Vertex Dynamics in Finite Two-Dimensional Square Spin Ices

Abstract

Local magnetic ordering in artificial spin ices is discussed from the point of view of how geometrical frustration controls dynamics and the approach to steady state. We discuss the possibility of using a particle picture based on vertex configurations to interpret time evolution of magnetic configurations. Analysis of possible vertex processes allows us to anticipate different behaviors for open and closed edges and the existence of different field regimes. Numerical simulations confirm these results and also demonstrate the importance of correlations and long range interactions in understanding particle population evolution. We also show that a mean field model of vertex dynamics gives important insights into finite size effects. Introduction.-Spin ices are geometrically frustrated magnetic systems, where interaction energies are minimized by local arrangements of spins resembling the ice rule for the ground state of solid water, i.e., two-in, twoout spin configurations [1,2]. Spin ices display several interesting features including zero point entropy [3], spin freezing, and hysteresis [4]. The role of long range interactions in three dimensional spin ices is also interesting, as the long range dipolar interactions between spins lead to a state that can be described using the short range ice rules [5].

Magnetic dipole configurations on honeycomb lattices: effect of finite size and boundaries

“…This reproducibility in a rotational field is astounding and unexpected. It is not in line with predictions by Budrikis et al [12], according to which a progressive change in the pattern should take place upon multiple rotations, favouring the low-energy vertices at the expense of the high-energy vertices. Instead, we find essentially a complete reversibility and no annihilation of the Q = ±3q vertices upon rotation.…”

“…But in the end, after a complete cycle, the dipole configurations are identical to the starting position. Therefore, we cannot confirm the predictions of Budrikis et al [12] for square ice patterns, according to which a progressive change in the pattern should occur upon multiple rotations, favouring the low-energy vertices at the expense of the high-energy vertices. Instead, we find a complete reversibility and no annihilation of the high-energy Q = ±3q vertices upon rotation.…”

“…On the other hand, only two islands meet in a vertex in the outermost hexagons if they are closed. In a recent publication, Budrikis et al [12] have calculated and simulated the effect of open and closed squares in square spin-ice patterns. In particular, they find that, upon rotation of the pattern in a magnetic field corresponding to the coercivity of the pattern, the frequency of type I vertices increases successively upon each complete rotation.…”

Disorder, Edge, and Field Protocol Effects in Athermal Dynamics of Artificial Spin Ice

“…In ideal systems, comparison between the cost of vertex processes and the Zeeman energy induced by external fields can be used to build up a picture of how array edge effects and the sequence of external fields control dynamics [8]. Topological constraints on dynamics enter as restrictions on how vertices can transition from one state to another.…”

“…This picture culminates in a mean-field population dynamics model for the response of square artificial spin ice to an external drive [8]. Three strands of work are presented here.…”