Understanding thermal annealing of artificial spin ice

Abstract

We have performed a detailed study of thermal annealing of the moment configuration in artificial spin ice. Permalloy (Ni 80 Fe 20 ) artificial spin ice samples were examined in the prototypical square ice geometry, studying annealing as a function of island thickness, island shape, and annealing temperature and duration. We also measured the Curie temperature as a function of film thickness, finding that thickness has a strong effect on the Curie temperature in regimes of relevance to many studies of the dynamics of artificial spin ice systems. Increasing the interaction energy between island moments and reducing the energy barrier to flipping the island moments allows the system to more closely approach the collective low energy state of the moments upon annealing, suggesting new channels for understanding the thermalization processes in these important model systems.Artificial spin ice systems are two-dimensional arrays of nanoscale elements, typically composed of single domain ferromagnetic islands 1 . These systems have been the subject of extensive study and have provided models for the study of a range of novel collective behaviors 2 . Certain artificial spin ice geometries have well-defined collective magnetic ground states, such as the square lattice 1 , while others have intrinsically disordered and complex ground states, such as the Shakti lattice 3-5 . These low-energy collective states have sparked considerable interest in attempting to realize the lowest energy state of different artificial spin ice lattices 6-10 . One successful approach to collective energy minimization involves annealing the arrays by heating them to temperatures near or above the Curie temperature (T C ) of the ferromagnetic material 11,12 . Upon cooling, the island moments arrange themselves into a low energy state via magnetostatic interactions. Using this method, both long-range-ordered 11-13 and intrinsically disordered ground states 4,14 have been achieved, both in permalloy (Ni 80 Fe 20 ) and in other alloys 9,10 . Notably, the method works well even for geometries known to exhibit slow relaxation toward the low energy state 4 . Given the high T C of permalloy, and its importance as a model material for these systems, we investigated thermal annealing of permalloy artificial spin ice by varying the annealing conditions and the geometry of the islands, with the goal of understanding how to improve the effectiveness of annealing.We fabricated our artificial square spin ice samples on Si wafers coated with a 200-nm-thick layer of Si-N deposited a) Electronic mail: peter.schiffer@yale.edu by low pressure chemical vapor deposition. The nanoislands, with varied lateral dimensions and inter-island gaps indicated below, were produced by electron beam lithography and liftoff as described previously 12 . The total area of all nanoislands in each square ice sample was about 200×200 µm 2 . In order to keep uniformity of all nanoislands, the write field for lithography was set to cover the whole sample. We deposited our samples with va...

String Phase in an Artificial Spin Ice

“…Thermal annealing of the thicker islands is very efficient in reaching low energy states 6 , 27 – 29 , because it starts near the Curie point, at which the permalloy has reduced magnetization. Thus, the constraints predicated upon the binary nature of the island magnetization necessarily break down during this process.…”

Signatures of farther neighbor couplings in artificial square ice

“…Two-dimensional arrays of interacting magnetic nanostructures are now well-established model systems to explore the physics of highly frustrated magnets [1][2][3]. Complementing what can be done with chemically synthesized compounds [4,5], artificially made spin lattices offer a laboratory-on-chip approach: almost any kind of geometry can be designed [3,[6][7][8][9], magnetic interactions can be tuned [10][11][12][13], structural defects can be engineered [14], thermal fluctuations are adjustable in the desired temperature range [15][16][17], the spin degree of freedom can be controlled [18][19][20], etc. Combined with the capability to image spin configurations directly in real space, at the scale of a nanomagnet, artificial spin systems can be viewed as experimental simulators of frustrated magnetism.…”

Dependence of energy barrier reduction on collective excitations in square artificial spin ice: A comprehensive comparison of simulation techniques

“…Namely, in order to reproduce the relaxation timescale observed experimentally, the energy barriers need to be artificially reduced. Such a reduction is usually ascribed to extrinsic factors like fabrication defects, reduction of the Curie temperature T Curie [22] or saturation magnetization M s [7].…”