagnet with the experimental spinspin correlations of a kagome lattice of chirally coupled nanomagnets. Even though the ratios between the farther-neighbor couplings and the nearest-neighbor coupling estimated from micromagnetic simulations are much smaller than for dipolar-coupled nanomagnets, we show that they still play an essential role in the selection of the correlations.

Partial lifting of degeneracy in the $J_1-J_2-J_3$ Ising antiferromagnet on the kagome lattice

“…Yet, the ground-state degeneracy is not completely lifted. Comparing this phase with the ground-state phase of the J 1 − J 2 − J 3|| model (where J 3 = 0 underlines again the determinant role of the J 3 interaction in this ground-state phase diagram: as compared to the latter (S ∼ = 0.1439... [38]), the residual entropy in the chevrons phase (Fig. 14, Table I) is reduced by almost a factor 8 :…”

“…At these specific points, a finite residual entropy is recovered, for instance in the J 1 −J 2 −J 3|| model when J 2 = J 3|| [45,46]; this line was thoroughly studied, be it for the Ising model [45][46][47], the classical and the quantum Heisenberg models ( [48][49][50][51] and references therein), and the macroscopic degeneracy on this fine-tuned line has been showed to be particularly stable (due to the completion of squares on this line). In a different context, it was also recently noticed that the macroscopic ground-state degeneracy in the Ising model is not completely lifted when J 2 < J 3|| [38]. Furthermore, in the J 1 − J 2 − J 3 model, when J 1 is ferromagnetic, there is a phase with a macroscopic ground-state degeneracy [43].…”

“…, with an exact value that can vary with the details of the system [21,38]. The first few interactions for this Hamiltonian are illustrated in Fig.…”

“…It is well-known that the second-neighbor Ising an- tiferromagnet on the kagome lattice has a macroscopic ground-state degeneracy [34,38,39]. This motivated an attempt by Hamp et.…”

“…1, which gives an overview of our results for the ground-state phase diagram of this model. It is already well-known that the J 1 − J 2 Ising antiferromagnet on the kagome lattice with antiferromagnetic J 2 has a macroscopic ground-state degeneracy [34,38]. However, the fact that the spin-spin correlations in that ground state are long-ranged [34] makes it all the more surprising that a macroscopic degeneracy survives in a wide range of values of a third neighbor interactions, a result which is also in contrast to simple Pauling estimates that yield a negative residual entropy, suggesting an ordered ground-state [39].…”