The role of magnetic dipolar interactions in skyrmion lattices

Magnetic skyrmions are topological two-dimensional (2D) spin textures that can be stabilized at room temperature and low magnetic fields in magnetic multilayer stacks. Besides their envisioned applications in data storage and processing, these 2D quasiparticles constitute an ideal model system to study 2D particle properties. More precisely, the role of inter-particle dipolar interactions in 2D ensembles can be fully captured in skyrmion lattices. We engineer a multilayer stack hosting skyrmion lattices and increase the relevance of the dipolar coupling by increasing the number of repetitions <i>n</i> from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn></mml:mrow> </mml:math> to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>n</mml:mi> <mml:mo>=</mml:mo> <mml:mn>30</mml:mn></mml:mrow> </mml:math> . To ascertain the impact on the spin structure, we carry out a series of imaging experiments and find a drastic change of the skyrmion size. We develop an analytical description for the skyrmion radius in the whole multilayer regime, from thin to thick film limits, identifying the key impact of the nucleation process leading to the skyrmion lattice. Our work provides a detailed understanding of the skyrmion-skyrmion interaction, clarifying the role of dipolar interactions as the multilayer stack is expanded in the z direction.