These files form the open data deposit for the article "Thermally and field-driven mobility of emergent magnetic charges in square artificial spin ice" by Sophie A. Morley, Jose Maria Porro, Aleš Hrabec, Mark C. Rosamond, Diego Alba Venero, Edmund H. Linfield, Gavin Burnell, Mi-Young Im, Peter Fischer, Sean Langridge & Christopher H. Marrows, published as Scientific Reports volume 9, Article number: 15989 (2019). The data are organised into directories corresponding to the figures in the paper.