Exploring hyper-cubic energy landscapes in thermally active finite artificial spin-ice systems

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.…”

“…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 .…”

Thermal stability of magnetic states in submicron magnetic islands

“…Experimental estimates for islands falling within a more limited range in shape and size are in close agreement with the calculated values [16]. An HTST estimate for larger permalloy islands used in kagome spin ice systems [17] gave a smaller value, 9.9×10 8 sec −1 [18] while analysis of the experimental data had assumed a value of 10 12 sec −1 [17].…”

“…For a permalloy island in a spin ice structure [17], K 1 > 0 and K 2 > 0 describe easy axis shape anisotropy and easy plane shape anisotropy, respectively. For CoPt islands [31,32], there is an intrinsic out of plane anisotropy and K 2 < 0 whereas K 1 ≈ 0 due to the round shape of the islands.…”