Direct Observation of Thermal Relaxation in Artificial Spin Ice

Abstract

We study the thermal relaxation of artificial spin ice with photoemission electron microscopy, and are able to directly observe how such a system finds its way from an energetically excited state to the ground state. On plotting vertex-type populations as a function of time, we can characterize the relaxation, which occurs in two stages, namely a string and a domain regime. Kinetic Monte Carlo simulations agree well with the temporal evolution of the magnetic state when including disorder, and the experimental results can be explained by considering the effective interaction energy associated with the separation of pairs of vertex excitations.

Emergent reduced dimensionality by vertex frustration in artificial spin ice

“…Because the rate at which thermal fluctuations occur depends very sensitively on island thickness, this ensured that some of the arrays would undergo observable thermal fluctuations near room temperature. We found that 3 to 3.5 nm thick arrays were thermally active around room temperature, consistent with previous studies 17,18 . A 2 nm capping layer of Al was deposited on top of the permalloy to inhibit oxidation.…”

“…A 2 nm capping layer of Al was deposited on top of the permalloy to inhibit oxidation. The island dimensions (470×170×3 nm) were similar to those used in previous studies 17,18 of thermally active artificial spin ice, which facilitates comparison. Also, because these islands are thermally active around room temperature, problems associated with thicker islands (high temperature annealing and associated complications involving substrate-island interdiffusion 10 ) are avoided.…”

“…We experimentally investigated the tetris lattice's ice manifold predicted by the vertex model by fabricating tetris artificial spin ice lattices with single-domain permalloy (Ni 81 Fe 19 ) islands (nominal island dimensions of 470×170×3 nm and island spacings of a = 600 nm and 800 3 nm). The energy barrier to reversal of the magnetic moment of these islands is approximately equal to the thermal energy available at room temperature 17,18 (due to the low thicknesses of 3-3.5 nm), so thermal fluctuations cause the island moments to flip rapidly at room temperature. The exact mechanism of island moment reversal (via coherent rotation or more complex intermediate states 25 ) is unclear, but by slowly cooling below room temperature, we can drive the arrays into their thermalized ground state.…”

“…Simple square and kagome artificial spin ice lattices have been subject to intense study because they provide unique insight into the consequences of frustrated magnetism, such as residual entropy 9,10 and magnetic charge excitations [11][12][13][14] . In the last few years, improved thermalization methods have provided access to the low energy phases of artificial spin ice structures 10,15,16 and even their dynamics [17][18][19] . There is now growing awareness that one could even employ these artificial systems to design desired emergent behaviors and exotic states 20 .…”

Emergent geometric frustration of artificial magnetic skyrmion crystals

“…Despite theoretical predictions [47], however, a complete GS has not been achieved in nanomagnetic ice systems; instead, only short-range-ordered GS can be reached experimentally by rotating-field demagnetization protocols [43,70]. Only recently, the long-rangeordered ground state has been achieved nearly perfectly over extended regions using a single-shot thermal annealing technique during fabrication [51,94] and a thermally induced melting-freezing protocol is presented to explore experimentally the formation of thermally induced long-range ground-state ordering in a square artificial spin-ice systems of elongated ferromagnetic nanoislands [95][96][97]. A long-range ground-state magnetic ordering region separated by chains of higher energy vertex configurations has been observed.…”