Imaging the stochastic microstructure and dynamic development of correlations in perpendicular artificial spin ice

Abstract

We use spatially resolved magneto-optical Kerr microscopy to track the complete microstates of arrays of perpendicular anisotropy nanomagnets during magnetization hysteresis cycles. These measurements allow us to disentangle the intertwined effects of nearest neighbor interaction, disorder, and stochasticity on magnetization switching. We find that the nearest neighbor correlations depend on both interaction strength and disorder. We also find that although the global characteristics of the hysteretic switching are repeatable, the exact microstate sampled is stochastic with the behavior of individual islands varying between nonminally identical runs.

Field-tunable interactions and frustration in underlayer-mediated artificial spin ice

“…The sum is taken over NN pairs, and S is the magnetization direction of each island (up or down, denoted as ±1). This form matches the form used in previous publications [20].…”

“…Measurements shown here are on square and hexagonal lattices with spacings ranging from 500 nm to 800 nm. Using methodology developed elsewhere [20], we construct a dimensionless x-axis using the interaction strength from the dipole approximation and the measured disorder in the arrays.…”

“…are of particular interest since the entire microstate can be probed in full detail using spatially-resolved magneto-optical Kerr effect (MOKE) microscopy [19,20]. This is because the polar MOKE effect has a large enough magnitude to readily allow extreme diffractionlimited microscopy with the spatial resolution (∼ 300 nm) required to measure the magnetic state of each individual island in an array.…”

Field-driven Reversal Models in Artificial Spin Ice

“…Disorder in ASI may arise from a number of mechanisms, and can be separated into physical properties and dipolar interactions. [50,51] The former include variance in the material volume and moment, in the island shape and rotation, in its position within the array, and from edge roughness, [23,26,52] while the later results from stochastic inter-island interactions and are strongly influenced by the geometry of the array. In the square lattice, it has been shown that several different sources of disorder have a similar effect on the properties of the array, [53] and that disorder can be designed into a system to enable access to the ice-rule phase when the sub-lattices lie on separate planes.…”

“…In the square lattice, it has been shown that several different sources of disorder have a similar effect on the properties of the array, [53] and that disorder can be designed into a system to enable access to the ice-rule phase when the sub-lattices lie on separate planes. [16] While detailed procedures have been developed for the assessment of disorder in coupled systems, [50,51,54] it is commonly estimated using collective properties such as avalanche critical exponents [11] and M-H loops [55,56] in the kagome lattice; from correlations [57] and vertex populations [43,57] in the square one; and from mesoscale magnetic texture during reversal in pinwheel arrays. [40] In addition to considering both sources of disorder, it is also important to consider the appropriateness of the assumptions of any model used to compare against experimental data.…”